I. Yamada

Tokyo Institute of Technology, Tokyo, Tokyo-to, Japan

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Publications (153)221.96 Total impact

  • [Show abstract] [Hide abstract]
    ABSTRACT: Using a novel characterization of texture, we propose an image decomposition technique that can effectively decomposes an image into its cartoon and texture components. The characterization rests on our observation that the texture component enjoys a blockwise low-rank nature with possible overlap and shear, because texture, in general, is globally dissimilar but locally well patterned. More specifically, one can observe that any local block of the texture component consists of only a few individual patterns. Based on this premise, we first introduce a new convex prior, named the block nuclear norm (BNN), leading to a suitable characterization of the texture component. We then formulate a cartoon-texture decomposition model as a convex optimization problem, where the simultaneous estimation of the cartoon and texture components from a given image or degraded observation is executed by minimizing the total variation and BNN. In addition, patterns of texture extending in different directions are extracted separately, which is a special feature of the proposed model and of benefit to texture analysis and other applications. Furthermore, the model can handle various types of degradation occurring in image processing, including blur+missing pixels with several types of noise. By rewriting the problem via variable splitting, the so-called alternating direction method of multipliers becomes applicable, resulting in an efficient algorithmic solution to the problem. Numerical examples illustrate that the proposed model is very selective to patterns of texture, which makes it produce better results than state-of-the-art decomposition models.
    IEEE Transactions on Image Processing 03/2014; 23(3):1128-42. · 3.20 Impact Factor
  • Tuan Duong Nguyen, Isao Yamada
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    ABSTRACT: Recently, we presented a first deterministic discrete time (DDT) analysis of the normalized normalized projection approximation subspace tracking (Normalized PAST) algorithms, for estimating principal and minor components of an input signal. The analysis shows that the DDT systems of the Normalized PAST algorithms converge to the desired eigenvectors under certain sufficient conditions on the forgetting factor @b@?(0,1]. However, it has not yet been clarified whether the sufficient conditions can be relaxed or not for guaranteed convergence. In this paper, by characterizing the maximal ranges of the forgetting factor, we establish the necessary and sufficient conditions for convergence of the DDT systems of the Normalized PAST algorithms. The proposed maximal range of the forgetting factor, for the minor component estimation, is doubled from the range assumed in the first DDT analysis, while the proposed maximal range of the forgetting factor, for principal component estimation, achieves the full range (0, 1]. Numerical examples further confirm the results.
    Signal Processing. 01/2014; 94:288-299.
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    ABSTRACT: The contribution of this paper is three-fold: first, we propose a novel scheme for generalized minor subspace extraction by extending an idea of dimension reduction technique. The key of this scheme is the reduction of the problem for extracting the ith (i ≥ 2) minor generalized eigenvector of the original matrix pencil to that for extracting the first minor generalized eigenvector of a matrix pencil of lower dimensionality. The proposed scheme can employ any algorithm capable of estimating the first minor generalized eigenvector. Second, we propose a pair of such iterative algorithms and analyze their convergence properties in the general case where the generalized eigenvalues are not necessarily distinct. Third, by using these algorithms inductively, we present adaptive implementations of the proposed scheme for estimating an orthonormal basis of the generalized minor subspace. Numerical examples show that the proposed adaptive subspace extraction algorithms have better numerical stability than conventional algorithms.
    Multidimensional Systems and Signal Processing 09/2013; 24(3). · 0.86 Impact Factor
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    ABSTRACT: This letter establishes a novel analysis of the Adaptive Projected Subgradient Method (APSM) in the intersection of the stochastic and robust estimation paradigms. Utilizing classical worst-case bounds on the noise process, drawn from the robust estimation methodology, the present study demonstrates that the hyperslab-inspired version of the APSM generates a sequence of estimates which converges to a point located, with probability one, arbitrarily close to the estimand. Numerical tests and comparisons with classical time-adaptive algorithms corroborate the theoretical findings of the study.
    IEEE Signal Processing Letters 07/2013; 20(7):729-732. · 1.67 Impact Factor
  • Source
