Cosparsity-based Stagewise Matching Pursuit algorithm for reconstruction of the cosparse signals

The cosparse analysis model has been introduced as an interesting alternative to the standard sparse synthesis model. Given a set of corrupted measurements, finding a signal belonging to this model is known as analysis pursuit, which is an important problem in analysis model based sparse representation. Several pursuit methods have already been proposed, such as the methods based on l(1)-relaxation and greedy approaches based on the cosparsity of the signal. This paper presents a novel greedy-like algorithm, called Cosparsity-based Stagewise Matching Pursuit (CSMP), where the cosparsity of the target signal is estimated adaptively with a stagewise approach composed of forward and backward processes. In the forward process, the cosparsity is estimated and the signal is approximated, followed by the refinement of the cosparsity and the signal in the backward process. As a result, the target signal can be reconstructed without the prior information of the cosparsity level. Experiments show that the performance of the proposed algorithm is comparable to those of the l1-relaxation and Analysis Subspace Pursuit (ASP)/Analysis Compressive Sampling Matching Pursuit (ACoSaMP) in noiseless case and better than that of Greedy Analysis Pursuit (GAP) in noisy case.