On a stochastic column-block bregman method for nonlinear systems

TL;DR

This paper introduces a stochastic column-block nonlinear Bregman method designed to efficiently find sparse solutions to nonlinear systems, with proven convergence properties and demonstrated effectiveness in image recovery tasks.

Contribution

The paper presents a novel stochastic column-block nonlinear Bregman algorithm with convergence analysis for sparse nonlinear system solutions.

Findings

Convergence of the proposed method is established under certain assumptions.

The method demonstrates efficiency in numerical experiments, including image recovery.

An upper bound for the convergence rate is derived.

Abstract

Sparse solution problems play an important role in both signal processing and image restoration. In this paper, we propose a stochastic column-block nonlinear Bregman method for efficiently computing sparse solutions to nonlinear systems. Under certain assumptions, we analyze the convergence of the proposed method and derive an upper bound for its convergence rate. Numerical experiments, including an image recovery problem, are presented to illustrate the efficiency of the proposed method.