Deterministic Construction of Compressed Sensing Measurement Matrix with Arbitrary Sizes via QC-LDPC and Arithmetic Sequence Sets

It is of great significance to construct deterministic measurement matrices with good practical characteristics in Compressed Sensing (CS), including reconstruction performance, low memory cost and computing resources. Low-density-parity check (LDPC) codes CS can be closely related. This paper presents a method constructing compressed sensing based on quasi-cyclic (QC) LDPC arithmetic sequence sets. The cyclic shift factor each submatrix QC-LDPC determined by Compared random matrices, the proposed has advantages because it generated matrix, which requires less storage lower Because restricted isometric property (RIP) difficult verify, mutual coherence girth are used as computationally tractable indicators evaluate matrix performance. several typical minimum superior capability signal according one-dimensional (1D) signals two-dimensional (2D) image simulation results. When sampling rate 0.2, maximum (minimum) gain peak signal-to-noise ratio (PSNR) structural similarity index (SSIM) up 2.89 dB (0.33 dB) 0.031 (0.016) while using 10 test images. Meanwhile, time reduced nearly half.