Application and Study of A Superimposed Measurement Matrix in Signal Reconstruction

In order to improve the quality of the signal which using compressed sensing algorithm for reconstruction, based on the construction method of fourier random measurement matrix, this paper presents a superimposed matrix. The matrix superposed deterministic ring matrix on the basis of fourier random matrix, readjust measurement structure and range, so that the signal retain the useful information completely and accurately in the process of compressed sensing. This paper focuses on the construction methods of the superimposed measurement matrix by analysis types of common measurement matrix, which applied to 1D and 2D signals reconstruction. Through the simulation comparison of the reconstruction effects of these matrixes, we find that the improved measurement matrix can improve the quality of the signal reconstructed in the same signal sparsity, measuring proportion and reconstruction algorithm.