A fast block nonlinear Bregman-Kaczmarz method with averaging for nonlinear sparse signal recovery

TL;DR

This paper introduces a fast, convergent block nonlinear Bregman-Kaczmarz method with averaging for efficient nonlinear sparse signal recovery, outperforming existing methods in convergence speed.

Contribution

It proposes a novel averaging block nonlinear Bregman-Kaczmarz algorithm with proven convergence for nonlinear sparse signal recovery.

Findings

Converges faster than existing nonlinear Bregman-Kaczmarz methods.

Works with both constant and adaptive stepsizes.

Effective in practical applications like compressive sensing and image reconstruction.

Abstract

Recovery of a sparse signal from a nonlinear system arises in many practical applications including compressive sensing, image reconstruction and machine learning. In this paper, a fast block nonlinear Bregman-Kaczmarz method with averaging is presented for nonlinear sparse signal recovery problems. Theoretical analysis proves that the averaging block nonlinear Bregman-Kaczmarz method with both constant stepsizes and adaptive stepsizes are convergent. Numerical experiments demonstrate the effectiveness of the averaging block nonlinear Bregman-Kaczmarz method, which converges faster than the existing nonlinear Bregman-Kaczmarz methods.