Spare Sensing Matrix Construction for Compressed Sensing

Compressed sensing (CS) enables new sampling theories to provide revolutionary approaches for data acquisition. Unlike traditional methods, it allows a parse or compressible signal to be reconstructed from much fewer measurements. To guarantee exact recovery from compressed measurements, a specific matrix satisfying the Restricted Isometry Property (RIP) is necessary in the sensing procedure. In this paper, we first propose matrix, which only contains 0 and 1. Then we propose spare sensing matrix (SSM) based on the binary matrix. Additionally, we propose a RIP testing method to prove that SSM satisfy RIP. However, the size of SSM is constrained by sum of elements in every column and the maximum inner product of any two different column of binary matrix. To solve the problem, we propose two methods to increase the number of column and the number of row for SSM correspondingly. Simulation experiments show that SSM performs almost the same as Gauss sensing matrix. While the performance of improved SSM is much better than SSM and Gauss sensing matrix.