Blind compressive sensing using block sparsity and nonlocal low-rank priors

Abstract

Without knowing the sparsity basis, Blind Compressive Sensing (BCS) can achieve similar results with those Compressive Sensing (CS) methods which rely on prior knowledge of the sparsity basis. However, BCS still suffers from two problems. First, compared with block-based sparsity, the global image sparsity ignores the local image features and BCS approaches based on it cannot obtain the competitive results. Second, since BCS only exploits the weaker sparsity prior than CS, the sampling rate required by BCS is still very high in practice. In this paper, we firstly propose a novel blind compressive sensing method based on block sparsity and nonlocal low-rank priors (BCS-BSNLR) to further reduce the sampling rate. In addition, we take alternating direction method of multipliers to solve the resulting optimization problem. Experimental results have demonstrated that the proposed algorithm can significantly reduce the sampling rate without sacrificing the quality of the reconstructed image.