Review of Sparsity Known and Blind Sparsity Greedy Algorithms for Compressed Sensing

Abstract

Sparsity level is crucial to Compressive Sensing (CS) reconstruction, but in practice it is often unknown. Recently, several blind sparsity greedy algorithms have emerged to recover signals by exploiting the underlying signal characteristics. Sparsity Adaptive Matching Pursuit (SAMP) estimates the sparsity level and the true support set stage by stage, while Backtracking-Based Adaptive OMP (BAOMP) selects atoms by thresholds related to the maximal residual projection. This chapter reviews typical sparsity known greedy algorithms including OMP, StOMP, and CoSaMP, as well as those emerging blind sparsity greedy algorithms. Furthermore, the algorithms are analysed in structured diagrammatic representation and compared by exact reconstruction probabilities for Gaussian and binary signals distributed sparsely.