Sparse Matrix Reconstruction Based on Sequential Sparse Recovery for Multiple Measurement Vectors

Abstract

This paper considers recovery of two-dimensional (2D) sparse signals from incomplete measurements. The 2D sparse signals can be reconstructed by solving a sparse representation problem for Multiple Measurement Vectors (MMV). However, the extension of the sparse recovery algorithms to the MMV case may be inefficient if the vectors do not have the same sparsity profile. In this paper, a sequential sparse recovery (SSR) algorithm is proposed to reconstruct the two-dimensional (2D) sparse matrix. The sparsity of the matrix is much reduced after down-sampling observation and the sparse matrix can be reconstructed after sequential observations and reconstructions. Simulation results verify the effectiveness of the proposed method in 2D sparse signal reconstruction.