A Compressed Sensing Random Measurement Matrix Construction Method: Block Sparse Random Measurement Matrix

Abstract

Compressed sensing (CS) has shown a huge advantage on data compressing and transmission, and designing a suitable measurement matrix is helpful for performance of the CS. Recently, traditional CS measurement matrices have been well applied in many fields, however, there are still problems, such as long construction time, large storage space, and poor real-time performance. Aiming at above problems, combining the advantages of sparse measurement matrix and identity matrix, a new construction method of measurement matrix named Block Sparse Random Measurement Matrix (BSRMM) is proposed. The proposed matrix satisfies restricted isometry property (RIP) with high probability, has faster construction speed, smaller storage space, and is easy to implement. Finally, the compressed sampling process with the BSRMM is implemented on a wireless sensor node with microprocessor STM32F407, and a good reconstruction effect is achieved on the simulated leak signals from a small gas pipeline network, which verifies the effectiveness of the BSRMM.