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arXiv · 2502.15529

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

Aqin Xiao·Xiangyu Gao·Jun-Feng Yin
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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.

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Aqin Xiao, Xiangyu Gao, Jun-Feng Yin. 2025-02-21. A fast block nonlinear Bregman-Kaczmarz method with averaging for nonlinear sparse signal recovery. https://arxiv.org/abs/2502.15529

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