Variable step size stagewise adaptive matching pursuit algorithm for image compressed sensing

Compressed sensing is a widely used framework for signal reconstruction. In order to handle some practical cases in which the sparsity level is unknown, we present an improved sparsity adaptive matching pursuit (SAMP) algorithm, named variable step size stagewise adaptive matching pursuit (VSStAMP) algorithm. The proposed algorithm alternatively estimates the sparsity level and the support set of signal stage by stage. The attractive characteristic is that VSStAMP can adaptively choose the best matched estimated sparsity level by using different step sizes in different stages. The simulation results show that the stagewise adaptive matching pursuit algorithm with variable step size is feasible with higher reconstruction performance comparable with other matching pursuit algorithms.

I. Introduction

Over the past few years, a new sampling framework called compressed sensing (CS) has emerged. It provides us with a sub-Nyquist [1] sampling scheme to acquire the compressed signals directly. CS has been widely used in image reconstruction/acquisition [2]–[4]. The framework of compressed sensing is described as follows.