Researcher Profile and Settings

Master

Affiliation (Master)

• Faculty of Information Science and Technology　Computer Science and Information Technology Mathematical Science

Affiliation (Master)

• Faculty of Information Science and Technology　Computer Science and Information Technology Mathematical Science

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Profile and Settings

Profile and Settings

• Name (Japanese)

  Tanaka

• Name (Kana)

  Akira

• Name

  200901041736373951

Alternate Names

http://ims2.main.ist.hokudai.ac.jp/
http://ims2.main.eng.hokudai.ac.jp/

Achievement

Research Interests

• 標本化理論   画像信号処理   機械学習理論   音響信号処理   

Research Areas

• Informatics / Mathematical informatics / acoustic signal processing, image processing, general signal processing
• Natural sciences / Mathematical analysis / inverse problem, sampling theory
• Informatics / Human interfaces and interactions
• Informatics / Database science
• Informatics / Intelligent informatics

Research Experience

• 2016 - Today Hokkaido University Graduate School of Information Science and Technology
• 2011 - 2016 Hokkaido University Graduate School of Information Science and Technology
• 2007 - 2011 Hokkaido University Graduate School of Information Science and Technology
• 2004 - 2007 Hokkaido University Graduate School of Information Science and Technology
• 2004 - 2007 Research Associate
• 2000 - 2004 Hokkaido University Graduate School of Engineering
• 2000 - 2004 Research Associate
• 1996 - 1998 松下通信工業株式会社

Education

• 1998/04 - 2000/09  北海道大学大学院
• 1994/04 - 1996/03  北海道大学大学院
• 1990/04 - 1994/03  Hokkaido University  School of Engineering  Department of Information Engineering

Awards

• 2005 CASYS'05 Best Paper Award
  
• 1996 電子情報通信学会北海道支部奨励賞
  

Published Papers

• Minimum upper bound of the Cayley transform of an orthogonal matrix multiplied by signed permutation matrices

  Takuma Mitamura, Akira Tanaka

  Linear Algebra and its Applications 659 24 - 32 0024-3795 2023/02 [Refereed]
  
• Characterization of the Blast Furnace Burden Surface: Experimental Measurement and Roughness Statistics

  Jiuzhou Tian, Akira Tanaka, Di Gao, Zenghua Liu, Qingwen Hou, Xianzhong Chen

  ISIJ International 0915-1559 2023 [Refereed][Not invited]
  
• Properties of The Set of Orthogonal Matrices Obtained as The Cayley Transform of Skew-Symmetric Matrices

  Takuma MITAMURA, Akira TANAKA

  電子情報通信学会論文誌A J105-A (11) 125 - 135 2022/11 [Refereed][Not invited]
  
• Kernelized Supervised Laplacian Eigenmap for Visualization and Classification of Multi-Label Data

  Mariko Tai, Mineichi Kudo, Akira Tanaka, Hideyuki Imai, Keigo Kimura

  Pattern Recognition 123 108399 - 108399 0031-3203 2022/03 [Refereed]
  
• Kernel-Based Regressors Equivalent to Stochastic Affine Estimators

  Akira TANAKA, Masanari NAKAMURA, Hideyuki IMAI

  IEICE Transactions on Information and Systems E105.D (1) 116 - 122 0916-8532 2022/01/01 [Refereed][Not invited]
  
• MODEL SELECTION OF KERNEL RIDGE REGRESSION FOR EXTRAPOLATION

  Akira Tanaka, Masanari Nakamura, Hideyuki Imai

  Proceedings of 2021 IEEE International Workshop on Machine Learning for Signal Processing (MLSP2021) 1 - 6 2021/10 [Refereed]
  
• Kernel Ridge Regression with Autocorrelation Prior: Optimal Model and Cross-Validation

  Akira Tanaka, Hideyuki Imai

  ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 3867 - 3871 2020/05 [Refereed][Not invited]
  
• Tracking the Burden Surface Radial Profile of a Blast Furnace by a B-mode Mechanical Swing Radar System

  Jiuzhou Tian, Akira Tanaka, Yue Meng, Qingwen Hou, Xianzhong Chen

  ISIJ International 60 (2) 297 - 307 2020/02 [Refereed][Not invited]
  
• A Fast Cross-Validation Algorithm for Kernel Ridge Regression by Eigenvalue Decomposition

  TANAKA Akira, IMAI Hideyuki

  IEICE Transactions on Electronics, Communications and Computer Sciences E102-A (9) 1317 - 1320 2019/09 [Refereed][Not invited]
  
• Radar detection-based modeling in a blast furnace: a prediction model of burden surface descent speed

  J. Tian, A. Tanaka, Q. Hou, X. Chen

  Metals 9 (5) 1 - 23 2019/05 [Refereed][Not invited]
  
• Binary Sparse Representation Based on Arbitrary Quality Metrics and Its Applications

  T. Ogawa, S. Takahashi, N. Wada, A. Tanaka, M. Haseyama

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E101-A (11) 1776 - 1785 2018/11 [Refereed][Not invited]
  
• Radar Detection-based Modeling in a Blast Furnace: a Prediction Model of Burden Surface Shape after Charging

  J. Tian, A. Tanaka, Q. Hou, X. Chen

  ISIJ International 58 (11) 1999 - 2008 2018/11 [Refereed][Not invited]
  
• Kernel-Induced Sampling Theorem for Translation-Invariant Reproducing Kernel Hilbert Spaces with Uniform Sampling

  TANAKA Akira

  2018 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP2018) 4554 - 4558 2018/04 [Refereed][Not invited]
  
• Optimal Kernel in Kernel Regression Problems with Autocorrelation Prior

  SAITO Yuuki, TANAKA Akira

  APSIPA Annual Summit & Conference 2017 ID : 78  2017/12 [Refereed][Not invited]
  
• Wiener-Based Inpainting Quality Prediction

  Takahiro Ogawa, Akira Tanaka, Miki Haseyama

  IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS E100D (10) 2614 - 2626 1745-1361 2017/10 [Refereed][Not invited]
   

  A Wiener-based inpainting quality prediction method is presented in this paper. The proposed method is the first method that can predict inpainting quality both before and after the intensities have become missing even if their inpainting methods are unknown. Thus, when the target image does not include any missing areas, the proposed method estimates the importance of intensities for all pixels, and then we can know which areas should not be removed. Interestingly, since this measure can be also derived in the same manner for its corrupted image already including missing areas, the expected difficulty in reconstruction of these missing pixels is predicted, i.e., we can know which missing areas can be successfully reconstructed. The proposed method focuses on expected errors derived from the Wiener filter, which enables least-squares reconstruction, to predict the inpainting quality. The greatest advantage of the proposed method is that the same inpainting quality prediction scheme can be used in the above two different situations, and their results have common trends. Experimental results show that the inpainting quality predicted by the proposed method can be successfully used as a universal quality measure.
• Kernel regression with autocorrelation prior

  Akira Tanaka

  2017 12th International Conference on Sampling Theory and Applications, SampTA 2017 318 - 321 2017/09/01 [Refereed][Not invited]
   

  In this paper, we discuss a function reconstruction problem by kernel regressors in which the autocorrelation of the unknown true function is given a priori. In general, a reconstructed function in the kernel regression problem, using a certain reproducing kernel Hilbert space, is represented by a linear combination of the corresponding kernel specified by each input point. We introduce a framework to reflect the autocorrelation prior of the unknown true function on the estimation of the coefficients for the linear combination and give a closed-form solution of the optimal coefficients. We also give numerical examples, using the popular Gaussian kernel, to confirm the behavior of the proposed method.
• Sampling theorem through the theory of reproducing kernel Hilbert spaces

  田中 章

  日本音響学会誌 日本音響学会 73 (9) 577 - 584 0369-4232 2017/09 [Not refereed][Invited]
  
• Iterative Zero Phase Method for White and Impulse Noise Reduction

  TANAKA Akira, KAWAMURA Arata

  22th International Conference on Digital Signal Procerssing ID:42  2017/08 [Refereed][Not invited]
  
• ブロックベース線形回帰を利用したデモザイキング

  河野 克也, 田中 章

  電子情報通信学会論文誌D J100-D (5) 605 - 612 2017/05 [Refereed][Not invited]
  
• Theoretical Analyses on 2-Norm-Based Multiple Kernel Regressors

  Akira Tanaka, Hideyuki Imai

  IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES E100A (3) 877 - 887 1745-1337 2017/03 [Refereed][Not invited]
   

  The solution of the standard 2-norm-based multiple kernel regression problem and the theoretical limit of the considered model space are discussed in this paper. We prove that 1) The solution of the 2-norm-based multiple kernel regressor constructed by a given training data set does not generally attain the theoretical limit of the considered model space in terms of the generalization errors, even if the training data set is noise-free, 2) The solution of the 2-norm-based multiple kernel regressor is identical to the solution of the single kernel regressor under a noise free setting, in which the adopted single kernel is the sum of the same kernels used in the multiple kernel regressor; and it is also true for a noisy setting with the 2-norm-based regularizer. The first result motivates us to develop a novel framework for the multiple kernel regression problems which yields a better solution close to the theoretical limit, and the second result implies that it is enough to use the single kernel regressors with the sum of given multiple kernels instead of the multiple kernel regressors as long as the 2-norm based criterion is used.
• Digital Image Restoration of Faded Color Films Based on Polynomial Approximation

  TANAKA Akira, KAGIYA Takahiro, MIYAMATSU Takeshi, NAMIE Kazuma, OKUYAMA Toshiyasu

  IEICE Transactions on Information and Systems (Japanese Edition) J99-D (3) 367 - 376 2016/03 [Refereed][Not invited]
  
• Computational complexity in the design of voting rules

  Koji Takamiya, Akira Tanaka

  THEORY AND DECISION 80 (1) 33 - 41 0040-5833 2016/01 [Refereed][Not invited]
   

  This paper considers the computational complexity of the design of voting rules, which is formulated by simple games. We prove that it is an NP-complete problem to decide whether a given simple game is stable, or not.
• Ensemble and Multiple Kernel Regressors: Which Is Better?

  Akira Tanaka, Hirofumi Takebayashi, Ichigaku Takigawa, Hideyuki Imai, Mineichi Kudo

  IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES E98A (11) 2315 - 2324 1745-1337 2015/11 [Refereed][Not invited]
   

  For the last few decades, learning with multiple kernels, represented by the ensemble kernel regressor and the multiple kernel regressor, has attracted much attention in the field of kernel-based machine learning. Although their efficacy was investigated numerically in many works, their theoretical ground is not investigated sufficiently, since we do not have a theoretical framework to evaluate them. In this paper, we introduce a unified framework for evaluating kernel regressors with multiple kernels. On the basis of the framework, we analyze the generalization errors of the ensemble kernel regressor and the multiple kernel regressor, and give a sufficient condition for the ensemble kernel regressor to outperform the multiple kernel regressor in terms of the generalization error in noise-free case. We also show that each kernel regressor can be better than the other without the sufficient condition by giving examples, which supports the importance of the sufficient condition.
• A Simple Proof for The Equivalence of Multiple Kernel Regressors and Single Kernel Regressors with Sum of Kernels

  Akira Tanaka

  2015 ASIA-PACIFIC SIGNAL AND INFORMATION PROCESSING ASSOCIATION ANNUAL SUMMIT AND CONFERENCE (APSIPA) 242 - 245 2015 [Refereed][Not invited]
   

  It is widely recognized that the kernel-based learning scheme is one of powerful tools in the field of machine learning. Recently, learning with multiple kernels, instead of a single kernel, attracts much attention in this field. Although their efficacy was investigated in terms of practical sense, their theoretical grounds were not sufficiently discussed in the past studies. In our previous work, we theoretically analyzed the standard 2-norm-based multiple-kernel regressor, and proved that the solution of the multiple kernel regressor obtained by 2-norm-based criterion reduces to the solution of the single kernel regressor with the sum of the kernels. However, the proof was hard to understand intuitively. In this work, we give a simple proof for the theorem in which the roles of the 2-norm-based criteria are intuitively convincing.
• ANALYSES ON EMPIRICAL ERROR MINIMIZATION IN MULTIPLE KERNEL REGRESSORS

  Akira Tanaka

  2015 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING (ICASSP) 2046 - 2050 1520-6149 2015 [Refereed][Not invited]
   

  Theoretical validity of empirical error minimization in multiple kernel regressors is discussed in this paper. Generalization error of a kernel machine is usually evaluated by the induced norm of the difference between an unknown true function and an estimated one in an appropriate reproducing kernel Hilbert space. It is well known that empirical error minimization also achieves the minimum generalization error in single kernel regressors. However, it is not clarified whether or not that is true for multiple kernel regressors. Moreover, possibility of constructing the minimizer of the generalization error by a given training date set is not also clarified. In this paper, we give negative conclusions for these problems through theoretical analyses on the generalization error of multiple kernel regressors and also give an example by popular Gaussian kernels.
• "Theoretical Analyses on Ensemble and Multiple Kernel Regressors

  TANAKA Akira, TAKIGAWA Ichigaku, IMAI Hideyuki, KUDO Mineichi

  Proceedings of the 6th Asian Conference on Machine Learning (ACML2014) 2014/11 [Refereed][Not invited]
  
• Analyses on Generalization Error of Ensemble Kernel Regressors

  Akira Tanaka, Ichigaku Takigawa, Hideyuki Imai, Mineichi Kudo

  STRUCTURAL, SYNTACTIC, AND STATISTICAL PATTERN RECOGNITION 8621 273 - 281 0302-9743 2014 [Refereed][Not invited]
   

  Kernel-based learning is widely known as a powerful tool for various fields of information science such as pattern recognition and regression estimation. For the last few decades, a combination of different learning machines so-called ensemble learning, which includes learning with multiple kernels, have attracted much attention in this field. Although its efficacy was revealed numerically in many works, its theoretical grounds are not investigated sufficiently. In this paper, we discuss regression problems with a class of kernels and show that the generalization error by an ensemble kernel regressor with the class of kernels is smaller than the averaged generalization error by kernel regressors with each kernel in the class.
• MUSIC-BASED DOA ESTIMATION BY OBLIQUE PROJECTION ALONG THE SIGNAL SUBSPACE

  Akira Tanaka, Hideyuki Imai

  2014 IEEE WORKSHOP ON STATISTICAL SIGNAL PROCESSING (SSP) 300 - 303 2014 [Refereed][Not invited]
   

  In the MUSIC-based direction of arrival (DOA) estimation technique, the orthogonal projection of a steering vector onto the socalled noise subspace plays a crucial role. The noise subspace is defined as the orthogonal complement of the signal subspace spanned by the unknown true steering vectors of target signals, which implies that the correlation structure of noise does not contribute to the DOA estimation performance after the signal subspace is specified. In this paper, we introduce a novel noise subspace, called the proper noise subspace, which is a complementary subspace of the signal subspace and reflects the correlation structure of the noise; and construct a novel MUSIC-based DOA estimation algorithm based on the oblique projector onto the proper noise subspace along the signal subspace.
• Parametric Wiener Filter with Linear Constraints for Unknown Target Signals

