The Design of a Dual-structured Measurement Matrix in Compressed Sensing

The design of measurement matrices is one of the key contents of the compressed sensing (CS) theory. This paper constructs a new dual-structured measurement matrix-unit array + random matrix, by combining the advantages of the random measurement matrices with high recovery probability and the structured measurement matrices of low storage. The experiments show that the reconstruction errors can be gotten lower through using the measurement matrix designed than those of the simple application of the random measurement matrix. Then a method of sub-frame overlapping is proposed for reconstructing the entire signal, which can remove large errors caused by unit array in the measurement matrix, and ensure the stability of the whole signal reconstruction. Simulation results demonstrate that the signal to noise ratio (SNR) is increased significantly and the reconstruction performance of signal is improved remarkably.