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    ABSTRACT: The articles in this special issue report on up-to-date advances in the broad area of information processing over graphs. Due to the highly cross-disciplinary nature of complex networks, the technical articles in this April 2013 issue of the IEEE Journal of Selected Topics in Signal Processing are coupled with valuable tutorial articles that appear in a second special issue, organized by the same Guest Editors, and which is published as the May 2013 issue of the IEEE Signal Processing Magazine. The survey articles in the magazine are meant to introduce readers to the main tools and concepts, while the more focused technical articles in J-STSP cover state-of-the-art results. Through this combination of tutorial and technical articles in both journals, readers will become better acquainted with the challenges and opportunities that the broader field of network science has to offer across the domains of information sciences, system science, computer science, social sciences,machine learning, and optimization theory. Complex networks represent a typical paradigm that helps demonstrate well how barriers among seemingly different disciplines are becoming more transparent.
    IEEE Journal of Selected Topics in Signal Processing 04/2013; 7(2):161-162. · 3.30 Impact Factor
  • Tuan Duong Nguyen, Isao Yamada
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    ABSTRACT: The main contributions of this paper are to propose and analyze fast and numerically stable adaptive algorithms for the generalized Hermitian eigenvalue problem (GHEP), which arises in many signal processing applications. First, for given explicit knowledge of a matrix pencil, we formulate two novel deterministic discrete-time (DDT) systems for estimating the generalized eigen-pair (eigenvector and eigenvalue) corresponding to the largest/smallest generalized eigenvalue. By characterizing a generalized eigen-pair as a stationary point of a certain function, the proposed DDT systems can be interpreted as natural combinations of the normalization and quasi-Newton steps for finding the solution. Second, we present adaptive algorithms corresponding to the proposed DDT systems. Moreover, we establish rigorous analysis showing that, for a step size within a certain range, the sequence generated by the DDT systems converges to the orthogonal projection of the initial estimate onto the generalized eigensubspace corresponding to the largest/smallest generalized eigenvalue. Numerical examples demonstrate the practical applicability and efficacy of the proposed adaptive algorithms.
    IEEE Transactions on Signal Processing 03/2013; 61(6):1404-1418. · 2.81 Impact Factor
  • Tomasz Piotrowski, Isao Yamada
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    ABSTRACT: The stochastic MV-PURE estimator has been developed to provide linear estimation robust to ill-conditioning, high noise levels, and imperfections in model knowledge. In this paper, we investigate the theoretical performance of the stochastic MV-PURE estimator under varying level of additive noise. More precisely, we prove that the mean-square-error (MSE) of this estimator in the low signal-to-noise (SNR) region is much smaller than that obtained with its full-rank version, the minimum-variance distortionless estimator, and that the gap in performance is the larger the higher the noise level. These results shed light on the excellent performance of the stochastic MV-PURE estimator in highly noisy settings obtained in simulations so far. We extend here previously conducted numerical simulations to demonstrate a new insight provided by results of this paper in practical applications.
    Journal of the Franklin Institute. 03/2013;
  • S Ono, M Yamagishi, I Yamada
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    ABSTRACT: Observing that sparse systems are almost smooth, we propose to utilize the newly-introduced adaptively-weighted total variation (AWTV) for sparse system identification. In our formulation, a sparse system identification problem is posed as a sequential suppression of a time-varying cost function: the sum of AWTV and a data-fidelity term. In order to handle such a non-differentiable cost function efficiently, we propose a time-varying extension of a primal-dual splitting type algorithm, named the adaptive primal-dual splitting method (APDS). APDS is free from operator inversion or other highly complex operations, resulting in computationally efficient implementation in online manner. Moreover, APDS realizes that the sequence defined in a certain product space monotonically approaches the solution set of the current cost function, i.e., the sequence generated by APDS pursues desired replicas of the unknown system in each time-step. Our scheme is applied to a network echo cancellation problem where it shows excellent performance compared with conventional methods.
    Proc. IEEE ICASSP; 01/2013
  • M. Yamagishi, I. Yamada
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    ABSTRACT: Observing that a typical primary path in Active Noise Control (ANC) system is sparse, i.e., having a few significant coefficients, we propose an adaptive learning which promotes the sparsity of the concatenation of the adaptive filter and the secondary path. More precisely, we propose to suppress a time-varying sum of the data-fidelity term and the weighted ℓ1 norm of the concatenation by the adaptive Douglas-Rachford splitting scheme. Numerical examples demonstrate that the proposed algorithm shows excellent performance of the ANC by exploiting the sparsity and has robustness against a violation of the sparsity assumption.
