Deterministic construction of Quasi-Cyclic sparse sensing matrices from one-coincidence sequence

In this paper, a new class of deterministic sparse matrices derived from Quasi-Cyclic (QC) low-density parity-check (LDPC) codes is presented for compressed sensing (CS). In contrast to random and other deterministic matrices, the proposed matrices are generated based on circulant permutation matrices, which require less memory for storage and low computational cost for sensing. Its size is also quite flexible compared with other existing fixed-sizes deterministic matrices. Furthermore, both the coherence and null space property of proposed matrices are investigated, specially, the upper bounds of signal sparsity k is given for exactly recovering. Finally, we carry out many numerical simulations and show that our sparse matrices outperform Gaussian random matrices under some scenes.