  Akira Tanaka, Hideyuki Imai

  IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES E97A (1) 322 - 330 0916-8508 2014/01 [Refereed][Not invited]
   

  In signal restoration problems, we expect to improve the restoration performance with a priori information about unknown target signals. In this paper, the parametric Wiener filter with linear constraints for unknown target signals is discussed. Since the parametric Wiener filter is usually defined as the minimizer of the criterion not for the unknown target signal but for the,filter, it is difficult to impose constraints for the unknown target signal in the criterion. To overcome this difficulty, we introduce a criterion for the parametric Wiener filter defined for the unknown target signal whose minimizer is equivalent to the solution obtained by the original formulation. On the basis of the newly obtained criterion, we derive a closed-form solution for the parametric Wiener filter with linear constraints.
• Image inpainting based on block-based linear regression and minimum variance convex combinations

  Katsuya Kohno, Akira Tanaka

  Proceedings of the IASTED International Conference on Signal and Image Processing, SIP 2013 368 - 373 2013 [Refereed][Not invited]
   

  Estimation of missing entries in a multivariate data is one of classical problems in the field of statistical science. Linear regression with the EM algorithm is well known as one of popular approaches for this problem. When this approach is applied to block-based image inpainting problems, multiple candidates of estimate for a target lost pixel may be obtained. In our previous work, we proposed a denoising technique for multiple images using the convex combination which minimizes its variance of errors from a true image. In this paper, we propose a novel image in-painting method incorporating the application of the de-noising technique to multiple estimates for a target pixel. We also show several results of numerical experiments in order to verify the efficacy of the proposed method.
• Performance improvement of the FFdiag algorithm based on pre-diagonalization by closed-form joint diagonalizers

  Miho Murota, Akira Tanaka

  Proceedings of the IASTED International Conference on Signal and Image Processing, SIP 2013 345 - 350 2013 [Refereed][Not invited]
   

  In this paper, we try to improve the performance of the FFDiag algorithm, which is one of the state-of-the-art iteration-based approximate joint diagonalizers of a given set of real-valued symmetric matrices. The key idea of the improvement is pre-diagonalization by a closed-form joint diagonalizer whose computational cost is smaller than that of the FFDiag algorithm. Numerical experiments for approximate joint diagonalization of a set of real-valued symmetric matrices, that are randomly generated, are conducted to verify the efficacy of the proposed scheme in terms of computational costs and joint diagonalization performance.
• KERNEL-INDUCED SAMPLING THEOREM FOR BANDPASS SIGNALS WITH UNIFORM SAMPLING

  Akira Tanaka

  2013 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP) 5450 - 5453 1520-6149 2013 [Refereed][Not invited]
   

  In this paper, a sampling theorem for bandpass signals with uniformly spaced sampling points is discussed. We firstly show that a function space consisting of all functions with a specific bandpass property is a reproducing kernel Hilbert space and also give a closed-form of the corresponding reproducing kernel. Moreover, on the basis of the framework of the kernel-induced sampling theorem, we give a simple perfect reconstruction formula for the bandpass signals by uniformly spaced sampling points with the bandpass Nyquist rate, which is defined as twice the signal bandwidth, for the cases that the maximum frequency of the signals is identical to bandwidth multiplied by some positive integer.
• Multi-frame image denoising based on minimum noise variance convex combination with difference-based noise variance estimation

  Akira Tanaka, Katsuya Kohno

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E96-A (10) 2066 - 2070 1745-1337 2013 [Refereed][Not invited]
   

  In this paper, we propose a novel multi-frame image denoising technique, which achieves the minimum variance of noise. Zeromean and unknown variance white noise with an arbitrary distribution is considered in this paper. The proposed method consists of two parts. The first one is the estimation of the variance of noise for each image by considering the differences of all pairs of images. The second one is an actual denoising process in which the convex combination of all images with weight coefficients determined by the estimated variances is constructed. We also give an efficient algorithm by which we can obtain the same result by successive convex combinations. The efficacy of the proposed method is confirmed by computer simulations. Copyright © 2013 The Institute of Electronics, Information and Communication Engineers.
• Image inpainting by block-based linear regression with optimal block selection.

  Akira Tanaka, Takahiro Ogawa, Miki Haseyama

  Asia-Pacific Signal and Information Processing Association Annual Summit and Conference(APSIPA) ID:8 - 4 2012/12 [Refereed][Not invited]
  
• A Novel Criterion for Quality Improvement of JPEG Images Based on Image Database and Re-application of JPEG

  Katsuya Kohno, Akira Tanaka, Hideyuki Imai

  2012 ASIA-PACIFIC SIGNAL AND INFORMATION PROCESSING ASSOCIATION ANNUAL SUMMIT AND CONFERENCE (APSIPA ASC) ID:112  2012 [Refereed][Not invited]
   

  Image compression is one of important technologies in the fields of image processing. JPEG has been commonly used for image compression. Since JPEG is a lossy compression method, decoded images exhibit visually unwanted noises. A need for techniques for improving the quality of JPEG images remains because there still exist many images compressed by JPEG today. Many methods for improving the quality of JPEG images have been proposed. Among them, a method based on reapplication of JPEG, which means compression and decoding, is recognized as one of efficient methods. In our previous study, we improved this method by incorporating an image database and novel distance measures between two images. In this paper, we propose a new distance measure between two images to improve the performance of our previous method. We also show some results of numerical experiments to verify the efficacy of the proposed criterion.
• Performance Improvement of Closed-Form Joint Diagonalizer of Non-Negative Hermitian Matrices

  Akira Tanaka, Miho Murota

  2012 ASIA-PACIFIC SIGNAL AND INFORMATION PROCESSING ASSOCIATION ANNUAL SUMMIT AND CONFERENCE (APSIPA ASC) ID:44  2012 [Refereed][Not invited]
   

  Joint diagonalization of a series of non-negative Hermitian matrices is one of important techniques in the fields of signal processing, such as blind source separation based on second order statistics. In our previous works, we introduced a closed-form solution of a joint diagonalizer of non-negative Hermitian matrices and also proposed a method for improving the performance of the solution for the cases where given series of Hermitian matrices are not jointly diagonalizable strictly. However, the performance of the method may degrade when the number of given Hermitian matrices are comparatively small. In this paper, we propose an improved version of the closed-form joint diagonalizer of given set of Hermitian matrices by increasing the number of Hermitian matrices virtually. Some numerical examples are also shown to verify the efficacy of the proposed method.
• Diffusion Noise Suppression by Crystal-Shape Subtraction Array

  Akira Tanaka, Ryo Takahashi

  2012 ASIA-PACIFIC SIGNAL AND INFORMATION PROCESSING ASSOCIATION ANNUAL SUMMIT AND CONFERENCE (APSIPA ASC) ID:9  2012 [Refereed][Not invited]
   

  Noise suppression of diffusion noise by microphone arrays is discussed in this paper. In our previous work, we proposed a method for jointly estimating signal and noise correlation matrices from observations with diffusion noise by using so-called crystal shape microphone arrays; and discussed the performance of the Wiener filter based on those correlation matrices. In this paper, we propose a novel method for noise suppression of diffusion noise based on the newly adopted spectral subtraction scheme with the estimated correlation matrices by our previous work. We also verify the efficacy of the proposed method by some computer simulations and show that the proposed method outperforms our previous method by the Wiener filter.
• VARIANCE ANALYSES FOR KERNEL REGRESSORS WITH NESTED REPRODUCING KERNEL HILBERT SPACES

  Akira Tanaka, Hideyuki Imai, Koji Takamiya

  2012 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP) 2001 - 2004 1520-6149 2012 [Refereed][Not invited]
   

  Learning based on kernel machines is widely known as a powerful tool for various fields of information science including signal processing such as function estimation from finite sampling points. One of central topics of kernel machines is model selection, especially selection of a kernel or its parameters. In our previous works, we investigated the generalization error of a model space itself corresponding to a selected kernel in kernel regressors. In this paper, we discuss the generalization error in a model space corresponding to a selected kernel in kernel regressors; and prove that the variance of a learning result is reduced when we adopt a kernel corresponding to a larger reproducing kernel Hilbert space.
• Extended Analyses for an Optimal Kernel in a Class of Kernels with an Invariant Metric

  Akira Tanaka, Ichigaku Takigawa, Hideyuki Imai, Mineichi Kudo

  STRUCTURAL, SYNTACTIC, AND STATISTICAL PATTERN RECOGNITION 7626 345 - 353 0302-9743 2012 [Refereed][Not invited]
   

  Learning based on kernel machines is widely known as a powerful tool for various fields of information science such as pattern recognition and regression estimation. An appropriate model selection is required in order to obtain desirable learning results. In our previous work, we discussed a class of kernels forming a nested class of reproducing kernel Hilbert spaces with an invariant metric and proved that the kernel corresponding to the smallest reproducing kernel Hilbert space, including an unknown true function, gives the best model. In this paper, we relax the invariant metric condition and show that a similar result is obtained when a subspace with an invariant metric exists.
• Analyses on Interpolation Accuracy of Eigenspace-BPLP

  TANAKA Akira, OGAWA Takahiro, HASEYAMA Miki, MIYAKOSHI Masaaki

  The IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences (Japanese edition) A 一般社団法人電子情報通信学会 J94-A (2) 116 - 126 0913-5707 2011/02 [Refereed][Not invited]
   

  欠損領域を有する数値データの補間技術として, 固有空間BPLP(Back Projection for Lost Pixels)法, 及び, その改良手法が提案されている.これらの手法は, 所与のデータから切り出したブロックデータの主成分構造を利用して欠損領域を推定する手法であり, 主要な固有空間の次元等を適切に選択することによって, 効果的に欠損部を補間することができる.一方, 重要なパラメータの一つである, 主要な固有空間の次元の選択の指針はこれまで与えられていなかった.本論文では, 主成分分析に用いる分散共分散行列と欠損ブロックに対応する分散共分散行列が等しいという理想的な条件下では, 固有空間BPLP法の改良手法の, 期待二乗誤差最小の意味での最適解が古典的なウィーナーフィルタであることを指摘するとともに, 固有空間として全空間を用いた解が, 上で述べた最適解であるウィーナーフィルタによる解に帰着することを示し, 結果として固有空間の最適な次元がブロックの次元そのものであることを示す.また, 主成分分析に用いる分散共分散行列と欠損ブロックに対応する分散共分散行列が完全に一致しない場合についても考察し, 上記理想的な条件下同様, 固有空間として全空間を採用することが最適となる十分条件を与える.また, 当該十分条件を満たさない場合についても, 数値実験によりウィーナーフィルタによる解の優位性を確認する.
• Music interpolation by Wiener filter and its application to music arrangement

  Yoshifumi Mizuno, Akira Tanaka, Masaaki Miyakoshi

  Proceedings - 2011 IEEE International Conference on Granular Computing, GrC 2011 468 - 472 2011 [Refereed][Not invited]
   

  When composers and arrangers compose music, they depend not only on their sense, but also on music theory. Therefore, there is possibility of automatic composition and automatic arrangement by computers. Some studies on automatic composition using computers have been studied continuously for 50 years. For example, an automatic music composition based on counterpoint and imitation using stochastic models and a melody generation method using a tree structure of generative theory of tonal music, are cited as previous studies. In this paper, we propose a method of music interpolation by applying the Wiener filter to scores with missing parts. In addition, we propose a method of music arrangement based on the proposed interpolation method. © 2011 IEEE.
• Non-negative matrix factorization considering given vectors in a basis

  Yuta Amano, Akira Tanaka, Masaaki Miyakoshi

  Proceedings - 2011 IEEE International Conference on Granular Computing, GrC 2011 48 - 53 2011 [Refereed][Not invited]
   

  Recently, a novel matrix factorization, named non-negative matrix factorization (NMF), attracts much attention in the field of signal processing. A matrix with non-negative elements can be decomposed into a product of two matrices with non-negative elements by the NMF. One resulting matrix can be regarded as a basis matrix and the other can be regarded as a coefficient matrix giving linear combinations of the basis vectors. In practical problems, there exists a case where an ideal basis is partially known. In this paper, we propose a novel method for NMF considering given vectors in an ideal basis. We introduce a criterion for the method and construct an algorithm to optimize the criterion. Moreover, we prove that the proposed algorithm surely converges. Some results of computer simulations are also given to verify the efficacy of the proposed method. © 2011 IEEE.
• Performance improvement of metric reconstruction based on partial joint diagonalization

  Atsushi Takizawa, Akira Tanaka, Masaaki Miyakoshi

  Proceedings - 2011 IEEE International Conference on Granular Computing, GrC 2011 625 - 629 2011 [Refereed][Not invited]
   

  Self-calibration is one of powerful tools in the field of computer vision such as 3-D shape reconstruction and camera motion reconstruction. Self-calibration consists of two main parts. One is projective reconstruction and the other is metric reconstruction. The latter one can be reduced to a problem to find a matrix that satisfies some absolute dual quadric (ADQ) constraint. However, it is difficult to formulate the problem with considering the constraint strictly, which may make the final result such as reconstructed 3-D shapes unstable. In this paper, we propose a novel method for metric reconstruction incorporating a partial joint diagonalization of symmetric matrices. Some results of computer simulations are also given to verify the efficacy of the proposed method. © 2011 IEEE.
• THEORETICAL ANALYSES ON A CLASS OF NESTED RKHS'S

  Akira Tanaka, Hideyuki Imai, Mineichi Kudo, Masaaki Miyakoshi

  2011 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING 2072 - 2075 1520-6149 2011 [Refereed][Not invited]
   

  One of central topics of kernel machines in the field of machine learning is a model selection, especially a selection of a kernel or its parameters. In our previous work, we discussed a class of kernels forming a class of nested reproducing kernel Hilbert spaces with an invariant metric; and proved that the kernel corresponding to the smallest reproducing kernel Hilbert space, including an unknown true function, gives the optimal model. In this paper, we consider a class of kernels forming a class of nested reproducing kernel Hilbert spaces whose metrics are not always invariant and show that a similar result to the invariant case is not obtained by providing a counter example using a class of Gaussian kernels.
• Analyses on kernel-specific generalization ability for kernel regressors with training samples

  Akira Tanaka, Masaaki Miyakoshi

  2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010 61 - 66 2011 [Refereed][Not invited]
   

  Theoretical analyses on generalization error of a model space for kernel regressors with respect to training samples are given in this paper. In general, the distance between an unknown true function and a model space tends to be small with a larger set of training samples. However, it is not clarified that a larger set of training samples achieves a smaller difference at each point of the unknown true function and the orthogonal projection of it onto the model space, compared with a smaller set of training samples. In this paper, we show that the upper bound of the squared difference at each point of these two functions with a larger set of training samples is not larger than that with a smaller set of training samples. We also give some numerical examples to confirm our theoretical result. © 2011 IEEE.
• Kernel-Induced Sampling Theorem

