摘要
Compressed Sensing (CS) is an emerging technology in the field of signal processing, which can recover a sparse signal by taking very few samples and solving a linear programming problem. In this paper, we study the application of Low-Density Parity-Check (LDPC) Codes in CS. Firstly, we find a sufficient condition for a binary matrix to satisfy the Restricted Isometric Property (RIP). Then, by employing the LDPC codes based on Berlekamp-Justesen (B-J) codes, we construct two classes of binary structured matrices and show that these matrices satisfy RIP. Thus, the proposed matrices could be used as sensing matrices for CS. Finally, simulation results show that the performance of the proposed matrices can be comparable with the widely used random sensing matrices.
Compressed Sensing （CS） is an emerging technology in the field of signal processing, which can recover a sparse signal by taking very few samples and solving a linear programming problem. In this paper, we study the application of Low-Density Parity-Check （LDPC） Codes in CS. Firstly, we find a sufficient condition for a binary matrix to satisfy the Restricted Isometric Property （RIP）. Then, by employing the LDPC codes based on Berlekamp-Justesen （B-J） codes, we construct two classes of binary structured matrices and show that these matrices satisfy RIP. Thus, the proposed matrices could be used as sensing matrices for CS. Finally, simulation results show that the performance of the proposed matrices can be comparable with the widely used random sensing matrices.
基金
Supported by the NSFC project (No. 60972011)
the Research Fund for the Doctoral Program of Higher Education of China (No. 20100002110033)
the open research fund of National Mobile Communications Research Laboratory of Southeast University (No. 2011D11)
