Deterministic Constructions of Compressed Sensing Matrices Based on Affine Singular Linear Space over Finite Fields

Gang WANG  Min-Yao NIU  Jian GAO  Fang-Wei FU  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.11   pp.1957-1963
Publication Date: 2018/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.1957
Type of Manuscript: LETTER
Category: Coding Theory
Keyword: 
compressed sensing,  coherence,  sparsity,  affine singular linear space,  finite fields,  

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Summary: 
Compressed sensing theory provides a new approach to acquire data as a sampling technique and makes sure that a sparse signal can be reconstructed from few measurements. The construction of compressed sensing matrices is a main problem in compressed sensing theory (CS). In this paper, the deterministic constructions of compressed sensing matrices based on affine singular linear space over finite fields are presented and a comparison is made with the compressed sensing matrices constructed by DeVore based on polynomials over finite fields. By choosing appropriate parameters, our sparse compressed sensing matrices are superior to the DeVore's matrices. Then we use a new formulation of support recovery to recover the support sets of signals with sparsity no more than k on account of binary compressed sensing matrices satisfying disjunct and inclusive properties.