  Akira Tanaka, Hideyuki Imai, Masaaki Miyakoshi

  IEEE TRANSACTIONS ON SIGNAL PROCESSING 58 (7) 3569 - 3577 1053-587X 2010/07 [Refereed][Not invited]
   

  A perfect reconstruction of functions in a reproducing kernel Hilbert space from a given set of sampling points is discussed. A necessary and sufficient condition for the corresponding reproducing kernel and the given set of sampling points to perfectly recover the functions is obtained in this paper. The key idea of our work is adopting the reproducing kernel Hilbert space corresponding to the Gramian matrix of the kernel and the given set of sampling points as the range space of a sampling operator and considering the orthogonal projector, defined via the range space, onto the closed linear subspace spanned by the kernel functions corresponding to the given sampling points. We also give an error analysis of a reconstructed function by incomplete sampling points.
• Performance Improvement of Second-Order-Statistics-Based Noisy BSS

  A. Tanaka, M. Miyakoshi

  Proceedings of the 7th IASTED International Conference on Signal Processing, Pattern Recognition and Applications (SPPRA2010) 16 - 21 2010/02 [Refereed][Not invited]
  
• A relationship between generalization error and training samples in kernel regressors

  Akira Tanaka, Hideyuki Imai, Mineichi Kudo, Masaaki Miyakoshi

  Proceedings - International Conference on Pattern Recognition 1421 - 1424 1051-4651 2010 [Refereed][Not invited]
   

  A relationship between generalization error and training samples in kernel regressors is discussed in this paper. The generalization error can be decomposed into two components. One is a distance between an unknown true function and an adopted model space. The other is a distance between an estimated function and the orthogonal projection of the unknown true function onto the model space. In our previous work, we gave a framework to evaluate the first component. In this paper, we theoretically analyze the second one and show that a larger set of training samples usually causes a larger generalization error. © 2010 IEEE.
• THEORETICAL ANALYSES FOR A CLASS OF KERNELS WITH AN INVARIANT METRIC

  Akira Tanaka, Masaaki Miyakoshi

  2010 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING 2074 - 2077 1520-6149 2010 [Refereed][Not invited]
   

  One of central topics of kernel machines in the field of machine learning is a model selection, especially a selection of a kernel or its parameters. In our previous work, we discussed a class of kernels whose corresponding reproducing kernel Hilbert spaces have an invariant metric and proved that the kernel corresponding to the smallest reproducing kernel Hilbert space, including an unknown true function, gives the optimal model. However, discussions for properties that make the metrics of reproducing kernel Hilbert spaces invariant are insufficient. In this paper, we show a necessary and sufficient condition that makes the metrics of reproducing kernel Hilbert spaces invariant.
• Localized Projection Learning

  Kazuki Tsuji, Mineichi Kudo, Akira Tanaka

  STRUCTURAL, SYNTACTIC, AND STATISTICAL PATTERN RECOGNITION 6218 90 - 99 0302-9743 2010 [Refereed][Not invited]
   

  It is interesting to compare different criteria of kernel machines. In this paper, the following is made: 1) to cope with the scaling problem of projection learning, we propose a dynamic localized projection learning using k nearest neighbors, 2) the localized method is compared with SVM from some viewpoints, and 3) approximate nearest neighbors are demonstrated their usefulness in such a localization. As a result, it is shown that SVM is superior to projection learning in many classification problems in its optimal setting but the setting is not easy.
• Real-Time Blind Source Extraction with Learning Period Detection Based on Closed-Form Second-Order ICA and Kurtosis

  FUJIHARA Yuuki, TAKAHASHI Yu, TACHIBANA Kentaro, MIYABE Shigeki, SARUWATARI Hiroshi, SHIKANO Kiyohiro, TANAKA Akira

  The IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences (Japanese edition) A 一般社団法人電子情報通信学会 J92-A (5) 314 - 326 0913-5707 2009/05 [Refereed][Not invited]
   

  従来の独立成分分析(ICA)を用いたリアルタイム音声強調システムでは,時々刻々と変化する環境に追従するために分離フィルタを逐次学習することが必要である.しかし,実環境で利用する場合,利用者が不在で雑音のみが存在する時間帯がほとんどである.このような時間帯において利用者が存在する時間帯と同様の学習を行うと,不適切な分離フィルタが生成され,システム自体の性能の低下につながる.本論文では,適切な分解フィルタを高速に構成するため,解析型ICAとkurtosisに基づく学習区間判定法及びフィルタ初期化法を提案する.本手法では,はじめに,解析型二次統計量ICAによってある程度の分離を行い,その分解信号のkurtosisに基づいて利用者の発話の有無を判断する.次に,発話のある時間帯では,解析型二次統計量ICAの分離フィルタを初期値として反復型高次統計量ICAの学習を行い,更に性能の良い分離フィルタを高速に再構成する.本論文では最後に,提案法を雑音推定部に導入したブラインド空間的サブトラクションアレーを用いて雑音抑圧実験を行い,提案法の有効性を示す.
• Real-time blind source extraction with learning period detection based on closed-form second-order ICA and kurtosis

  Yuuki Fujihara, Yu takahashi, Kentaro Tachibana, Shigeki Miyabe, Hiroshi Saruwatari, Kiyohiro Shikano, Akira Tanaka

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences (Japanese Edition) 一般社団法人電子情報通信学会 92-A (5) 314 - 326 0913-5707 2009/05 [Refereed][Not invited]
   

  従来の独立成分分析(ICA)を用いたリアルタイム音声強調システムでは,時々刻々と変化する環境に追従するために分離フィルタを逐次学習することが必要である.しかし,実環境で利用する場合,利用者が不在で雑音のみが存在する時間帯がほとんどである.このような時間帯において利用者が存在する時間帯と同様の学習を行うと,不適切な分離フィルタが生成され,システム自体の性能の低下につながる.本論文では,適切な分解フィルタを高速に構成するため,解析型ICAとkurtosisに基づく学習区間判定法及びフィルタ初期化法を提案する.本手法では,はじめに,解析型二次統計量ICAによってある程度の分離を行い,その分解信号のkurtosisに基づいて利用者の発話の有無を判断する.次に,発話のある時間帯では,解析型二次統計量ICAの分離フィルタを初期値として反復型高次統計量ICAの学習を行い,更に性能の良い分離フィルタを高速に再構成する.本論文では最後に,提案法を雑音推定部に導入したブラインド空間的サブトラクションアレーを用いて雑音抑圧実験を行い,提案法の有効性を示す.
• GCD-Based Blind Deconvolution Using PCA-Based Noise Reduction

  A. Tanaka, K. Azuma, M. Miyakoshi

  Proceedings of the 6th IASTED International Confderence on Signal Processing, Pattern Recognition and Applications (SPPRA2009) 89 - 94 2009/02 [Refereed][Not invited]
  
• Fast and Versatile Blind Separation of Diverse Sounds Using Closed-Form Estimation of Probability Density Functions of Sources

  Hiroshi Saruwatari, Yu Takahashi, Kentaro Tachibana, Yoshimitsu Mori, Shigeki Miyabe, Kiyohiro Shikano, Akira Tanaka

  2009 3RD IEEE INTERNATIONAL WORKSHOP ON COMPUTATIONAL ADVANCES IN MULTI-SENSOR ADAPTIVE PROCESSING (CAMSAP) 249 - 252 2009 [Refereed][Not invited]
   

  In this paper, we propose a fast and versatile blind source separation including closed-form estimation of sources' probability density functions (PDFs), where the ICA's activation function is automatically adapted to various noise conditions. In the proposed method, closedform second-order ICA and closed-form PDF estimation are introduced as a computational-cost-efficient preprocessing to extract sources' PDFs. Compared with various type of conventional ICAs, e. g., fixed activation-function type and ML-based type, our proposed algorithm can give a faster and higher convergence. Experimental assessment reveals that the proposed method is versatile for handling non-speech sound sources.
• ANALYSIS ON BLIND DECORRELATION OF ISOTROPIC NOISE CORRELATION MATRICES BASED ON SYMMETRIC DECOMPOSITION

  Akira Tanaka, Masaaki Miyakoshi, Nobutaka Ono

  2009 IEEE/SP 15TH WORKSHOP ON STATISTICAL SIGNAL PROCESSING, VOLS 1 AND 2 421 - + 2009 [Refereed][Not invited]
   

  Recently, a technique named 'blind decorrelation' was proposed by which we can blindly diagonalize correlation matrices of isotropic noises observed by particular crystal-shape sensor arrays. This technique enables us to estimate the power of unknown target signals, which may improve the performance of inverse filters such as the Wiener filter. It was clarified that several classes of crystal-shape arrays achieve the blind decorrelation; and some necessary conditions imposed on a sensor array to realize the blind decorrelation were revealed. However, we do not have a necessary and sufficient condition for a sensor array to achieve the blind decorrelation. In this paper, we show a necessary and sufficient condition for a sensor array to achieve the blind decorrelation, using a novel matrix analysis scheme named 'symmetric decomposition!
• SOURCE ADAPTIVE BLIND SIGNAL EXTRACTION USING CLOSED-FORM ICA FOR HANDS-FREE ROBOT SPOKEN DIALOGUE SYSTEM

  Takahashi Yu, Hiroshi Saruwatari, Yuki Fujihara, Kentaro Tachibana, Yoshimitsu Mori, Shigeki Miyabe, Kiyohiro Shikano, Akira Tanaka

  2009 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOLS 1- 8, PROCEEDINGS 3681 - + 1520-6149 2009 [Refereed][Not invited]
   

  In this paper, we propose a new ICA-based BSS algorithm including estimation of sources' probability density functions (PDFs) to adapt the nonlinear activation function to various noise conditions. In the proposed method, closed-form second-order ICA is introduced as a computational-cost-efficient preprocessing to extract sources' PDFs, which is beneficial for real-time application. Compared with various type of conventional ICAs, e.g., fixed activation-function type and ML-based type, our proposed algorithm can give a faster and higher convergence. Based on the proposed source-adaptive ICA, we show a real-time noise reduction results under diffuse noise environment. Also we can demonstrate our recently developed hands-free robot spoken dialogue system via real-time ICA.
• JOINT ESTIMATION OF SIGNAL AND NOISE CORRELATION MATRICES AND ITS APPLICATION TO INVERSE FILTERING

  Akira Tanaka, Masaaki Miyakoshi

  2009 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOLS 1- 8, PROCEEDINGS 2181 - 2184 1520-6149 2009 [Refereed][Not invited]
   

  Noise suppression by linear filters for a time series is discussed. We propose a method for jointly estimating signal and noise correlation matrices by incorporating steering vectors of the noise or eigenvectors of the noise correlation matrix as well as steering vectors of the target signals. Our estimates bring us two significant advantages. One is reduction of computational cost in obtaining the Wiener filter since the Wiener post filter, which is combined to the minimum variance distortionless response filter (MVDRF), is no longer needed with the estimates of signal and noise correlation matrices. The other is an improvement of the performance of the MVDRF since we can construct the regularized version of it with an estimate of the noise correlation matrix.
• Fast and Versatile Blind Separation of Diverse Sounds Using Closed-Form Estimation of Probability Density Functions of Sources

  Hiroshi Saruwatari, Yu Takahashi, Kentaro Tachibana, Yoshimitsu Mori, Shigeki Miyabe, Kiyohiro Shikano, Akira Tanaka

  2009 3RD IEEE INTERNATIONAL WORKSHOP ON COMPUTATIONAL ADVANCES IN MULTI-SENSOR ADAPTIVE PROCESSING (CAMSAP 2009) 249 - + 2009 [Refereed][Not invited]
   

  In this paper, we propose a fast and versatile blind source separation including closed-form estimation of sources' probability density functions (PDFs), where the ICA's activation function is automatically adapted to various noise conditions. In the proposed method, closed. form second-order ICA and closed-form PDF estimation are introduced as a computational-cost-efficient preprocessing to extract sources' PDFs. Compared with various type of conventional ICAs, e.g., fixed activation-function type and ML-based type, our proposed algorithm can give a faster and higher convergence. Experimental assessment reveals that the proposed method is versatile for handling non-speech sound sources.
• Perturbation Analysis of Joint Diagonalizers and Its Application to Second-Order-Statistics-Based BSS

  TANAKA Akira, MISAGAWA Yusuke, MIYAKOSHI Masaaki

  The IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences (Japanese edition) A 一般社団法人電子情報通信学会 J91-A (11) 1093 - 1097 0913-5707 2008/11 [Refereed][Not invited]
   

  本論文では,厳密には同時対角化ができない複数の非負定植エルミート行列に対する同時対角化行列の解析的表現に関する摂動解析を行う.また,当該結果の,二次統計量に基づくブラインド信号分離問題への応用について論じる.
• Performance Improvement of Higher-Order ICA Using Learning Period Detection Based on Closed-Form Second-Order ICA and Kurtosis

  Y. Fujihara, Y. Takahashi, S. Miyabe, H. Saruwatari, K. Shikano, A. Tanaka

  Proceedings of the 11th International Workshop for Acoustic Echo and Noise Control (IWAENC2008) 2008/09 [Refereed][Not invited]
  
• Noisy BSS Based on Joint Diagonalization of Differences of Correlation Matrices

  A. Tanaka, H. Imai, M. Miyakoshi

  Proceedings of the 10th IASTED International Conference Signal and Image Processing (SIP 2008) 368 - 373 2008/08 [Refereed][Not invited]
  
• 相関行列差分の同時対角化によるNoisy BSSにおける相関行列選択

  今井雄基, 田中章, 宮腰政明

  電子情報通信学会技術研究報告, 応用音響 107 (532) 91 - 95 2008/03 [Not refereed][Not invited]
  
• Wiener Implementation of Kernel Machines

  A. Tanaka, H. Imai, J. Toyama, M. Kudo, M. Miyakoshi

  Proceedings of the Fifth IASTED International Conference on Signal Processing, Pattern Recognition, and Applications (SPPRA2008) 1 - 6 2008/02 [Refereed][Not invited]
  
• Optimal Kernel in a Class of Kernels with an Invariant Metric

  Akira Tanaka, Hideyuki Imai, Mineichi Kudo, Masaaki Miyakoshi

  STRUCTURAL, SYNTACTIC, AND STATISTICAL PATTERN RECOGNITION 5342 530 - 539 0302-9743 2008 [Refereed][Not invited]
   

