Deterministic Sensing Matrices Based on Multidimensional Pseudo-Random Sequences

An approach is proposed for producing compressed sensing (CS) matrices via multidimensional pseudo-random sequences. The columns of these matrices are binary Gold code vectors where zeros are replaced by ?1. This technique is mainly applied to restore sub-Nyquist-sampled sparse signals, especially image reconstruction using block CS. First, for the specific requirements of message length and compression ratio, a set Λ which includes all preferred pairs of m-sequences is obtained by a searching algorithm. Then a sensing matrix A _M×N is produced by using structured hardware circuits. In order to better characterize the correlation between any two columns of A, the average coherence is defined and the restricted isometry property (RIP) condition is described accordingly. This RIP condition has strong adaptability to different sparse signals. The experimental results show that with constant values of N and M, the sparsity bound of A is higher than that of a random matrix. Also, the recovery probability may have a maximum increase of 20 % in a noisy environment.