Block Sparse Signal Recovery in Compressed Sensing: Optimum Active Block Selection and Within-Block Sparsity Order Estimation

Abstract

In this paper, we develop a new algorithm for recovery of block sparse signals in compressed sensing framework based on orthogonal matching pursuit. Furthermore, we point out that a major issue in conventional sparse signal recovery is the lack of prior knowledge about the order of sparsity. Consequently, block sparse signal recovery algorithms suffer even more from the same problem since two parameters are needed for exact recovery of the signal, order of active blocks and within-block sparsity order. Therefore, we propose a new approach to determining both of the active blocks and within-block sparsity order which is embedded in the proposed block sparse signal recovery algorithm. The simulation results illustrate the improved performance of the proposed method for recovery of block sparse signals compared to the conventional methods which are not aware of the prior information. We also apply our proposed algorithm to ECG signal compression, where the obtained results reveal its efficiency.