  Learning based oil kernel machines is widely known as a, powerful tool for various fields of information science such as pattern recog nition and regression estimation. One of central topics of kernel machines is model selection, especially selection of a kernel or its parameters. In this paper, we consider a. class of kernels that forms a monotonic classes of reproducing kernel Hilbert spaces with an invariant metric and show that the kernel corresponding to the smallest reproducing kernel Hilbert space including an unknown true function gives the optimal model for the unknown true function.
• Fast Nonclosed-Form Higher-Order ICA with Frequency-Subband Selection Using Closed-Form Second-Order ICA

  Kentaro Tachibana, Yu Takahashi, Yoshimitsu Mori, Hiroshi Saruwatari, Kiyohiro Shikano, Akira Tanaka

  Journal of Signal Processing 信号処理学会 12 (4) 327 - 330 1342-6230 2008 [Refereed][Not invited]
   

  大きな残響のある条件でのブラインド信号分離(BSS)の問題を扱った。一般的に,二次独立成分分析(ICA)や高次ICAのような,ほとんど全てのICAアルゴリズムは開形式,すなわち逐次最適化により行われ,実時間処理には適用できない。最近,著者ら一人が閉形式二次ICAを求め,それにより著者らは閉形式ICAの後に開形式高次ICAを行う効率的なBSSの方法を提案した。本論文では,適切なコスト関数に基づいた高次ICAに対する最適化周波数サブバンドの選択による,BSSのより高速な収束法を提案した。提案した方法の有効性を評価するために,残響環境での音源分離実験を行った。その結果,提案した方法の収束速度が,先の方法よりも大きいことが分かった。
• Fast parameter selection algorithm for linear parametric filters

  Akira Tanaka, Masaaki Miyakoshi

  IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES E90A (12) 2952 - 2956 0916-8508 2007/12 [Refereed][Not invited]
   

  A parametric linear filter for a linear observation model usually requires a parameter selection process so that the filter achieves a better filtering performance. Generally, criteria for the parameter selection need not only the filtered solution but also the filter itself with each candidate of the parameter. Obtaining the filter usually costs a large amount of calculations. Thus, an efficient algorithm for the parameter selection is required. In this paper, we propose a fast parameter selection algorithm for linear parametric filters that utilizes a joint diagonalization of two non-negative definite Hermitian matrices.
• Closed-form 2 次統計量 ICA に基づく周波数選択および確率密度関数推定による nonclosed-form 高次統計量 ICA の高速化

  橘健太郎, 高橋祐, Even Jani, 森康充, 宮部滋樹, 猿渡洋, 鹿野清宏, 田中章

  第22回SIPシンポジウム講演論文集 P1-1  2007/11 [Not refereed][Not invited]
  
• 音場再現システムにおける最適スピーカー配置に関する一検討

  横関誠, 田中章, 宮腰政明

  第22回SIPシンポジウム講演論文集 B2-2  2007/11 [Not refereed][Not invited]
  
• Integrated kernels and their properties

  Akira Tanaka, Hideyuki Imai, Mineichi Kudo, Masaaki Miyakoshi

  PATTERN RECOGNITION 40 (11) 2930 - 2938 0031-3203 2007/11 [Refereed][Not invited]
   

  Kernel machines are widely considered to be powerful tools in various fields of information science. By using a kernel, an unknown target is represented by a function that belongs to a reproducing kernel Hilbert space (RKHS) corresponding to the kernel. The application area is widened by enlarging the RKHS such that it includes a wide class of functions. In this study, we demonstrate a method to perform this by using parameter integration of a parameterized kernel. Some numerical experiments show that the unresolved problem of finding a good parameter can be neglected. (c) 2007 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.
• Improvement of Eigenspace-BPLP Based on Linear Estimation Theory

  TANAKA Akira, MIYAKOSHI Masaaki

  The IEICE transactions on information and systems 一般社団法人電子情報通信学会 J90-D (10) 2840 - 2847 1880-4535 2007/10 [Refereed][Not invited]
   

  欠損領域を有する数値データの補間技術として,固有空間BPLP法という手法が提案されている.この手法は,所与のデータから切り出したブロックデータの主成分構造を利用して欠損領域を推定する手法であり,いくつかのパラメータを適切に選択することによって,非常に効果的に欠損部を補間することができる.この手法の核心は,主成分ベクトルの線形結合を実現する係数ベクトルを,欠損領域を有するブロックの非欠損領域の情報のみを用いて推定することにある.しかしながら,その推定法は必ずしも数理的に明確な形で与えられておらず,また,手法の機序と処理結果に未解決の不整合がある等の問題がある.本論文では,当該係数ベクトルの推定を,線形推定理論の枠組みで解釈し直すとともに,その解釈,及び,欠損領域を有しないブロックの確率構造に基づき,より効果的に補間を行う手法を提案する.
• 高次統計量に基づく混合比推定による Blind-MINT 法の拡張

  田中章, 宮腰政明

  電子情報通信学会技術研究報告, 応用音響 107 (120) 7 - 12 2007/06 [Not refereed][Not invited]
  
• Eigen Analysis of Unitary Matrices Used in Signal Processing

  MIYAKOSHI Masaaki, TANAKA Akira, KAWAGUCHI Mayuka F.

  The IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences (Japanese edition) A 一般社団法人電子情報通信学会 J90-A (5) 403 - 414 0913-5707 2007/05 [Refereed][Not invited]
   

  離散信号解析には多くのユニタリ行列が用いられる.それらは,信号をユニタリ行列の互いに正規直交な列ベクトルによって展開し,各基底成分が信号の構成に寄与する仕方を解析するものであり,また逆変換は逆行列であるが,ユニタリ行列の場合の逆行列は随伴行列であり,転置と複素共役によって求まり,掃き出し法などを用いる必要がないため,極めて信号の処理等に適している.しかし,この立場は,ユニタリ行列を変換対としてとらえており,そのユニタリ行列がどのように信号に関する情報を空間や部分空間である各固有空間の中で保持しているかを明らかにした研究はない.本論文では,信号解析に用いるユニタリ行列に関する固有値や固有空間に着目し,対称群によって表される信号の対称性と変換に用いられるユニタリ行列の関係を明らかにし,それらが信号解析に果たす役割を考察する.
• A unified framework of subspace identification for DOA estimation

  Akira Tanaka, Hideyuki Imai, Masaaki Miyakoshi

  IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES E90A (2) 419 - 428 0916-8508 2007/02 [Refereed][Not invited]
   

  In D.O.A. estimation, identification of the signal and the noise subspaces plays an essential role. This identification process was traditionally achieved by the eigenvalue decomposition (EVD) of the spatial correlation matrix of observations or the generalized eigenvalue decomposition (GEVD) of the spatial correlation matrix of observations with respect to that of an observation noise. The framework based on the GEVD is not always an extension of that based on the EVD, since the GEVD is not applicable to the noise-free case which can be resolved by the framework based on the EVD. Moreover, they are not applicable to the case in which the spatial correlation matrix of the noise is singular. Recently, a quotient-singular-value-decomposition-based framework, that can be applied to problems with singular noise correlation matrices, is introduced for noise reduction. However, this framework also can not treat the noise-free case. Thus, we do not have a unified framework of the identification of these subspaces. In this paper, we show that a unified framework of the identification of these subspaces is realized by the concept of proper and improper eigenspaces of the spatial correlation matrix of the noise with respect to that of observations.
• Selection of correlation matrices for second-order-statistics-based blind source separation

  Akira Tanaka, Hideyuki Imai, Masaaki Miyakoshi

  2007 IEEE/SP 14TH WORKSHOP ON STATISTICAL SIGNAL PROCESSING, VOLS 1 AND 2 109 - 113 2007 [Refereed][Not invited]
   

  The aim of blind source separation is to recover mutually independent unknown source signals from observations obtained through an unknown linear mixture system. A simultaneous diagonalization of correlation matrices (second-order statistics) of the observations is a possible resolution for the case when the unknown source signals are non-stationary. In general, unknown source signals are not strictly uncorrelated; this may cause a degradation in the separation performance. In this study, we propose a method for selecting a combination of correlation matrices that yields a better separation performance, and verify the efficacy of the proposed method by computer simulations.
• Efficient blind source separation combining closed-form second-order ICA and nonclosed-form higher-order ICA

  Kentaro Tachibana, Hiroshi Saruwatari, Yoshimitsu Mori, Shigeki Miyabe, Kiyohiro Shikano, Akira Tanaka

  2007 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOL I, PTS 1-3, PROCEEDINGS 45 - + 1520-6149 2007 [Refereed][Not invited]
   

  In this paper, first, we propose a computational-cost efficient blind source separation combining closed-form 2nd-order independent component analysis (ICA) and nonclosed-form higher-order ICA. The closed-form solution of the 2nd-order ICA has been recently presented by one of the authors. This finding motivates us to combine the closed-form 2nd-order ICA and higher-order ICA, where the preceding closed-form ICA produces a good initial value and the following higher-order ICA updates the separation filters from the advantageous status. Secondly, we utilize the proposed architecture to address an essential question that which type of statistics is more beneficial to ICA among non-stationarity and non-Gaussianity. This can be conducted owing to the attractive property that the closed-form ICA can provide a good estimate of the theoretical upper limitation of the separation performance among 2nd-order ICAs without suffering from poor-convergence problems. Experimental results reveal that the non-Gaussianity-based ICA can outperform the nonstationarity-based ICA.
• BLIND SOURCE SEPARATION USING CLOSED-FORM SECOND-ORDER ICA AND NONCLOSED-FORM HIGHER-ORDER ICA

  TACHIBANA Kentaro, SARUWATARI Hiroshi, MORI Yoshimitsu, MIYABE Shigeki, SHIKANO Kiyohiro, TANAKA Akira

  IEICE technical report 一般社団法人電子情報通信学会 106 (432) 37 - 42 0913-5685 2006/12 [Not refereed][Not invited]
   

  In this paper, first, we propose a computational-cost efficient blind source separation combining closed-form 2nd-order independent component analysis (ICA) and nonclosed-form higher-order ICA. The closed-form solution of the 2nd-order ICA has been recently presented by one of the authors. This finding motivates us to combine the closed-form 2nd-order ICA and higher-order ICA, where the preceding closed-form ICA updates the separation filters from the advantageous status. Secondly, we utilize the proposed architecture to address an essential question that which type of statistics is more beneficial to ICA among non-stationarity and non-Gaussianity. Experimental results reveal that the non-Gaussianity-based ICA can outperform the non-stationarity-based ICA.
• Another Interpretation of the Parametric Partial Projection Filter Based on the General Solution of Linear Constraints and Its Application to Restoration with Affine Constraints

  TANAKA Akira, IMAI Hideyuki, MIYAKOSHI Masaaki

  The IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences (Japanese edition) A 一般社団法人電子情報通信学会 J89-A (8) 679 - 681 0913-5707 2006/08 [Refereed][Not invited]
   

  パラメトリック部分射影フィルタによる復元が,適当な線形制約の一般解の自由パラメータをパラメトリック射影フィルタにより推定した復元と同値であることを示す.また,この知見に基づく一般化により,アフィン制約付き復元問題に適用可能なフィルタを構成する.
• Second-order-statistics-based blind source separation for non-stationary sources with stationary noise

  Akira Tanaka, Hideyuki Imai, Masaaki Miyakoshi

  2006 IEEE INTERNATIONAL SYMPOSIUM ON SIGNAL PROCESSING AND INFORMATION TECHNOLOGY, VOLS 1 AND 2 647 - + 2006 [Refereed][Not invited]
   

  The aim of "Blind Source Separation" is to recover mutually independent unknown source signals from observations obtained through an unknown linear mixture system. Simultaneous diagonalization of correlation matrices (second-order statistics) of observations is one of resolutions, when the unknown source signals are non-stationary. When observation noise exists, this method needs to correct the correlation matrices based on an estimation of the variance of the noise. However the estimation of the variance of the noise requires additional information such as redundant observations. In this paper we propose a new method of estimating the variance of the noise without additional information by utilizing a necessary and sufficient condition that simultaneous diagonalization of the correlation matrices is always achieved. We also verify the efficacy of the proposed method by numerical examples.
• Theoretical foundations of second-order-statistics-based Blind Source Separation for non-stationary sources

  Akira Tanaka, Hideyuki Imai, Masaaki Miyakoshi

  2006 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING, VOLS 1-13 3051 - 3054 1520-6149 2006 [Refereed][Not invited]
   

  The aim of "Blind Source Separation" is to recover mutually independent unknown source signals from observations obtained through an unknown linear mixture system. Simultaneous diagonalization of correlation matrices (second-order statistics) of observations is one of the resolutions, when the unknown source signals are non-stationary. Although it is trivial that the true separation matrix simultaneously diagonalizes all the correlation matrices, it is not well investigated whether a simultaneous diagonalizer of the correlation matrices is always a separation matrix. In this paper, we give explicit solutions of simultaneous diagonalizers of the correlation matrices and we also clarify the condition that the solutions always achieve the blind source separation.
• Mathematical interpretations of kernel ridge regression

  Akira Tanaka, Hideyuki Imai, Mineichi Kudo, Masaaki Miyakoshi

  AIP Conference Proceedings 839 347 - 353 0094-243X 2006 [Refereed][Not invited]
   

  Learning based on kernel machines is widely known as a powerful tool for various fields of information science. The kernel ridge regression is one of simple and classical kernel machines and it gives a foundation for other kernel machines such as the support vector machine. However, it has some problems such as arbitrariness of the model and theoretical validity of an ad hoc kernelization of the ridge regression. The essence of using a kernel in learning problems is that the unknown target is representable by a function belonging to the reproducing kernel Hilbert space corresponding to the adopted kernel. In this paper, on the basis of the essence, we give two identical interpretations, whose theoretical grounds are clarified, for the kernel ridge regression. One is the ridge regression on the reproducing kernel Hilbert space and the other is the parametric projection learning with a specific condition. © 2006 American Institute of Physics.
• Model selection using a class of Kernels with an invariant metric

  Akira Tanaka, Masashi Sugiyama, Hideyuki Imai, Mineichi Kudo, Masaaki Miyakoshi

  STRUCTURAL, SYNTACTIC, AND STATISTICAL PATTERN RECOGNITION, PROCEEDINGS 4109 862 - 870 0302-9743 2006 [Refereed][Not invited]
   

  Learning based on kernel machines is widely known as a powerful tool for various fields of information science such as pattern recognition and regression estimation. The efficacy of the model in kernel machines depends on the distance between the unknown true function and the linear subspace, specified by the training data set, of the reproducing kernel Hilbert space corresponding to an adopted kernel. In this paper, we propose a framework for the model selection of kernel-based learning machines, incorporating a class of kernels with an invariant metric.
• アフィン制約を考慮した画像復元フィルタの構成

  田中章, 今井英幸, 宮腰政明

  第20回信号処理シンポジウム講演論文集 D7-3  2005/11 [Not refereed][Not invited]
  
