Simultaneous Sensing Matrix and Sparsifying Dictionary Optimization for Block-sparse Compressive Sensing

In this paper, we propose a new method to optimize the sensing matrix and the overcomplete dictionary simultaneously in a block-sparse system. This method mainly includes two parts: the optimization of the sensing matrix for a given dictionary and the optimization of the overcomplete dictionary with a block structure for a predefined sensing matrix. Simulation results show that our novel method can significantly improve the dictionary recovery ability and lower the representation error compared with other dictionary learning methods in block-sparse systems.