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

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

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.

Suggested Citation

  • Wang, Gang & Niu, Min-Yao & Fu, Fang-Wei, 2019. "Deterministic constructions of compressed sensing matrices based on optimal codebooks and codes," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 128-136.
    • Handle: RePEc:eee:apmaco:v:343:y:2019:i:c:p:128-136
    DOI: 10.1016/j.amc.2018.09.042
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    Cited by:

    1. Liang, Junying & Peng, Haipeng & Li, Lixiang & Tong, Fenghua & Yang, Yixian, 2022. "Flexible construction of measurement matrices in compressed sensing based on extensions of incidence matrices of combinatorial designs," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    2. Tong, Fenghua & Li, Lixiang & Peng, Haipeng & Yang, Yixian, 2020. "An effective algorithm for the spark of sparse binary measurement matrices," Applied Mathematics and Computation, Elsevier, vol. 371(C).

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