• D.O.A. estimation with singular noise correlation matrix

  Akira Tanaka, Masaaki Miyakoshi

  ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings III III257 - III260 1520-6149 2005 [Refereed][Not invited]
   

  In this paper, a new method of direction of arrival (D.O.A.) estimation with environmental noise, whose spatial correlation matrix is singular, is proposed. In D.O.A. estimation, identification of signal and noise subspaces plays a very important role. The identification process can be achieved by (generalized) eigenvalue decomposition of the spatial correlation matrix of observations (with respect to that of noise), if these spatial correlation matrices are non-singular. However, these mathematical tools can not be applied to the problems in which the spatial correlation matrices are singular. The main idea of this work deeply depends on identification of proper and improper eigenvectors of the spatial correlation matrix of noise with respect to that of observations. The results of computer simulations are also presented to verify the efficacy of the proposed method. ©2005 IEEE.
• Image restoration with an affine constraint

  A Tanaka, H Imai, M Miyakoshi

  Proceedings of the Fifth IASTED International Conference on Visualization, Imaging, and Image Processing 326 - 331 2005 [Refereed][Not invited]
   

  In image restoration problems, an effective restoration is achieved by a priori, knowledge of the unknown original image. An affine constraint could be considered as such a priori knowledge, which may appear when we know intensities of particular pixels of the unknown original image, for instance. Adopting the least-squares criterion with an affine constraint seems to be one of simple and reasonable approaches. However, it was reported in past studies that some problems may occur with the least squares criterion based methods, even if no constraint is imposed. The family of (parametric) projection filters was proposed as one of resolutions for the problems. However, they do not have a framework to deal with an affine constraint, while a linear constraint can be considered. In this paper, we propose a new restoration filter in which an affine constraint is appropriately considered by extending the (parametric) partial projection filter which belongs to the family of (parametric) projection filters. Numerical examples are also presented to verify the efficacy of the proposed method.
• Image restoration in singular observation processes based on complementary space component estimation

  A Tanaka, H Imai, M Miyakoshi

  ELECTRONICS AND COMMUNICATIONS IN JAPAN PART II-ELECTRONICS 88 (8) 54 - 65 8756-663X 2005 [Refereed][Not invited]
   

  Image restoration is a problem in which an unknown original image is to be estimated from a degraded image obtained from some observation process. Various restoration methods have been proposed. Most of the conventional methods assume that the observation process is regular or almost regular. However, in general there is no guarantee that the observation process is regular, and the restoration performance of past methods is insufficient for a singular observation process. The degradation of restoration performance in a singular observation process arises from the fact that it is difficult to estimate the components related to the null space, which is eliminated in the observation process. There have recently been many studies of the properties and representations of the image signal. In one such study it was reported that the difference signal of the image approximately follows the Laplace distribution. This paper is based on that stochastic property of the image, and proposes a method of restoring images with high precision by positively estimating the image component which is eliminated in a singular observation process. The effectiveness of the proposed method is investigated by numerical experiment. (c) 2005 Wiley Periodicals, Inc.
• Regularized Inverse Filter Design for Sound Reproduction Systems

  TANAKA Akira, OTANI Naohisa, MIYAKOSHI Masaaki

  The Transactions of the Institute of Electronics, Information and Communication Engineers. A 一般社団法人電子情報通信学会 J87-A (11) 1466 - 1467 0913-5707 2004/11 [Refereed][Not invited]
   

  本論文では,音場再現システムにおける最適性の定義を与え,その解かよく知られている正則化一般逆フィルタに帰着することを示すとともに,当該フィルタの音場再現システムヘの適用の際に問題となるパラメータ設定及び計算量の問題の解決を図る.
• On formulations and solutions in linear image restoration problems

  A Tanaka, H Imai, M Miyakoshi

  IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES E87A (8) 2144 - 2151 0916-8508 2004/08 [Refereed][Not invited]
   

  In terms of the formulation of the optimality, image restoration filters can be divided into two streams. One is formulated as an optimization problem in which the fidelity of a restored image is indirectly evaluated, and the other is formulated as an optimization problem based on a direct evaluation. Originally, the formulation of the optimality and the solutions derived from the formulation are identical each other. However in many studies adopting the former stream, an arbitrary choice of a solution without a mathematical ground passes unremarked. In this paper, we discuss the relation between the formulation of the optimality and the solution derived from the formulation from a mathematical point of view, and investigate the relation between a direct style formulation and an indirect one. Through these analyses, we show that the both formulations yield the identical filter in practical situations.
• A nearest neighbor method using bisectors

  M Kudo, H Imai, A Tanaka, T Murai

  STRUCTURAL, SYNTACTIC, AND STATISTICAL PATTERN RECOGNITION, PROCEEDINGS 3138 885 - 893 0302-9743 2004 [Refereed][Not invited]
   

  A novel algorithm for finding the nearest neighbor was proposed. According to the development of modern technology, the demand is increasing in large-scale datasets with a large number of samples and a large number of features. However, almost all sophisticated algorithms proposed so far are effective only in a small number of features, say, up to 10. This is because in a high-dimensional space many pairs of samples share a same distance. Then the naive algorithm outperforms the others. In this study, we considered to utilize a sequential information of distances obtained by the examined training samples. Indeed, a combinatorial information of examined samples was used as bisectors between possible pairs of them. With this algorithm, a query is processed in O(alphabetand) for n samples in a d-dimensional space and for alpha,beta < 1, in expense of a preprocessing time and space in O(n(2)). We examined the performance of the algorithm.
• Image restoration for observation processes with stochastic variation

  A Tanaka, H Imai, M Miyakoshi

  8TH WORLD MULTI-CONFERENCE ON SYSTEMICS, CYBERNETICS AND INFORMATICS, VOL V, PROCEEDINGS V 92 - 96 2004 [Refereed][Not invited]
   

  A new approach to restore images degraded by observation processes with stochastic variation is proposed. In practice, an observation process must be estimated by some empirical knowledges, since we can not obtain an exact one. A restored image by a, restoration filter based on an estimated observation process could suffer critical damages even if the deviation of the estimated observation process is comparatively small, sincle an image restoration is one of representative ill-posed problems as is well known. In this paper, we formulate the stochastic variation of observation processes and propose a new image restoration method in which the deviation of the observation process is appropriately considered. It is also clarified that our approach is reduced to a, kind of regularization scheme. Some numerical examples are also shown to verify the efficacy of the proposed method.
• A note on fuzzy granular reasoning

  Tetsuya Murai, Yasuo Kudo, Nam Van Huynh, Akira Tanaka, Mineichi Kudo

  IEEE International Conference on Fuzzy Systems 1 263 - 268 1098-7584 2004 [Refereed][Not invited]
   

  In this paper, firstly, processes of classical inference are reviewed as granular reasoning from a point of view of reconstructing Kripke-style models with granularity. The essential point of the reconstruction is that some possible worlds are amalgamated to generate granules of worlds and vice versa. It is also called zoom reasoning systems. Then, the idea is applied for fuzzy reasoning processes by considering fuzzily granularized possible worlds. There linguistic truth values with linguistic hedges can be naturally introduced.
• Projection learning based kernel machine design using series of monotone increasing reproducing kernel Hilbert spaces

  A Tanaka, Takigawa, I, H Imai, M Kudo, M Miyakoshi

  KNOWLEDGE-BASED INTELLIGENT INFORMATION AND ENGINEERING SYSTEMS, PT 1, PROCEEDINGS 3213 1058 - 1064 0302-9743 2004 [Refereed][Not invited]
   

  Kernel machines are widely known as powerful tools for various fields of information science. In general, they are designed based on a generalization criterion related to the complexity of the model and intuitive but ad hoe philosophy such as maximal margin principle shown in SVM. On the other hand, the project ion learning scheme was proposed in the field of neural networks. In the projection learning, the generalization ability is evaluated by the distance between the unknown target function and the estimated one. In,this paper, we construct projection learning based kernel machines and propose a method of making a kernel function that has necessary representability for the task. The method is reduced to a selection of an appropriate reproducing kernel Hilbert space from a series of monotone increasing subspaces. We also verify the efficacy of the proposed method by numerical examples.
• Digital Image Enlargement Based on Kernel Component Estimation

  A. Tanaka, H. Imai, M. Miyakoshi

  International Journal of Computing Anticipatory Systems 15 97 - 108 2004 [Refereed][Not invited]
  
• Image Restoration in Singular Observation Processes Based on Complementary Space Component Estimation

  TANAKA Akira, IMAI Hideyuki, MIYAKOSHI Masaaki

  The Transactions of the Institute of Electronics,Information and Communication Engineers. 一般社団法人電子情報通信学会 Vol.J86-D-II (12) 1745 - 1755 0915-1923 2003/12 [Refereed][Not invited]
   

  画像復元問題とは,何らかの観測過程により劣化を受けた画像から未知の原画像を推定する問題であり,これまで様々な復元法が提案されている.従来手法の多くでは,観測過程は正則であるか,若しくはそれに近い状況であることが前提となっているが,一般に観測過程が正則である保証はなく,そのような観測過程に対する復元性能は十分とはいえない.特異な観測過程に対する復元性能の低下は,観測過程によって消失した零空間に関連する成分の推定が困難であることに起因する.ところで,近年,画像信号の性質や表現に関する研究も数多くなされており,その中で得られた知見の一つとして,画像の差信号がおおむねラプラス分布に従うということが報告されている.本論文では,この画像の確率的性質に基づき,特異な観測過程によって消失した画像成分の推定を積極的に行うことにより,高精度の復元を行う手法を提案することを目的とする.また,数値実験により提案手法の有効性を検証する.
• Collaborative Filtering using Restoration Operators

  A. Nakamura, M. Kudo, A. Tanaka

  Proceedings of the 7th European Conference on Principles and Practice of Knowledge Discovery in Databases (PKDD2003) 339 - 349 2003/09 [Refereed][Not invited]
  
• Collaborative filtering using projective restoration operators

  A Nakamura, M Kudo, A Tanaka, K Tanabe

  DISCOVERY SCIENCE, PROCEEDINGS 2843 393 - 401 0302-9743 2003 [Refereed][Not invited]
   

  We propose a modified version of our collaborative filtering method using restoration operators, which was proposed in [6]. Our previous method was designed so as to minimize expected squared error of predictions for user's ratings, and we experimentally showed that, for users who have evaluated only small number of items, mean squared error of our method is smaller than that of correlation-base methods. After further experiments, however, we found that, for users who have evaluated many items, the best correlation-based method has smaller mean squared error than our method. In our modified version, we incorporated an idea of projecting on a low-dimensional subspace with our method using restoration operators. We experimentally showed that our modification overcame the shortcoming stated above.
• Image restoration with kernel component estimation in singular observation process

  A Tanaka, H Imai, M Miyakoshi

  PROCEEDINGS OF THE 2003 IEEE WORKSHOP ON STATISTICAL SIGNAL PROCESSING 186 - 189 2003 [Refereed][Not invited]
   

  A new approach to restore images degraded by singular observation processes is proposed. Existing image restoration filters usually assume non-singularity of observation processes. Therefore, we can not obtain desirable result by these filters, especially in case that the degradation processes have high singularity. By the way, it is well known that differential images can be assumed to be Laplacian distributed random vectors. In this paper, we propose a new restoration method for singular observation processes based on this statistical knowledge about images. A numerical example is also presented to verify the efficacy of the proposed method.
• Image restoration by the family of signal adaptive parametric projection filters

  A Tanaka, H Imai, M Miyakoshi

  ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE 86 (3) 77 - 86 1042-0967 2003 [Refereed][Not invited]
   

  Many of the image restoration techniques can roughly be classified into two types: those that are formulated as an optimization problem with regard to the restored image and those that are formulated as an optimization problem with regard to the restoration operator. The former has the advantage that the local information on the image can easily be expressed in the optimization reference. A problem is that the closeness of the image needs to be evaluated indirectly in the observation image space instead of the original image space. On the other hand, in the latter the closeness of the image can be evaluated in the original image space. However, because the optimization reference used to obtain the appropriate restoration operator does not include the information on the individual images, it is difficult to express the local information on the image, in contrast to the former type. Based on such a background, the objective of this paper is to propose a restoration method that can evaluate the closeness of images in the original image space while the local information on the images can be used systematically, based on improvement of the optimization reference of the parametric projection filter family belonging to the latter. The effectiveness of the proposed method is verified by numerical examples. (C) 2002 Wiley Periodicals, Inc.
• On Duality of Formulations in Image Restoration Problems

  A. Tanaka, H. Imai, M. Miyakoshi

  Proceedings of the 4th IASTED International Conference Signal and Image Processing 242 - 247 2002/08 [Refereed][Not invited]
  
• Separable Kernel Expression of Regularized MP-Inverse for Separable Kernel Operators

  TANAKA Akira, IMAI Hideyuki, MIYAKOSHI Masaaki

  The Transactions of the Institute of Electronics,Information and Communication Engineers. A 一般社団法人電子情報通信学会 J85-A (6) 730 - 734 0913-5707 2002/06 [Refereed][Not invited]
   

  一般に,分離核作用素に対する正則化一般逆行列は分離核とはならない.したがって,その算出には,Kronecker積及びvec作用素を用いた展開形を用いることになる.しかしながら,計算に要する記憶領域及び計算量双方の観点から,当該展開形を用いずに算出した方が効率が良いことは想像にかたくない.本論文では,分離核表現可能な正則化一般逆行列を提案することを目的とする.また,提案正則化一般逆行列の正則化効果についての定量的な評価も併せて行う.
• Choosing the parameter of image restoration filters by modified subspace information criterion

  A Tanaka, H Imai, M Miyakoshi

  IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES E85A (5) 1104 - 1110 0916-8508 2002/05 [Refereed][Not invited]
   

  Practical image restoration filters usually include a parameter that controls regularizability; trade-off between fidelity of a restored image and smoothness of it; and so on. Many criteria for choosing such a parameter have been proposed. However; the relation between these criteria and the squared error of a restored image; which is usually used to evaluate the restoration performance; has not been theoretically substantiated. Sugiyama and Ogawa proposed the subspace information criterion (SIC) for model selection of supervised learning problems and showed that the SIC is an unbiased estimator of the expected squared error between the unknown model function and an estimated one. They also applied it to restoration of images. However, we need an unbiased estimator of the unknown original image to construct the criterion; so it can not be used for general situations. In this paper; we present a modified version of the SIC as a new criterion for choosing a parameter of image restoration filters. Some numerical examples are also shown to verify the efficacy of the proposed criterion.
• Relations and differences between classical and modern formulations in image restoration problems

  A Tanaka, H Imai, M Miyakoshi

  6TH WORLD MULTICONFERENCE ON SYSTEMICS, CYBERNETICS AND INFORMATICS, VOL XVI, PROCEEDINGS XVI 324 - 325 2002 [Refereed][Not invited]
   

