Deterministic constructions of compressed sensing matrices based on optimal codebooks and codes

Gang Wang, Min-Yao Niu and Fang-Wei Fu

Applied Mathematics and Computation, 2019, vol. 343, issue C, 128-136

Abstract: 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. In this paper, the deterministic compressed sensing matrices are provided using optimal codebooks and codes. Using specific linear and nonlinear codes, we present deterministic constructions of compressed sensing matrices, which are generalizations of DeVore′s construction and Li et al.′s construction. Compared with DeVore′s matrices and Li et al.′s matrices, by using appropriate optimal codebooks and specific codes, the compressed sensing matrices we construct are superior to DeVore′s matrices and Li et al.′s matrices.

Keywords: Compressed sensing; Coherence; Sparsity; Restricted isometry property; Optimal codebooks; Codes (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:343:y:2019:i:c:p:128-136

DOI: 10.1016/j.amc.2018.09.042

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