Newton-Direction-Based ReLU-Thresholding Methods for Nonnegative Sparse Signal Recovery
Signal Processing
2026-02-19 v1 Information Theory
math.IT
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.
Cite
@article{arxiv.2602.15880,
title = {Newton-Direction-Based ReLU-Thresholding Methods for Nonnegative Sparse Signal Recovery},
author = {Ning Bian and Zhong-Feng Sun and Yun-Bin Zhao and Jin-Chuan Zhou and Nan Meng},
journal= {arXiv preprint arXiv:2602.15880},
year = {2026}
}