The reweighed greedy analysis pursuit algorithm for the cosparse analysis model

Abstract

Recently, a cosparse analysis model has been introduced as an interesting alternative to the sparse representation synthesis model. This model is focused on zero elements in the analysis representation vector rather than non-zero elements. Hence, finding cosparse solutions is a problem of important significance in signal processing. In this paper, we construct an adaptive weighted matrix in the greedy analysis pursuit algorithm and propose the reweighed greedy analysis pursuit (ReGAP) algorithm for cosparse signal reconstruction with noise. Using a weighted matrix, we fill the gap between greedy and convex relaxation techniques. Theoretical analysis shows that our algorithm is convergent. We estimate the error bound of ReGAP algorithm with cosparse analysis model, and then simulation results demonstrate that our algorithm is feasible and effective.