    Signal and Information Processing Association Annual Summit and Conference (APSIPA), 2013 Asia-Pacific; 01/2013
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    ABSTRACT: We consider the problem of dipole source signals estimation in electroencephalography (EEG) using beamforming techniques in ill-conditioned settings. We take advantage of the link between the linearly constrained minimum-variance (LCMV) beamformer in sensor array processing and the best linear unbiased estimator (BLUE) in linear regression modeling. We show that the recently introduced reduced-rank extension of BLUE, named minimum-variance pseudo-unbiased reduced-rank estimator (MV-PURE), achieves much lower estimation error not only than LCMV beamformer, but also than the previously derived reduced-rank principal components (PC) and cross-spectral metrics (CSM) beamformers in ill-conditioned settings. The practical scenarios where the considered estimation model becomes ill-conditioned are discussed, then we show the applicability of MV-PURE dipole source estimator under those conditions through realistic simulations.
    Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on; 01/2013
  • S Ono, I Yamada
    Proc. of IEEE ICIP; 01/2013
  • S Ono, I Yamada
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    ABSTRACT: This paper proposes a likelihood constrained optimization framework for Poisson image restoration. The likelihood constrained problem considered in this paper is the minimization of convex priors over the level set of the negative-log-likelihood function of the Poisson distribution. It has advantages in parameter selection compared with the minimization of the weighted sum of convex priors and the negative-log-likelihood function, which has been used in conventional methods. The level set is characterized as the fixed point set of a certain quasi-nonexpansive operator, which enables us to apply the hybrid steepest descent method to solve the constrained problem. The proposed framework not only can handle the level set of any convex function whose subgradient is available but also does not require any computationally-expensive procedure such as operator inversion and inner loop. Illustrative numerical examples are also presented.
    Proc. IEEE ICASSP; 01/2013
  • S Ono, I Yamada
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    ABSTRACT: We propose a new convex regularizer, named the local color nuclear norm (LCNN), for color image recovery. The LCNN is designed to promote a property inherent in natural color images - in which their local color distributions often exhibit strong linearity - and is thus expected to reduce color artifact effectively. In addition, the very nature of LCNN allows us to incorporate it into various types of color image recovery formulations, with the associated convex optimization problems solvable using proximal splitting techniques. Applications of LCNN are demonstrated with illustrative numerical examples.
    Proc. of CVPR; 01/2013
  • Tuan Duong Nguyen, Isao Yamada
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    ABSTRACT: We present a unified convergence analysis, based on a deterministic discrete time (DDT) approach, of the normalized projection approximation subspace tracking (Normalized PAST) algorithms for estimating principal and minor components of an input signal. The proposed analysis shows that the DDT system of the Normalized PAST algorithm (for PCA/MCA), with any forgetting factor in a certain range, converges to a desired eigenvector. This eigenvector is completely characterized as the normalized version of the orthogonal projection of the initial estimate onto the eigensubspace corresponding to the largest/smallest eigenvalue of the autocorrelation matrix of the input signal. This characterization holds in general case where the eigenvalues are not necessarily distinct. Numerical examples show that the proposed analysis demonstrates very well the convergence behavior of the Normalized PAST algorithms which uses a rank-1 instantaneous approximation of the autocorrelation matrix.
    Signal Processing. 01/2013; 93(1):176–184.
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    ABSTRACT: The topic of this special issue deals with a subject matter that has been receiving immense attention from various research communities, and not only within the signal processing community. Discusses research and development in the area of the adaption and learning over complex network systems. Extensive research efforts on information processing over graphs exist within other fields such as statistics, computer science, optimization, control, economics, machine learning, biological sciences, and social sciences. Different fields tend to emphasize different aspects and challenges; nevertheless, opportunities for mutual cooperation are abundantly clear, and the role that signal processing plays in this domain is of fundamental importance.
    IEEE Signal Processing Magazine 01/2013; 30(3):14-15. · 3.37 Impact Factor