  In view of formulation, image restoration filters can be divided into two streams. One is formulated as an optimization problem for a image, and the other is for a, restoration operator. The latter is proposed to deal with the lack of strictness in formulation that the former may have. However, the former formulation has been used in many studies without verification of its validity. In this paper, we discuss the relations and differences between these two formulations from a mathematical point of view, and verify the validity of some classical restoration filters.
• Choosing the Parameter of Regularized MP-Inverses by Modified SIC in Image Restoration Problems

  A. Tanaka, H. Imai, M. Miyakoshi

  International Journal of Computing Anticipatory Systems 12 166 - 178 2002 [Refereed][Not invited]
  
• Image restoration by the family of M-N-norm parametric projection filters

  A Tanaka, H Imai, M Miyakoshi

  ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE 85 (11) 9 - 17 1042-0967 2002 [Refereed][Not invited]
   

  In image restoration, if knowledge about the unknown original image could be used, reflecting that knowledge in the restoration process would enable effective restoration. However, in statistical image restoration that employs the family of projection filters or the family of parametric projection filters, the knowledge cannot be information other than information that limits the range in which the original image belongs to a linear subspace and limits the spatial measures to decisions based on the variance structure of the image population. We propose a family of signal-adaptive parametric projection filters that introduces knowledge about the image that should solve this problem in the form of Pareto optimization. In this paper, we construct a family of filters that can reflect knowledge about the image in the spatial measures as a new approach. We also present an example illustrating the construction of the measures and prove the effectiveness of these filters through numerical examples. (C) 2002 Wiley Periodicals, Inc.
• Image Restoration by the Family of M-N-Norm Parametric Projection Filters

  TANAKA Akira, IMAI Hideyuki, MIYAKOSHI Masaaki

  The Transactions of the Institute of Electronics,Information and Communication Engineers. A 一般社団法人電子情報通信学会 J84-A (8) 1063 - 1070 0913-5707 2001/08 [Refereed][Not invited]
   

  画像復元問題において, 未知の原画像に関する知識が利用可能である場合, その知識を復元過程に反映させることにより効果的な復元が可能となる. しかし, 射影フィルタ族やパラメトリック射影フィルタ族等のいわゆる統計的画像復元法では, 当該知識として, 原画像の属する範囲を線形部分空間に限定したり, 空間の計量を画像母集団の分散構造から決定する等の限られた情報以外は利用できない. 筆者らは, この問題を解決すべく画像の知識の反映をパレート最適という形で導入した信号適応型パラメトリック射影フィルタ族を提案している. 本論文では, 新たなアプローチとして, 画像の知識を空間の計量に反映可能なフィルタ族の構成を行う. また, 当該計量の構成例を示し, 数値例によりその効果を検証する.
• 信号適応型パラメトリック射影フィルタ族による画像復元

  田中章, 今井英幸, 宮腰政明

  電子情報通信学会論文誌A J83-A (8) 1011 - 1020 2000/08 [Refereed][Not invited]
  
• ノルム拘束に基づくパラメトリック射影フィルタ族の正則化

  田中章, 今井英幸, 宮腰政明

  電子情報通信学会論文誌A J83-A (6) 812 - 820 2000/06 [Refereed][Not invited]
  
• 階層的適応重みを用いたパラメトリック射影フィルタによる自然画像の復元

  田中章, 宮腰政明

  電子情報通信学会論文誌D-II J83-D-II (2) 662 - 670 2000/02 [Refereed][Not invited]
  
• Image restoration by multiscale spatial adaptive regularization

  A. Tanaka, M. Miyakoshi

  International Journal of Computing Anticipatory Systems 6 341 - 353 2000 [Refereed][Not invited]
  
• Separated Kernel Expression of the Family of Projection Filters

  TANAKA Akira, MIYAKOSHI Masaaki

  The transactions of the Institute of Electronics, Information and Communication Engineers. D-II 一般社団法人電子情報通信学会 J82-D-II (4) 838 - 840 0915-1923 1999/04 [Refereed][Not invited]
   

  画像復元問題において, 劣化作用素が分離核であるような場合がある. このような場合でも, 離散-離散モデルの場合はクロネッカー積とVec作用素を用いることにより問題を統一的に扱うことができる. しかし, 計算量及び必要とする記憶領域の観点からは, 分離核のままで扱う方が効率が良いことは想像に難しくない. しかし, 線形推定手法の中でも分散最小の推定を行うという点で有効な手法である射影フィルタ族には, 問題を分離核のまま扱う枠組みが与えられていない. 本論文では, 射影フィルタ族において, その構成要素がある条件を満たす場合に, 劣化・復元作用素を分離核のまま扱えること示す.
• The family of regularized parametric projection filters for digital image restoration

  H Imai, A Tanaka, M Miyakoshi

  IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES E82A (3) 527 - 534 0916-8508 1999/03 [Refereed][Not invited]
   

  Optimum filters for an image restoration are formed by a degradation operator, a covariance operator of original images, and one of noise. However, in a practical image restoration problem, the degradation operator and the covariance operators are estimated on the basis of empirical knowledge. Thus, it appears that they differ from the true ones. When we restore a degraded image by an optimum filter belonging to the family of Projection Filters and Parametric Projection Filters, it is shown that small deviations in the degradation operator and the covariance matrix can cause a large deviation in a restored image. In this paper, we propose new optimum filters based on the regularization method called the family of Regularized Projection Filters, and show that they are stable to deviations in operators. Moreover, some numerical examples follow to confirm that our description is valid.
• 2次形式不等式制約を用いた射影フィルタによる画像復元

  田中章, 今井英幸, 宮腰政明

  電子情報通信学会論文誌D-II J82-D-II (3) 415 - 421 1999/03 [Refereed][Not invited]
  
• A method of identifying influential data in fuzzy clustering

  H Imai, A Tanaka, M Miyakoshi

  IEEE TRANSACTIONS ON FUZZY SYSTEMS 6 (1) 90 - 101 1063-6706 1998/02 [Refereed][Not invited]
   

  In multivariate statistical methods, it is important to identify influential observations for a reasonable interpretation of the data structure, In this paper, we propose a method for identifying influential data in the fuzzy C-means (FCM) algorithm, To investigate such data, we consider a perturbation of the data points and evaluate the effect of a perturbation. As a perturbation, we consider two cases: one is the case in which the direction of a perturbation is specified and the other is the case in which the direction of a perturbation is not specified, By computing the change in the clustering result of FCM when given data points are slightly perturbed, we can look for data points that greatly affect the result, Also, we confirm an efficacy of the proposed method by numerical examples.
• The family of parametric projection filters and its properties for perturbation

  H Imai, A Tanaka, M Miyakoshi

  IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS E80D (8) 788 - 794 0916-8532 1997/08 [Refereed][Not invited]
   

  A lot of optimum filters have been proposed for an image restoration problem. Parametric filter, such as Parametric Wiener Filter, Parametric Projection Filter, or Parametric Partial Projection Filter, is often used because it requires to calculate a generalized inverse of one operator. These optimum filters are formed by a degradation operator, a covariance operator of noise, and one of original images. In practice, these operators are estimated based on empirical knowledge. Unfortunately it happens that such operators differ from the true ones. In this paper, we show the unified formulae of inducing them to clarify their common properties. Moreover, we investigate their properties for perturbation of a degradation operator. a covariance operator of noise. and one of original images. Some numerical examples follow to confirm that our description is valid.
• 摂動に対する射影フィルタ族の性質

  今井英幸, 田中章, 宮腰政明

  電子情報通信学会論文誌D-II J80-D-II (5) 1128 - 1135 1997/05 [Refereed][Not invited]
  
• 摂動法を用いた最適画像復元フィルタの評価

  今井英幸, 田中章, 宮腰政明

  電子情報通信学会論文誌D-II J80-D-II (3) 754 - 761 1997/03 [Refereed][Not invited]
  
• 多重解像度解析を用いたディジタル画像の拡大

  田中章, 今井英幸, 宮腰政明, 伊達惇

  電子情報通信学会論文誌D-II J79-D-II (5) 819 - 825 1996/05 [Refereed][Not invited]
  

MISC

• ピッチシフトおよびソフトクリッピングによるヴィオラからチェロへの音色変換

  吉野 夏樹, 田中 章  電子情報通信学会技術研究報告, EA2023-114  309  -314  2024/03  [Not refereed][Not invited]
  
• Kernel-Induced Sampling Theorem for A Class of Mapping-Prescribed Reproducing Kernel Hilbert Spaces

  Akira Tanaka  IEICE Technical Report, SIP2023-161  109  -114  2024/02  [Not refereed][Not invited]
  
• 調波打楽器音分離における低周波領 域での分離精度向上

  吉野 夏樹, 山口 菜海, 田中 章  第38回信号処理シンポジウム講演論文集  1  -2  2023/11  [Not refereed][Not invited]
  
• 正規化エルミートグラフラプラシアンとその性質

  鎌田 翔太, 田中 章  第38回信号処理シンポジウム講演論文集  1  -6  2023/10  [Not refereed][Not invited]
  
• モバイルデバイスを用いた複数音声同時放送手法における 音声品質改善

  川原 寛喜, 中村 将成, 田中 章  電子情報通信学会技術研究報告, センサネットワークとモバイルインテリジェンス  SeMI2023-  2023/06  [Not refereed][Not invited]
  
• モバイルデバイスを用いた複数音声同時放送手法の基礎検討

  川原 寛喜, 中村 将成, 田中 章  第37回信号処理シンポジウム講演論文集  303  -307  2022/12  [Not refereed][Not invited]
  
• Convolutive NMF における複数構造を含む基底の分離に関する一検討

  松野 祥汰, 中村 将成, 田中 章  第37回信号処理シンポジウム講演論文集  209  -210  2022/12  [Not refereed][Not invited]
  
• 誤差を含む構造化行列の一次元零空間推定における計算量削減

  吉野 夏樹, 田中 章  電子情報通信学会技術研究報告, 信号処理  SIP2022-  7  -12  2022/08  [Not refereed][Not invited]
  
• 基底選択に基づく教師付NMF

  小松 美咲, 田島 優, 田中 章  第33回信号処理シンポジウム講演論文集  47  -48  2018/11  [Not refereed][Not invited]
  
• 座標降下法を用いた高速マルチチャネルNMFアルゴリズム

  田島 優, 田中 章  第33回信号処理シンポジウム講演論文集  51  -52  2018/11  [Not refereed][Not invited]
  
• マルチチャネルNMFにおける空間相関行列の初期値設定法の性能評価

  田島 優, 田中 章  電子情報通信学会技術研究報告, 信号処理  117-  (515)  161  -162  2018/03  [Not refereed][Not invited]
  
• マハラノビス距離学習と主成分マッチングを用いた教師付クラスタリング

  杉江 祐哉, 田中 章  電子情報通信学会技術研究報告, 信号処理  117-  (515)  141  -142  2018/03  [Not refereed][Not invited]
  
• 一次元斜射影を用いた教師付NMFによる音源分離

  小松 美咲, 田中 章  電子情報通信学会技術研究報告, 信号処理  117-  (515)  133  -134  2018/03  [Not refereed][Not invited]
  
• マルチチャネルNMFにおける空間相関行列の初期値設定法

  田島 優, 田中 章  第32回信号処理シンポジウム講演論文集  77  -78  2017/11  [Not refereed][Not invited]
  
• 音響的に自然なつなぎ目の発見による楽曲ループ検出

  安井拓未, 中村篤祥, 中村篤祥, 田中章, 田中章, 工藤峰一, 工藤峰一  情報処理学会研究報告(Web)  2017-  (MUS-116)  Vol.2017‐MUS‐116,No.15,1‐4 (WEB ONLY)  2017/08/17  [Not refereed][Not invited]
  
• シングルチャネルNMFを用いたマルチチャネルNMFの初期値設定法の性能評価

  田島 優, 田中 章  電子情報通信学会技術研究報告, 信号処理  116-  (475)  67  -70  2017/03  [Not refereed][Not invited]
  
• Improvement of the Similarity Calculation of B-Spline Open Curves by the Optimal Normalization

  久保内 悠馬, 田中 章  電子情報通信学会技術研究報告, 信号処理  116-  (475)  83  -86  2017/03  [Not refereed][Not invited]
  
• シングルチャネルNMFを用いたマルチチャネルNMFの初期値設定法

  田島 優, 田中 章  第31回信号処理シンポジウム講演論文集  71  -72  2016/11  [Not refereed][Not invited]
  
• B-スプラインを用いた曲線類似度計算法の性能評価

  久保内 悠馬, 田中 章  第31回信号処理シンポジウム講演論文集  218  -221  2016/11  [Not refereed][Not invited]
  
• 再生核ヒルベルト空間の積空間におけるグラム行列の近似計算

  田中 章  第31回信号処理シンポジウム講演論文集  405  -408  2016/11  [Not refereed][Not invited]
  
• 走塁能力を考慮した打順の得点期待値算出モデル

  池田 啓, 田中 章  情報処理北海道シンポジウム2016講演論文集  177  -180  2016/10  [Not refereed][Not invited]
  
• QZ法の反復計算における変換行列の精緻化

  橋本 樹, 田中 章  情報処理北海道シンポジウム2016講演論文集  193  -194  2016/10  [Not refereed][Not invited]
  
• B-スプライン曲線を用いた高速な曲線類似度計算法

  久保内 悠馬, 田中 章  電子情報通信学会技術研究報告  115-  (521)  329  -334  2016/03  [Not refereed][Not invited]
  
• 修正零位相信号解析に基づく雑音抑制

  田中 章, 安間 悠貴, 川村 新  電子情報通信学会技術研究報告  115-  (521)  153  -157  2016/03  [Not refereed][Not invited]
  
• マルチカーネル回帰とアンサンブルカーネル回帰の汎化誤差解析

  田中 章, 瀧川 一学, 今井 英幸, 工藤 峰一  第29回信号処理シンポジウム講演論文集  120  -123  2014/11  [Not refereed][Not invited]
  
• ブロックベース線形回帰と非局所的冗長性を利用したデモザイキング

  河野 克也, 田中 章  第29回信号処理シンポジウム講演論文集  533  -534  2014/11  [Not refereed][Not invited]
  
• 一般化固有値展開に基づく信号部分空間推定と斜射影を用いたDOA推定

  安間 悠貴, 田中 章  第29回信号処理シンポジウム講演論文集  476  -477  2014/11  [Not refereed][Not invited]
  
• 非定常信号選択型独立成分分析によるブラインド信号源分離

  張 ケン, 田中 章  第29回信号処理シンポジウム講演論文集  277  -278  2014/11  [Not refereed][Not invited]
  
• アンサンブルカーネル回帰とマルチカーネル回帰の汎化性能に関する一考察

  竹林 裕史, 田中 章  第29回信号処理シンポジウム講演論文集  425  -426  2014/11  [Not refereed][Not invited]
  
