Isao Yamada

Tokyo Institute of Technology, Edo, Tōkyō, Japan

Are you Isao Yamada?

Claim your profile

Publications (194)288.06 Total impact

  • Shunsuke Ono · Isao Yamada
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper proposes an optimization framework that can efficiently deal with convex data-fidelity constraints onto which the metric projections are difficult to compute. Although such an involved data-fidelity constraint is expected to play an important role in signal recovery under non-Gaussian noise contamination, the said difficulty precludes existing algorithms from solving convex optimization problems with the constraint. To resolve this dilemma, we introduce a fixed point set characterization of involved data-fidelity constraints based on a certain computable quasi-nonexpansive mapping. This characterization enables us to mobilize the hybrid steepest descent method to solve convex optimization problems with such a constraint. The proposed framework can handle a variety of involved data-fidelity constraints in a unified manner, without geometric approximation to them. In addition, it requires no computationally expensive procedure such as operator inversion and inner loop. As applications of the proposed framework, we provide image restoration under several types of non-Gaussian noise contamination with illustrative examples.
    No preview · Article · Nov 2015 · IEEE Transactions on Signal Processing
  • Shintaro Ono · Isao Yamada
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper addresses the selection of a desirable solution among all the solutions of a convex optimization problem (referred to as the first-stage problem) mainly for inverse problems in signal processing. This is realized in the framework of hierarchical convex optimization, i.e., minimizing another convex function over the solution set of the first-stage problem. Hierarchical convex optimization is an ideal strategy when the first-stage problem has infinitely many solutions because of the non-strict convexity of its objective function, which could arise in various scenarios, e.g., convex feasibility problems. To this end, first, the fixed point set characterization behind a primal-dual splitting type method is incorporated into the framework of hierarchical convex optimization, which enables the framework to cover a broad class of first-stage problem formulations. Then, a pair of efficient algorithmic solutions to the hierarchical convex optimization problem, as certain realizations of the hybrid steepest descent method, are provided with guaranteed convergence. We also present a specialized form of the proposed framework to focus on a typical scenario of inverse problems, and show its application to signal interpolation.
    No preview · Article · Jan 2015 · IEEE Transactions on Signal Processing
  • Wemer M. Wee · Isao Yamada
    [Show abstract] [Hide abstract]
    ABSTRACT: We consider a unified approach to the tracking analysis of adaptive filters with error and matrix data nonlinearities. Using energyconservation arguments, we not only derive earlier results in a unified manner, but we also obtain new performance results for more general adaptive algorithms without requiring the restriction of the regression data to a particular distribution. Numerical simulations support the theoretical results. Copyright © 2014 The Institute of Electronics, Information and Communication Engineers.
    No preview · Article · Aug 2014 · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
  • [Show abstract] [Hide abstract]
    ABSTRACT: Common Spatial Pattern (CSP) methods are widely used to extract the brain activity for brain machine interfacing (BMI) based on electroencephalogram (EEG). For each mental task, CSP methods estimate a covariance matrix of EEG signals and adopt the uniform average of the sample covariance matrices over trials. However, the uniform average is sensitive to outliers caused by e.g. unrelated brain activity. In this paper, we propose an improvement of the estimated covariance matrix utilized in CSP methods by reducing the influence of the outliers as well as guaranteeing positive definiteness. More precisely, our estimation is the projection of the uniform average onto the intersection of two convex sets: the first set is a special reduced dimensional subspace which alleviates the influence of the outliers; the second is the positive definite cone. A numerical experiment supports the effectiveness of the proposed technique.
    No preview · Article · Aug 2014
  • Source
    Patrick L. Combettes · Isao Yamada
    [Show abstract] [Hide abstract]
    ABSTRACT: Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward-backward splitting algorithm for finding a zero of the sum of two monotone operators is obtained.
    Preview · Article · Jul 2014 · Journal of Mathematical Analysis and Applications
  • Shunsuke Ono · Isao Yamada
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper proposes a new vectorial total variation prior (VTV) for color images. Different from existing VTVs, our VTV, named the decorrelated vectorial total variation prior (D-VTV), measures the discrete gradients of the luminance component and that of the chrominance one in a separated manner, which significantly reduces undesirable uneven color effects. Moreover, a higher-order generalization of the D-VTV, which we call the decorrelated vectorial total generalized variation prior (D-VTGV), is also developed for avoiding the staircasing effect that accompanies the use of VTVs. A noteworthy property of the D-VT(G)V is that it enables us to efficiently minimize objective functions involving it by a primal-dual splitting method. Experimental results illustrate their utility.
