Convergence analysis for support recovery with quasi-Newton hard thresholding-based algorithm

Abstract

In compressed sensing, designing suitable algorithms for recovering sparse signals from an under-determined linear model is one of the important issues. Among these recovery algorithms, hard thresholding-based ones have attracted great attention in recent years. In this work, we propose a novel variant of hard thresholding-based algorithms called the quasi-Newton hard thresholding pursuit (QNHTP) algorithm by adopting the quasi-Newton search direction. We establish sufficient condition for support recovery guarantee in terms of the restricted isometry constant of the sensing matrix. In addition, we present a range of selectable stepsize parameters for applying the QNHTP algorithm to sparsity optimization problems that arise in compressive sensing. We demonstrate that by taking the stepsize parameter with a fixed constant of one, the optimal upper bound of RIC can be achieved.