• 斜射影を用いたMUSIC法によるDOA推定

  田中 章, 今井 英幸  日本音響学会2014年春季研究発表会講演論文集  CD-ROM:3-2-1  2014/03  [Not refereed][Not invited]
  
• 同時対角化解析解を用いたCVFFDIAGの収束性能改善

  MUROTA Miho, TANAKA Akira  第28回信号処理シンポジウム講演論文集  10  -14  2013/11  [Not refereed][Not invited]
  
• カーネル回帰を用いたJPEG再適用法によるJPEG画像の画質改善

  河野 克也, 田中 章  第28回信号処理シンポジウム講演論文集  446  -447  2013/11  [Not refereed][Not invited]
  
• "A Sufficient Condition For Reproducing Kernel Hilbert Spaces Being Separable

  TANAKA Akira, IMAI Hideyuki, KUDO Mineichi  第28回信号処理シンポジウム講演論文集  350  -354  2013/11  [Not refereed][Not invited]
  
• JPEG再適用と画像データベースを利用したJPEG画質改善法の性能評価

  河野克也, 田中章  第27回信号処理シンポジウム講演論文集  297  -302  2012/11  [Not refereed][Not invited]
  
• 非負値行列分解と基底ベクトルクラスタリングに基づく単一チャネル音楽信号分離

  小田智也, 田中章  第27回信号処理シンポジウム講演論文集  380  -384  2012/11  [Not refereed][Not invited]
  
• 最適解選択を用いた同時対角化解析解の性能評価

  室田美帆, 田中章  第27回信号処理シンポジウム講演論文集  328  -332  2012/11  [Not refereed][Not invited]
  
• NMFを用いた自動採譜における基底ベクトル数の決定手法

  水野賀文, 田中章  第27回信号処理シンポジウム講演論文集  391  -395  2012/11  [Not refereed][Not invited]
  
• Quality Improvement of JPEG Images by Re-application of JPEG and Image Database

  KOHNO Katsuya, TANAKA Akira  IEICE technical report. Signal processing  111-  (465)  13  -18  2012/03  [Not refereed][Not invited]
   

  Image compression is one of important technologies in the fields of image processing in terms of efficient transmission and storing of images. Since there exist efficient image compression methods today, we can compress a given image by those methods efficiently. However, many existing compressed images were compressed by the conventional JPEG. Thus, we need a technique for improving the quality of JPEG images especially with low bit-rates. Many methods for improving the quality of JPEG images have been proposed. Among them, a method based on re-application of JPEG is recognized as one of efficient methods. The key idea of this method is adopting a weighted sum of images constructed by re-application of JPEG, which means compression and decoding, to various shifted version of a given JPEG image. In this paper, we propose a method for constructing a better weights for the weighted sum of images in order to improve the performance of the method based on re-application of JPEG, incorporating a image database and novel distance measures between two images. We also show some results of numerical examples in order to verify the efficacy of the proposed method.
• Let's go to IEICE Workshops!:SIP Symposium

  HASEYAMA Miki, TANAKA Akira, OGAWA Takahiro  IEICE Fundamentals Review  5-  (4)  344  -344  2012
• トレース正規化による非負定値エルミート行列の同時対角化の性能改善

  田中章  第26回SIPシンポジウム講演論文集  C3-3  2011/11  [Not refereed][Not invited]
  
• KLダイバージェンスを用いたNMFアルゴリズムの変数選択に基づく高速化

  尾崎 大顕, 田中 章  第29回信号処理シンポジウム講演論文集  423  -424  2011/11  [Not refereed][Not invited]
  
• 自己校正法における射影変換の推定精度の向上

  滝沢篤史, 田中章, 宮腰政明  電子情報通信学会技術研究報告, 信号処理  110-  (440)  229  -233  2011/03  [Not refereed][Not invited]
  
• カーネルリッジ回帰における低計算量モデル選択法

  武井亨, 田中章, 宮腰政明  電子情報通信学会技術研究報告, 信号処理  110-  (440)  185  -190  2011/03  [Not refereed][Not invited]
  
• 既知の基底ベクトルを考慮した NMF

  天野雄太, 田中章, 宮腰政明  電子情報通信学会技術研究報告, 信号処理  110-  (440)  137  -141  2011/03  [Not refereed][Not invited]
  
• 未知観測に対する二次制約を考慮した線形系逆問題

  田中章, 滝沢篤史, 宮腰政明  第25回SIPシンポジウム講演論文集  A7-1  2010/11  [Not refereed][Not invited]
  
• D-12-57 Estimation of Fundamental Matrix by Mutual Projections

  Yoshida Naoki, Tanaka Akira, Kawaguchi Mayuka F., Miyakoshi Masaaki  Proceedings of the IEICE General Conference  2010-  (2)  168  -168  2010/03/02
• Triangulation from Multiple Views Using Surfaces of Circular Cones

  HUANG Shuangquan, YOSHIDA Naoki, TANAKA Akira, MIYAKOSHI Masaaki  ITE technical report  34-  (6)  179  -184  2010/02/15  

  This paper presents a novel idea for solving a problem of triangulation from multiple views. It is necessary to consider the influence of the difference of the focal lengths when the number of images increases. We find the 3D location of a point by minimizing the sum of aperture angles of the surfaces of circular cones that are formed by lines of sight instead of the common cost function based on the sum of squared errors in images. We verify the efficacy of the proposed method by computer simulations; and find that the proposed method improves the accuracy compared with conventional methods especially in case that the focal lengths of cameras are different.
• Triangulation from Multiple Views Using Surfaces of Circular Cones

  HUANG Shuangquan, YOSHIDA Naoki, TANAKA Akira, MIYAKOSHI Masaaki  IEICE technical report  109-  (414)  179  -184  2010/02/08  

  This paper presents a novel idea for solving a problem of triangulation from multiple views. It is necessary to consider the influence of the difference of the focal lengths when the number of images increases. We find the 3D location of a point by minimizing the sum of aperture angles of the surfaces of circular cones that are formed by lines of sight instead of the common cost function based on the sum of squared errors in images. We verify the efficacy of the proposed method by computer simulations; and find that the proposed method improves the accuracy compared with conventional methods especially in case that the focal lengths of cameras are different.
• カーネル法を用いた回帰分析の予測精度について

  今井英幸, 田中章, 池田盛一  電子情報通信学会技術研究報告, パターン認識・メディア理解  109-  (344)  61  -64  2009/12  [Not refereed][Not invited]
  
• パターン認識における都市伝説

  工藤峰一, 今井英幸, 田中章, 杉山将  電子情報通信学会技術研究報告, パターン認識・メディア理解  109-  (344)  29  -34  2009/12  [Not refereed][Not invited]
  
• 分離核近似による線形系逆問題の計算量削減

  上野元, 田中章, 宮腰政明  第24回SIPシンポジウム講演論文集  A1-4  2009/11  [Not refereed][Not invited]
  
• 重み付き最小二乗法によるGCDブラインドデコンボリューションの耐雑音性能の向上に関する一考察

  東克憲, 田中章 宮腰政明  第24回SIPシンポジウム講演論文集  A3-1  2009/11  [Not refereed][Not invited]
  
• 再生核ヒルベルト空間における標本化定理」

  田中章, 今井英幸, 宮腰政明  第24回SIPシンポジウム講演論文集  A1-2  2009/11  [Not refereed][Not invited]
  
• I-088 On The Optimal Number of Eigenvectors in Eigenspace-BPLP

  Akahira Hiroki, Tanaka Akira, Miyakoshi Masaaki  情報科学技術フォーラム講演論文集  7-  (3)  387  -388  2008/08/20
• 解析型二次統計量ICAとkurtosisに基づく学習区間判定を用いた高次統計量ICAの高速化

  藤原裕樹, 高橋祐, 宮部滋樹, 猿渡洋, 鹿野清宏, 田中章  電子情報通信学会技術研究報告, 応用音響  108-  (68)  53  -58  2008/05  [Not refereed][Not invited]
  
• A-4-35 A Relationship between Unitary Matrices for Signal Processing and Symmetric Groups

  Onodera Kei, Miyakoshi Masaaki, Tanaka Akira, Kawaguchi Mayuka F.  Proceedings of the IEICE General Conference  2008-  125  -125  2008/03/05
• A Study on Video Compression Using Redundant Wavelet Transform and Iterative Projection-Based Noise Shaping

  大茂 洋岳, 田中 章, 河口 万由香  ファジィシステムシンポジウム講演論文集  22-  43  -46  2006/09/06
• Another Interpretation of the Parametric Partial Projection Filter Based on the General Solution of Linear Constraints and Its Application to Restoration with Affine Constraints

  IEICE Transactions A  J89-A-  (8)  679  -681  2006  [Not refereed][Not invited]
  
• G-016 Consideration concerning decision method of stereo stage control parameter

  Take Shintaro, Tanaka Akira, Kawaguchi Mayuka F., Miyakoshi Masaaki  情報科学技術フォーラム一般講演論文集  4-  (2)  297  -298  2005/08/22
• G-010 Improvement of Digital Watermarks for Audio Signal Based on Psychoacoustic Masking Model

  Uemura Masaru, Tanaka Akira, Kawaguchi Mayuka F., Miyakoshi Masaaki  情報科学技術フォーラム一般講演論文集  4-  (2)  285  -286  2005/08/22
• J-054 Non-Linear Image Restoration by Volterra Series Considering Additive Noise

  Kimoto Tatsuya, Tanaka Akira, Kawaguchi Mayuka F., Miyakoshi Masaaki  情報科学技術フォーラム一般講演論文集  4-  (3)  303  -306  2005/08/22
• J-052 A Study on Image Denoising Using Undecimated Directional Wavelet Transform

  Ohshige Hirotake, Tanaka Akira, Kawaguchi Mayuka F., Miyakoshi Masaaki  情報科学技術フォーラム一般講演論文集  4-  (3)  299  -300  2005/08/22
• A-021 A Consideration on the Falk-Soland Branch-and-Bound Method for Concave Minimization Problems

  Saito Keiichi, Shi Jianming, Tanaka Akira, Kawaguchi Mayuka, Miyakoshi Masaaki  情報科学技術フォーラム一般講演論文集  4-  (1)  51  -52  2005/08/22
• I-070 A Consideration on Object Tracking based on Spatial-Temporal Features

  Takeda Yoshifumi, Tanaka Akira, Kawaguchi Mayuka F., Miyakoshi Masaaki  情報科学技術フォーラム一般講演論文集  4-  (3)  165  -167  2005/08/22
• D-022 Detection of Blood Vesssels by Undecimated Wavelet Transform

  Ohmori Yasuhiro, Suzuki Shigehito, Kuwamura Susumu, Tanaka Akira, Kawaguchi Mayuka, Miyakoshi Masaaki  FIT2005第4回情報科学技術フォーラム, 2005  49  -50  2005
• 線型画像復元問題における定式化と解に関する一考察

  田中章, 今井英幸, 宮腰政明  第18回DSPシンポジウム講演論文集  D1-1  2003/11  [Not refereed][Not invited]
  
• 共役勾配法によるブロック適応フィルタを用いた ANC システム

  藤沢勇希, 田中章, 河口万由香, 宮腰政明  第18回DSPシンポジウム講演論文集  B5-4  2003/11  [Not refereed][Not invited]
  
• 自己回帰・カオス合成モデルによる時系列予測

  安居吉典, 河口万由香, 田中章, 宮腰政明  電子情報通信学会技術研究報告, 非線形問題  102-  (625)  55  -60  2003/02  [Not refereed][Not invited]
  
• On Duality of Constrained Least-Squares Restoration and Parametric Wiener Restoration

  田中章, 今井英幸, 宮腰政明  第17回DSPシンポジウム講演論文集  A2-1  2002/11  [Not refereed][Not invited]
  
• 線形最適画像復元フィルタに関する一考察

  田中章, 今井英幸, 宮腰政明  第16回DSPシンポジウム講演論文集  53  -58  2001/11  [Not refereed][Not invited]
  
• 重み付きヒルベルト空間上でのパラメトリック射影フィルタ族の構成

  田中章, 今井英幸, 宮腰政明  第15回DSPシンポジウム講演論文集  581  -586  2000/11  [Not refereed][Not invited]
  
• パラメトリック射影フィルタ族の正則化に関する一考察

  田中章, 今井英幸, 宮腰政明  第14回DSPシンポジウム講演論文集  210  -206  1999/11  [Not refereed][Not invited]
  
• 多重解像度解析におけるスケール間関係を利用した自然画像の復元

  田中章, 今井英幸, 宮腰政明  第13回DSPシンポジウム講演論文集  141  -145  1998/11  [Not refereed][Not invited]
  
• Evaluation of optimum image restoration filters by perturbation of a degradation operator

  Hideyuki Imai, Akira Tanaka, Masaaki Miyakoshi  Systems and Computers in Japan  28-  (8)  25  -32  1997  [Not refereed][Not invited]
   

  The image restoration problem may be considered in the framework of Hilbert space. In such a framework, the optimal restoration filter is made of a degradation operator and a covariance operator of noise. In practice, the degradation operator is determined by experimental knowledge. Unfortunately, it happens that such a degradation operator differs from the true one. Thus, the discrepancy between these operators has essential effects on the restored image. In this paper, confining ourselves to a real-valued finite-dimensional space, we present a method of evaluating how the optimal restoration filter is affected by perturbation of a degradation operator. Some numerical examples follow to confirm that our description is valid. © 1997 Scripta Technica, Inc.
• A Method for Image Enlargement Using Multiresolution Analysis

  TANAKA Akira, IMAI Hideyuki, MIYAKOSHI Masaaki, DA-TE Tsutomu  Proceedings of the IEICE General Conference  1995-  (2)  57  -57  1995/03/27  

  Mallatにより提案された多重解像度解析は,2乗可積分関数空間を解像度の異なる部分空間列により表現する.各部分空間は一つ解像度の低い部分空間と,その直交補空間の直和として表現され,Mallatはこれを直交ウェーブレットとスケール関数を用いて記述した.本研究は,この多重解像度解析により得られた各系列の相関に着目し,画像の拡大に応用する試みである.

