Heavy-ball-based relaxed optimal s-thresholding algorithms for solving compressed sensing problem

Abstract

This paper focuses on the problem of compressed sensing. By merging heavy-ball acceleration method which is a multi-step extension of the traditional gradient descent method and a new thresholding technique -optimal s-thresholding, we propose two algorithms to solve the compressed sensing problem, which are heavy-ball-based relaxed optimal s-thresholding algorithm (HBROT) and heavy-ball-based relaxed optimal s-thresholding pursuit algorithm (HBROTP). Moreover, we prove that all the above algorithms can accurately recover a s-sparse signal if the restricted isometry constant of the measurement matrix satisfies some conditions.