Newton-Direction-Based ReLU-Thresholding Methods for Nonnegative Sparse Signal Recovery

TL;DR

This paper introduces Newton-Direction-Based ReLU-Thresholding algorithms for nonnegative sparse signal recovery, providing theoretical guarantees and demonstrating competitive performance through numerical experiments.

Contribution

It proposes two novel algorithms combining Newton-type thresholding with ReLU techniques, with theoretical recovery guarantees and empirical validation.

Findings

Guarantee of exact recovery under certain conditions

Competitive performance in noisy and noiseless scenarios

Effective integration of Newton methods with ReLU-based approaches

Abstract

Nonnegative sparse signal recovery has been extensively studied due to its broad applications. Recent work has integrated rectified linear unit (ReLU) techniques to enhance existing recovery algorithms. We merge Newton-type thresholding with ReLU-based approaches to propose two algorithms: Newton-Direction-Based ReLU-Thresholding (NDRT) and its enhanced variant, Newton-Direction-Based ReLU-Thresholding Pursuit (NDRTP). Theoretical analysis iindicates that both algorithms can guarantee exact recovery of nonnegative sparse signals when the measurement matrix satisfies a certain condition.. Numerical experiments demonstrate NDRTP achieves competitive performance compared to several existing methods in both noisy and noiseless scenarios.