Presentations

• 一般標本化定理における最良近似関数の誤差解析  [Not invited]

  田中章, 宮腰政明

  日本音響学会2010年秋季研究発表会  2010/09
• 再生核ヒルベルト空間に対する標本化定理  [Not invited]

  田中章, 今井英幸, 宮腰政明

  日本音響学会2010年春季研究発表会  2010/03
• 一般標本化定理における最適再生核の数理  [Not invited]

  田中章, 宮腰政明

  日本音響学会2009年春季研究発表会  2009/03
• 相関行列差分に基づく Noisy BSS の有効性に関する一検証  [Not invited]

  今井雄基, 田中章, 宮腰政明

  日本音響学会2008年秋季研究発表会  2008/09
• 等方的雑音共分散行列の対称分解に基づくブラインド無相関化の検討  [Not invited]

  田中和樹, 田中章, 宮腰政明, 小野順貴

  日本音響学会2008年秋季研究発表会  2008/09
• 主成分分析による雑音抑制を用いたGCDに基づくブラインドデコンボリューション  [Not invited]

  東克憲, 田中章, 宮腰政明

  日本音響学会2008年秋季研究発表会  2008/09
• 解析型ICA とkurtosis を利用した音源分離フィルタ学習区間判定における相関行列の選択  [Not invited]

  藤原裕樹, 高橋祐, 宮部滋樹, 猿渡洋, 鹿野清宏, 田中章

  日本音響学会2008年秋季研究発表会  2008/09
• 固有空間BPLP法における固有空間の最適次元について  [Not invited]

  赤平浩規, 田中章, 宮腰政明

  第7回情報科学技術フォーラム  2008/09
• 信号処理に用いられるユニタリ行列と対称群の関係」  [Not invited]

  小野寺慶, 宮腰政明, 田中章, 河口万由香

  電子情報通信学会2008年総合大会  2008/03
• Closed-form 二次統計量ICA と狭帯域 kurtosis を用いたnonclosed-form 高次統計量ICA の学習区間判定  [Not invited]

  藤原裕樹, 高橋祐, 宮部滋樹, 猿渡洋, 鹿野清宏, 田中章

  日本音響学会2008年春季研究発表会  2008/03
• Closed-form 2 次統計量 ICA を利用した確率密度関数推定による nonclosed-form 高次統計量 ICA の高速化  [Not invited]

  橘健太郎, 高橋祐, Even Jani, 森康充, 猿渡洋, 鹿野清宏, 田中章

  日本音響学会2008年春季研究発表会  2008/03
• Closed-form 2 次統計量 ICA と nonclosed-form 高次統計量 ICA を併用した高速ブラインド音源分離の性能評価  [Not invited]

  橘健太郎, 猿渡洋, 森康充, 宮部滋樹, 鹿野清宏, 田中章

  日本音響学会2007年秋季研究発表会  2007/09
• 相関行列差分の同時対角化に基づく Noisy BSS  [Not invited]

  田中章, 宮腰政明

  日本音響学会2007年秋季研究発表会  2007/09
• 相関行列選択に基づく二次統計量 BSS の数理的性質  [Not invited]

  三佐川祐輔, 田中章, 宮腰政明

  日本音響学会2007年秋季研究発表会  2007/09
• Closed-form2 次統計量ICA とnonclosed-form 高次統計量ICA を併用した高速ブラインド音源分離  [Not invited]

  橘健太郎, 猿渡洋, 森康充, 宮部滋樹, 鹿野清宏, 田中章

  日本音響学会2007年春季研究発表会  2007/03
• 二次統計量に基づくBSSにおける相関行列選択  [Not invited]

  田中章, 今井英幸, 宮腰政明

  日本音響学会2007年春季研究発表会  2007/03
• 冗長ウェーブレット変換と射影に基づくノイズシェイピングを用いた動画像圧縮に関する一考察  [Not invited]

  大茂洋岳, 田中章, 河口万由香, 宮腰政明

  第22回ファジィシステムシンポジウム  2006/09
• 二次統計量に基づくBSSのための定常雑音分散推定に関する一考察  [Not invited]

  田中章, 今井英幸, 宮腰政明

  日本音響学会2006年秋季研究発表会  2006/09
• D.O.A.推定における信号・雑音部分空間の数理  [Not invited]

  田中章, 今井英幸, 宮腰政明

  日本音響学会2006年春季研究発表会  2006/03
• 雑音を考慮した Volterra 級数による非線形画像復元  [Not invited]

  木本達也, 田中章, 河口万由香, 宮腰政明

  第4回情報科学技術フォーラム  2005/09
• 冗長なウェーブレット変換を用いた静止画像の雑音除去に関する一考察  [Not invited]

  大茂洋岳, 田中章, 河口万由香, 宮腰政明

  第4回情報科学技術フォーラム,  2005/09
• 時空間特徴を利用した移動物体追跡に関する一考察  [Not invited]

  武田吉史, 田中章, 河口万由香, 宮腰政明

  第4回情報科学技術フォーラム  2005/09
• 凹最小化問題に対する Falk-Soland の分岐限定法に関する一考察  [Not invited]

  斉藤恵一, 施建明, 田中章, 河口万由香, 宮腰政明

  第4回情報科学技術フォーラム  2005/09
• ステレオステージ制御パラメータの決定法に関する考察  [Not invited]

  武晋太郎, 田中章, 河口万由香, 宮腰政明

  第4回情報科学技術フォーラム  2005/09
• 冗長ウェーブレット変換を利用した血管検出  [Not invited]

  大森康宏, 鈴木茂人, 桑村進, 宮腰政明, 河口万由香, 田中章

  第4回情報科学技術フォーラム  2005/09
• 心理音響モデルを用いたオーディオ電子透かし法の改良  [Not invited]

  植村優, 田中章, 河口万由香, 宮腰政明

  第4回情報科学技術フォーラム  2005/09
• 二次統計量に基づくBSSにおける解の解析的表現  [Not invited]

  田中章, 今井英幸, 宮腰政明

  日本音響学会2005年秋季研究発表会  2005/09
• 特異共分散構造を有する雑音環境下における信号・雑音部分空間の特定  [Not invited]

  田中章, 外山淳, 宮腰政明

  日本音響学会2004年秋季研究発表会  2004/09
• 選別した時間領域基底を用いた単一チャネル音源分離  [Not invited]

  門脇亮太, 田中章, 河口万由香, 宮腰政明

  情報処理北海道シンポジウム2004  2004/05
• チェロ奏法におけるビブラート速度と音色評価の評定尺度法による解析  [Not invited]

  木敦之, 田中章, 河口万由香, 宮腰政明

  情報処理北海道シンポジウム2004  2004/05
• Bark尺度に適合したウェーブレット・パケット帯域分割に基づく音響信号圧縮  [Not invited]

  大橋亮, 田中章, 河口万由香, 宮腰政明

  情報処理北海道シンポジウム2004  2004/05
• 並列構成二重くし型フィルタを用いた音程修復  [Not invited]

  小峰規行, 田中章, 河口万由香, 宮腰政明

  情報処理北海道シンポジウム2004  2004/05
• Undecimated ウェーブレット変換と Directional Filter Bank による画像の雑音除去  [Not invited]

  大茂洋岳, 田中章, 河口万由香, 宮腰政明

  情報処理北海道シンポジウム2004  2004/05
• 混合信号ヒストグラムによる適応分布推定に基づく独立成分分析  [Not invited]

  斉藤優樹, 田中章, 宮腰政明

  日本音響学会2003年秋期研究発表会  2003/09
• 混合信号分布の局所近似を用いた独立成分分析  [Not invited]

  斉藤優樹, 田中章, 河口万由香, 宮腰政明

  情報処理北海道シンポジウム2003  2003/04
• 仮想誤差法を用いた ANC システムの計算量低減  [Not invited]

  藤沢勇希, 田中章, 河口万由香, 宮腰政明

  情報処理北海道シンポジウム2003  2003/04
• 多チャンネル音場制御における正則化係数の選択  [Not invited]

  大谷尚之, 田中章, 河口万由香, 宮腰政明

  情報処理北海道シンポジウム2003  2003/04
• 独立性指標を用いた Blind-MINT法の受音点配置制限の緩和  [Not invited]

  川尻崇文, 田中章, 河口万由香, 宮腰政明

  情報処理北海道シンポジウム2003  2003/04
• The Role of Small Irrationarity in Communication and Strategic Decisions: An Example with the Electronic Mail Game  [Not invited]

  K. Takamiya, A. Tanaka

  Taj-IBM Conference on Game Theory & its Applications (Game Theory-2003)  2003/01
• 時系列予測における自己回帰・カオス混合モデル  [Not invited]

  安居吉典, 河口万由香, 田中章, 宮腰政明

  平成14年度電気関係学会北海道支部連合大会  2002/10
• 周波数成分の重なりを用いた音源同定における適応処理の改善  [Not invited]

  土田慎也, 田中章, 宮腰政明

  情報処理北海道シンポジウム2002  2002/04
• Blind-MINT法における受音点配置制限の緩和  [Not invited]

  川尻崇文, 田中章, 宮腰政明

  情報処理北海道シンポジウム2002  2002/04
• 混合信号分布推定に基づく学習則を用いた独立成分分析  [Not invited]

  斉藤優樹, 田中章, 宮腰政明

  情報処理北海道シンポジウム2002  2002/04
• ノイズの影響を考慮した多チャンネル音場制御システム  [Not invited]

  大谷尚之, 田中章, 宮腰政明

  情報処理北海道シンポジウム2002  2002/04
• 2次経路の推定を用いたアクティブノイズコントロールシステム  [Not invited]

  藤沢勇希, 田中章, 宮腰政明

  情報処理北海道シンポジウム2002  2002/04
• ウェーブレット変換係数の特性を利用した自然画像の復元  [Not invited]

  田中章, 今井英幸, 宮腰政明

  情報処理北海道シンポジウム'98,  1998/05
• 非線形エルゴード定理の画像復元への適用  [Not invited]

  中田靖久, 田中章, 今井英幸, 河口万由香, 宮腰政明

  情報処理北海道シンポジウム'96  1996/04
• 多重解像度解析を用いたディジタル画像拡大手法の有効性に関する一検証  [Not invited]

  田中章, 今井英幸, 宮腰政明

  平成7年度電気関係学会北海道支部連合大会  1995/10
• 多重解像度解析を用いた画像の拡大  [Not invited]

  田中章, 今井英幸, 宮腰政明, 伊達惇

  1995年電子情報通信学会総合大会  1995/03
• コンピュータグラフィックスを用いた４次元空間上物体の可視化技法について  [Not invited]

  田中章, 今井英幸, 宮腰政明, 伊達惇

  情報処理北海道シンポジウム'94  1994/04

Association Memberships

• IEEE   日本音響学会   電子情報通信学会   ASJ   IEICE   IEEE   

Research Projects

• 機械学習のための再生核の生成と選択

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

  Date (from‐to) : 2020/04 -2025/03 

  Author : 田中 章

   

  今年度の主要な研究成果は以下の三点である。 1) 再生核ヒルベルト空間論を用いる機械学習法において、従来の交叉検証法のような枠組みとは全く異なる新しいモデル選択手法を開発した。具体的には、本来未知である汎化誤差を近似的に推定し、当該近似値を最小化する手法を構成することに成功した。当該手法により、交叉検証法が主に対象とする内挿問題だけでなく、これまで扱いが難しいとされてきた外挿問題におけるモデル選択も可能となった。当該成果は、国際会議にて発表済である。 2) カーネルリッジ回帰は、統計的線形推定子と等価であることが広く知られている。一方、統計的線形推定子の拡張である統計的アフィン推定子に対応するカーネル回帰問題の定式化はこれまで明らかになっていなかった。今年度、この問題に対して理論的に肯定的な結論を得た。すなわち、統計的アフィン推定子と等価となるようなカーネル回帰問題の定式化を明らかにした。この成果により、再生核ヒルベルト空間論に基づく機械学習法において、表現し得る問題のクラスを広げることに成功したと言える。当該成果は、学術論文として公表済である。 3) 本研究課題の最も重要な論点の一つである、広範な再生核の族の生成に関して、実用に繋がる重要な理論的成果を得た。具体的には、歪対称行列のケーリー変換によって、全ての正規直交基底の同値類の代表元を生成できることを理論的に明らかにした。この成果により、再生核の族の生成の根幹をなす二次形式を構成する非負定値対称行列を、歪対称行列と固有値に対応するパラメーターによって完全にパラメトライズが可能であることが明らかになった。当該成果は、学術論文誌に投稿中である。
• マルチカーネル学習の新展開

  Date (from‐to) : 2016 -2018 

  Author : 田中 章
• 再生核ヒルベルト空間における標本化定理の数理

  Date (from‐to) : 2012 -2014 

  Author : 田中 章
• A New Direction in Market Design: Studies on Non-two-sided Matchings

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research

  Date (from‐to) : 2011 -2013 

  Author : TAKAMIYA Koji, TANAKA Akira

   

  Applications of matching theory to mechanism design have recently brought significant improvements to real-life institutions for resource allocation. But these applications are mostly based on a specific class of matching models. Aiming at expanding the applicability of matching mechanisms, our research analyzed, with the aid of computer simulation, some classes of matching models which had not been much considered in application. We have obtained some theoretical results; one of our results has made more flexible certain preceding conditions for truthful revelation of preferences in matching mechanisms.
• Classification of large scale qualitative data and visualization of their structure.

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research

  Date (from‐to) : 2011 -2013 

  Author : IMAI Hideyuki, KUDO Mineichi, TANAKA Akira

   

  To perform knowledge discovery from large data sets as signals from various sensors or texts accumulated in the web, it is required to classify into groups which have some common attribute as a pretreatment for detailed analysis even for such large and irregular data sets. Though such data sets contain a large number of items, it is often sufficient to use a small number of items for reasonable classification. We have studied mainly variable selection and regularization method for classification of qualitative data both from theoretical analysis and numerical experiments. These results have applied to the system for estimating human behavior using the data from the infrared sensors placed in the ceiling of the room.
• 標本化と最適再生核の数理

  Date (from‐to) : 2009 -2011 

  Author : 田中 章
• 再生核ヒルベルト空間と機械学習の数理

  Date (from‐to) : 2006 -2008 

  Author : 田中 章
• Clifford代数を用いた画像処理・復元に関する基礎的研究

  Date (from‐to) : 2005 -2007 

  Author : 宮腰 政明
• Sampling theory based on reproducing kernel Hilbert spaces

  Date (from‐to) : 2006
• 線形系逆問題の定式化と解の数理

  Date (from‐to) : 2004 -2005 

  Author : 田中 章
• 情報通信インターフェースとしてユビキタスパターン認識

  Date (from‐to) : 2003 -2005 

  Author : 工藤 峰一
• 大規模パターン認識問題に対する識別系の開発と応用

  Date (from‐to) : 2002 -2005 

  Author : 工藤 峰一
• Reproducing kernel Hilbert space for machine learning

  Date (from‐to) : 2003
• Mathematical properties of "Blind Source Separtion"

  Date (from‐to) : 2003
• 正則化パラメトリック射影フィルタ族の構築に関する研究

  Date (from‐to) : 2001 -2002 

  Author : 宮腰 政明
• 人間の視覚特性を考慮した画像復元手法の開発

  Date (from‐to) : 2001 -2002 

  Author : 田中 章
• Image restoration

  Date (from‐to) : 2000

Industrial Property Rights

• 特許第4660773号:信号到来方向推定装置、信号到来方向推定方法、および信号到来方向推定用プログラム  

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