arXiv subjects

Wataru Yata

Publications and source records attributed to Wataru Yata.

5 recordsLinked to original sources

arXiv2025

Linearly involved Generalized Moreau Enhanced Model with Non-quadratic Smooth Convex Data Fidelity Functions

In this paper, we introduce an overall convex model incorporating a nonconvex regularizer. The proposed model is designed by extending the least squares term in the constrained LiGME model [Yata Yamagishi Yamada 2022] to fairly general smooth convex functions for flexible utilization of non-quadratic data fidelity functions. Under an overall convexity condition for the proposed model, we present sufficient conditions for the existence of a minimizer of the proposed model and an inner-loop free algorithm with guaranteed convergence to a global minimizer of the proposed model. To demonstrate the effectiveness of the proposed model and algorithm, we conduct numerical experiments in scenarios of Poisson denoising problem and simultaneous declipping and denoising problem.

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arXiv2025

A convexity preserving nonconvex regularization for inverse problems under non-Gaussian noise

We propose a nonconvexly regularized convex model for linear regression problems under non-Gaussian noise. The cost function of the proposed model is designed with a possibly non-quadratic data fidelity term and a nonconvex regularizer via the generalized Moreau enhancement of a seed convex regularizer. We present sufficient conditions (i) for the cost function of the proposed model to be convex over the entire space, and (ii) for the existence of a minimizer of the proposed model. Under such conditions, we propose a proximal splitting type algorithm with guaranteed convergence to a global minimizer of the proposed model. As an application, we enhance nonconvexly a convex sparsity-promoting regularizer in a scenario of simultaneous declipping and denoising.

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arXiv2025

An LiGME Regularizer of Designated Isolated Minimizers -- An Application to Discrete-Valued Signal Estimation

For a regularized least squares estimation of discrete-valued signals, we propose a Linearly involved Generalized Moreau Enhanced (LiGME) regularizer, as a nonconvex regularizer, of designated isolated minimizers. The proposed regularizer is designed as a Generalized Moreau Enhancement (GME) of the so-called sum-of-absolute-values (SOAV) convex regularizer. Every candidate vector in the discrete-valued set is aimed to be assigned to an isolated local minimizer of the proposed regularizer while the overall convexity of the regularized least squares model is maintained. Moreover, a global minimizer of the proposed model can be approximated iteratively by using a variant of the constrained LiGME (cLiGME) algorithm. To enhance the accuracy of the proposed estimation, we also propose a pair of simple modifications, called respectively an iterative reweighting and a generalized superiorization. Numerical experiments demonstrate the effectiveness of the proposed model and algorithms in a scenario of multiple-input multiple-output (MIMO) signal detection.

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arXiv2024

Imposing early and asymptotic constraints on LiGME with application to bivariate nonconvex enhancement of fused lasso models

For the constrained LiGME model, a nonconvexly regularized least squares estimation model, we present an iterative algorithm of guaranteed convergence to its globally optimal solution. The proposed algorithm can deal with two different types of constraints simultaneously. The first type constraint, called the asymptotic one, requires the limit of estimation sequence to achieve the corresponding condition. The second type constraint, called the early one, requires every vector in estimation sequence to achieve the condition. We also propose a bivariate nonconvex enhancement of fused lasso models with effective constraint for sparse piecewise constant signal estimations. (This is an improved version of [Yata and Yamada, ICASSP 2024].)

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arXiv2021

A Convexly Constrained LiGME Model and Its Proximal Splitting Algorithm

For the sparsity-rank-aware least squares estimations, the LiGME (Linearly involved Generalized Moreau Enhanced) model was established recently in [Abe, Yamagishi, Yamada, 2020] to use certain nonconvex enhancements of linearly involved convex regularizers without losing their overall convexities. In this paper, for further advancement of the LiGME model by incorporating multiple a priori knowledge as hard convex constraints, we newly propose a convexly constrained LiGME (cLiGME) model. The cLiGME model can utilize multiple convex constraints while preserving benefits achieved by the LiGME model. We also present a proximal splitting type algorithm for the proposed cLiGME model. Numerical experiments demonstrate the efficacy of the proposed model and the proposed optimization algorithm in a scenario of signal processing application.

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