    No preview · Conference Paper · Jun 2014
  • Shunsuke Ono · Isao Yamada
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper proposes to use the Total Generalized Variation (TGV) of second order in a constrained form for image processing, which we call the TGV constraint. The main contribution is twofold: i) we present a general form of convex optimization problems with the TGV constraint, which is, to the best of our knowledge, the first attempt to use TGV as a constraint and covers a wide range of problem formulations sufficient for image processing applications; and ii) a computationally-efficient algorithmic solution to the problem is provided, where we mobilize several recently-developed proximal splitting techniques to handle the complicated structured set, i.e., the TGV constraint. Experimental results illustrate the potential applicability and utility of the TGV constraint.
    No preview · Conference Paper · May 2014
  • Masao Yamagishi · Masahiro Yukawa · Isao Yamada
    [Show abstract] [Hide abstract]
    ABSTRACT: Effective utilization of sparsity of the system to be estimated is a key to achieve excellent adaptive filtering performances. This can be realized by the adaptive proximal forward-backward splitting (APFBS) with carefully chosen parameters. In this paper, we propose a systematic parameter tuning based on a minimization principle of an unbiased MSE estimate. Thanks to the piecewise quadratic structure of the proposed MSE estimate, we can obtain its minimizer with low computational load. A numerical example demonstrates the efficacy of the proposed parameter tuning by its excellent performance over a broader range of SNR than a heuristic parameter tuning of the APFBS.
    No preview · Conference Paper · May 2014
  • Wemer M. Wee · Masao Yamagishi · Isao Yamada
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper is concerned with the mean-square performance of the hyperslab-based adaptive projected subgradient method, a set theoretic estimation tool that has been successfully applied in a wide variety of signal processing tasks. Using energy-conservation arguments, general performance results are derived without restricting the regression data to being Gaussian or white. Numerical simulations are provided to illustrate the theoretical developments.
    No preview · Conference Paper · May 2014
  • Hiroki Kuroda · Masao Yamagishi · Isao Yamada
    [Show abstract] [Hide abstract]
    ABSTRACT: For the nonlinear acoustic echo cancellation, we present an adaptive learning of the saturation effect of the amplifier and the room propagation in terms of the hard-clipping and the FIR system. The conventional learning algorithms are based on a gradient descent method, i.e., rely on local information, which results in a major drawback that the estimation of the hard-clipping is trapped in local minima. In this paper, we solve this drawback by exploiting global information embodied as a set including the desired hard-clipping with high-probability. The proposed adaptive learning of the hard-clipping is designed to track the sets with a projection-based algorithm. In the adaptive learning of the FIR system, we propose the use of the Huber loss function for the robustness against the error in the estimation of the hard-clipping. Numerical examples show that the proposed algorithm is never trapped in the local minima and has an excellent steady-state behavior.
    No preview · Conference Paper · May 2014
  • Daichi Kitahara · Isao Yamada
    [Show abstract] [Hide abstract]
    ABSTRACT: Phase unwrapping is a reconstruction problem of the continuous phase function from its finite wrapped samples. Especially the two-dimensional phase unwrapping has been a common key for estimating many crucial physical information, e.g, the surface topography measured by interferometric synthetic aperture radar. However almost all two-dimensional phase unwrapping algorithms are suffering from either the path dependence or the excess smoothness of the estimated result. In this paper, to guarantee the path independence and the appropriate smoothness of the estimated result, we present a novel algebraic approach by combining the ideas in the algebraic phase unwrapping with techniques for a piecewise polynomial interpolation of two-dimensional finite data sequence.
    No preview · Conference Paper · May 2014
  • [Show abstract] [Hide abstract]
    ABSTRACT: We consider the problem of electroencephalography (EEG) and magnetoencephalography (MEG) source localization using beamforming techniques. Specifically, we propose a reduced-rank extension of the recently derived multi-source activity index (MAI), which itself is an extension of the classical neural activity index to the multi-source case. We show that, for uncorrelated dipole sources and any nonzero rank constraint, the proposed reduced-rank multi-source activity index (RR-MAI) achieves the global maximum when evaluated at the true source positions. Therefore, the RR-MAI can be used to localize multiple sources simultaneously. Furthermore, we propose another version of the RR-MAI which can be seen as a natural generalization of the proposed index to arbitrarily correlated sources. We present a series of numerical simulations showing that the RR-MAI can achieve a more precise source localization than the full-rank MAI in the case when the EEG/MEG forward model becomes ill-conditioned, which in our settings corresponds to the case of closely positioned sources and low signal-to-noise ratio.
