Deterministic Constructions of Compressive Sensing Matrices Based on Berlekamp-Justesen Codes

Nowadays the deterministic construction of sensing matrices is a hot topic in compressed sensing. Two classes of deterministic sensing matrices based on the Berlekamp-Justesen (B-J) codes are proposed. Firstly, a class of sparse sensing matrices with near-optimal coherence is constructed. It satisfies the Restricted Isometry Property (RIP) well. Afterwards, a class of deterministic complex-valued matrices is proposed. The row and column numbers of these matrices are tunable through the row and column puncturing. Moreover, the first proposed matrices are high sparsity and the second matrices are able to obtain from the cyclic matrices, thus the storage costs of them are relatively low and both the sampling and recovery processes can be simpler. The simulation results demonstrate that the proposed matrices often perform comparably to, or even better than some random matrices and deterministic measurement matrices.