Paper Info
Title
Deterministic Constructions of Binary Measurement Matrices From Finite Geometry
Abstract
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 l(1)-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 l(0)-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.
Year
DOI
Venue
2015
10.1109/TSP.2014.2386300
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Keywords
Field
DocType
Compressed sensing,finite geometry,low-density parity-check codes,measurement matrix,quasi-cyclic,spark
Discrete mathematics,Mathematical optimization,Matrix analysis,Low-density parity-check code,Matrix (mathematics),Algorithm,Integer matrix,Finite geometry,Mathematics,Restricted isometry property,Binary number,Random matrix
Journal
Volume
Issue
ISSN
63
4
1053-587X
Citations 
PageRank 
References 
15
0.68
37
Authors
4
Name
Order
Citations
PageRank
Xia Shu-Tao134275.29
Xin-Ji Liu2476.81
Jiang Yong315641.60
Zheng Hai-Tao414224.39