Cosamp and SP for the cosparse analysis model

Abstract

CoSaMP and Subspace-Pursuit (SP) are two recovery algorithms that find the sparsest representation for a given signal under a given dictionary in the presence of noise. These two methods were conceived in the context of the synthesis sparse representation modeling. The cosparse analysis model is a recent construction that stands as an interesting alternative to the synthesis approach. This new model characterizes signals by the space they are orthogonal to. Despite the similarity between the two, the cosparse analysis model is markedly different from the synthesis one. In this paper we propose analysis versions of the CoSaMP and the SP algorithms, and demonstrate their performance for the compressed sensing problem.