    No preview · Conference Paper · May 2014
  • [Show abstract] [Hide abstract]
    ABSTRACT: We propose to detect edges of reflections, which we call the REF-edges, from a single image via convex optimization. Our method is designed based on two observations on reflections: (i) reflections have almost monotone color and (ii) color around REF-edges varies smoothly. The first one can be translated into the property that gradients around REF-edges distribute linearly in the RGB color space, which we call the REF-linearity. The second one can be interpreted as follows: color differences around REF-edges are small; for an entry of REF-edges, gradients among its surrounding entries have small variance. Using the above properties, we characterize REF-edges as a solution of a constrained convex optimization problem. The optimization problem is solved by the Alternating Direction Method of Multipliers (ADMM). Experiments using real-world images with reflections show the utility of our proposed method.
    No preview · Conference Paper · May 2014
  • Shunsuke Ono · Takamichi Miyata · Isao Yamada
    [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.
    No preview · Article · Mar 2014 · IEEE Transactions on Image Processing
  • Takehiko Mizoguchi · Isao Yamada
    [Show abstract] [Hide abstract]
    ABSTRACT: The m-dimensional Cayley-Dickson number system Am is a standard extension of real (m=1), complex (m=2), quaternion (m=22), octonion (m=23) and sedenion (m=24) etc. In this paper, we present a systematic algebraic translation of the Cayley-Dickson hypercomplex valued linear systems into a real vector valued linear model. This translation is designed by using jointly two new isomorphisms between real vector spaces and enables us to straightforwardly apply the well established schemes in real domain to problems for the hypercomplex linear model. We also clarify useful algebraic properties of the proposed translation. As an example of many potential algorithms through the proposed algebraic translation, we present Am-adaptive projected subgradient method ( Am-APSM) for Am valued adaptive system identification, and show that many hypercomplex adaptive filtering algorithms can be viewed as special cases of this algorithm. Moreover, we also apply the Am-APSM to nonlinear adaptive filtering by using the kernel trick. Numerical examples show that the effectiveness of the Am-APSM in many Cayley-Dickson valued linear system identification and nonlinear channel equalization problems.
    No preview · Article · Feb 2014 · IEEE Transactions on Signal Processing
  • Tuan Duong Nguyen · Isao Yamada
    [Show abstract] [Hide abstract]
    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.
    No preview · Article · Jan 2014 · Signal Processing
  • Wemer M. Wee · Isao Yamada
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper presents a unified treatment of the tracking analysis of adaptive filters with data normalization and error nonlinearities. The approach we develop is based on the celebrated energy-conservation framework, which investigates the energy flow through each iteration of an adaptive filter. Aside from deriving earlier results in a unified manner, we obtain new performance results for more general filters without restricting the regression data to a particular distribution. Simulations show good agreement with the theoretical findings.
    No preview · Article · Nov 2013 · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
  • [Show abstract] [Hide abstract]
    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.
    No preview · Conference Paper · Oct 2013
  • Shunsuke Ono · Masao Yamagishi · Isao Yamada
    [Show abstract] [Hide abstract]
    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.
    No preview · Conference Paper · Oct 2013
  • Takehiko Mizoguchi · Isao Yamada
    [Show abstract] [Hide abstract]
    ABSTRACT: The hypercomplex (e.g., complex, quaternion) valued linear model often arises in the signal processing field and attract increasing attention recently. In this paper, we present an algebraic translation of a hypercomplex valued linear systems into a real valued linear model. This translation is designed by taking advantage of isomorphism between hypercomplex numbers and multi-dimensional real vectors and enables us to straightforwardly apply real valued optimization frameworks to various estimation problems for the hypercomplex linear model. We also clarify the useful algebraic properties of the translation. As an application to hypercomplex valued adaptive filtering problems, we derived Am-adaptive projected subgradient method (Am-APSM) for hypercomplex valued system identification problems, and show that many hypercomplex adaptive filtering algorithms can be viewed as a special case of this algorithm. Numerical example shows that a new algorithm derived from proposed algorithm outperforms existing hypercomplex adaptive algorithms.
    No preview · Conference Paper · Oct 2013