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    ABSTRACT: In this paper, a novel regularization-parameter design for the adaptive proximal forward-backward splitting algorithm is proposed for sparse system identification. The regularization parameter is controlled adaptively based on sparsity of an estimated unknown system. The regularizer is designed by approximating an !p quasi-norm (0 < p < 1) linearly. Numerical examples show that the proposed algorithm is robust to the variation of the system sparsity.
    Wireless Communication Systems (ISWCS 2013), Proceedings of the Tenth International Symposium on; 01/2013
  • Source
    M Yamagishi, S Ono, I Yamada
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    ABSTRACT: We propose variants of Alternating Direction Method of Multipliers (ADMM) employing simplified updates under additional assumptions. ADMM iteratively solves the minimization of the sum of two nonsmooth convex functions. Each iterations of ADMM itself consists of solving a certain convex optimization problem which often requires the use of some iterative solver. Such inner iterations cause slow convergence. Our proposed algorithms avoid some of inner iterations by employing simplified updates. An efficacy of the proposed algorithm is shown in an image super-resolution problem. In this application, the resultant algorithm does not require matrix inversion which causes inner iterations of the original ADMM. A numerical example in the image super-resolution setting demonstrates that our proposed algorithms reduce CPU time to about 70-80 percent of the original ADMM.
    Proc. of IEEE ICASSP; 01/2012
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    ABSTRACT: We propose a novel sparsity-aware adaptive filtering algorithm based on iterative use of weighted soft-thresholding. The weights are determined based on a rough local approximation of the ℓp norm (0
    Circuits and Systems (ISCAS), 2012 IEEE International Symposium on; 01/2012
  • T. Piotrowski, I. Yamada
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    ABSTRACT: The stochastic MV-PURE estimator is a linear estimator for stochastic linear model that is highly robust to mismatches in model knowledge and which is specially designed for efficient estimation in noisy and ill-conditioned cases. To date, its properties were analyzed in the theoretical settings of perfect model knowledge and thus could not explain clearly the reason behind its superior performance compared to the Wiener filter observed in simulations in practical cases of imperfect model knowledge. In this paper we derive closed form expressions of the mean-square-error (MSE) of both Wiener filter and the stochastic MV-PURE estimator for the case of perturbed singular values of a model matrix in the linear model considered. These expressions provide in particular conditions under which the stochastic MV-PURE estimator achieves smaller MSE not only than Wiener filter, but also than its full-rank version, the minimum-variance distortionless (MVDR) estimator in such settings. We provide numerical simulations confirming the main theoretical results presented.
    Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE International Conference on; 01/2012
  • Hideaki Iiduka, Isao Yamada
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    ABSTRACT: We discuss a stochastic linear-quadratic control problem in which a stochastic algebraic Riccati equation derived from the problem is unsolvable. The Riccati equation has no solution when the state and control weighting matrices in the objective function of the problem are indefinite, and the conventional methods cannot solve the problem when the Riccati equation itself is unsolvable. We first show that the optimal value of the problem is finite. Next, we formulate a compromise solution to the stochastic algebraic Riccati equation and show that the problem can be solved via this compromise solution under certain assumptions. Moreover, we propose a novel computational method for finding the compromise solution based on iterative techniques for a convex optimization problem over the fixed-point set of a certain nonexpansive mapping. Numerical examples demonstrate the effectiveness of this method.
    SIAM Journal on Control and Optimization 01/2012; 50(4). · 1.38 Impact Factor

Publication Stats

940 Citations
221.96 Total Impact Points

Institutions

  • 1991–2013
    • Tokyo Institute of Technology
      • • Department of Communications and Integrated Sytems
      • • Electrical and Electronic Engineering Department
      Tokyo, Tokyo-to, Japan
  • 2011
    • Fraunhofer Heinrich-Hertz-Institute HHI
      Berlín, Berlin, Germany
  • 2007–2011
    • Athens State University
      Athens, Alabama, United States
  • 2008–2010
    • University of Peloponnese
      • Department of Telecommunications Science and Technology
      Trípolis, Peloponnisos, Greece
  • 2007–2010
    • RIKEN
      • Laboratory for Mathematical Neuroscience
      Wako, Saitama-ken, Japan
  • 2009
    • The University of Edinburgh
      • Institute for Digital Communications (IDCoM)
      Edinburgh, SCT, United Kingdom
  • 2006
    • Nagoya University
      • Department of Electrical Engineering and Computer Science
      Nagoya-shi, Aichi-ken, Japan