Non-binary Sparse Measurement Matrices for Binary Signal Recovery

Abstract

Binary sparse measurement matrices are widely used in compressed sensing (CS) due to their low computational complexity. However, binary sparse measurement matrices perform well in CS-based binary signal recovery only when the source signals are very sparse (e.g., k/n=0.1, where k is the sparsity of the source signal, n is the length of the source signal). In this paper, we propose to construct a non-binary sparse measurement matrix to recover binary source signals which are not so sparse (e.g., k/n=0.2) accurately with few measurements. The novel measurement matrix enables us to design a suboptimal and effective recovery algorithm by fully exploiting the structural features. Moreover, we analyze and estimate the un-recovery probability based on the tree structure to evaluate the recovery performance. The simulation results validate that non-binary sparse measurement matrices can be used to recover binary source signals which are not so sparse, the recovery performance of non-binary sparse measurement matrices is better than that of binary sparse measurement matrices in terms of the un-recovery probability.