2013/01/25 by Shu‐Tao Xia, Xia, Shu-Tao, Xinji Liu +5
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Blind Source Separation Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1301.5952
openalex publication_date 2013/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
Deterministic constructions of measurement matrices in compressed sensing (CS) are considered in this paper. The constructions are inspired by the recent discovery of Dimakis, Smarandache and Vontobel which says that parity-check matrices of good low-density parity-check (LDPC) codes can be used as provably good measurement matrices for compressed sensing under ℓ1-minimization. The performance of the proposed binary measurement matrices is mainly theoretically analyzed with the help of the analyzing methods and results from (finite geometry) LDPC codes. Particularly, several lower bounds of the spark (i.e., the smallest number of columns that are linearly dependent, which totally characterizes the recovery performance of ℓ0-minimization) of general binary matrices and finite geometry matrices are obtained and they improve the previously known results in most cases. Simulation results show that the proposed matrices perform comparably to, sometimes even better than, the corresponding Gaussian random matrices. Moreover, the proposed matrices are sparse, binary, and most of them have cyclic or quasi-cyclic structure, which will make the hardware realization convenient and easy.