A Sparsity Adaptive Compressive Sampling Matching Pursuit Algorithm

Abstract

In the area of compressed sensing (CS), the compressive sampling matching pursuit (CoSaMP) algorithm offers a theoretical reconstruction guarantee in noise environment by exploiting a backtracking framework. But it relies on the sparsity of signal. With a stage by stage reconstruction structure, the sparsity adaptive matching pursuit (SAMP) algorithm can reconstruct signals when the sparsity is unknown. By taking both advantages of CoSaMP and SAMP, we propose a greedy algorithm for reconstruction of sparse signals, called the sparsity adaptive compressive sampling matching pursuit (SACoSaMP). The proposed algorithm can reconstruct signals without prior information of sparsity, and it is robust to noise. In this paper, we give a residual upper bound of the proposed SACoSaMP algorithm, and demonstrate the performance of it through simulation experiments.