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

The paper provides two constructions of compressed sensing matrices using the subspaces of symplectic space and singular symplectic space over finite fields. Then we compare the matrices constructed in this paper with the matrix constructed by DeVore, and compare the two matrices based on symplectic geometry and singular symplectic geometry over finite fields.

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Deterministic Construction of Compressed Sensing Matrices via Vector Spaces Over Finite Fields

IEEE Access ◽

10.1109/access.2020.3034912 ◽

2020 ◽

Vol 8 ◽

pp. 203301-203308

Author(s):

Xuemei Liu ◽

Lihua Jia

Keyword(s):

Compressed Sensing ◽

Finite Fields ◽

Vector Spaces ◽

Compressed Sensing Matrices ◽

Deterministic Construction ◽

Sensing Matrices

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A new construction of compressed sensing matrices for signal processing via vector spaces over finite fields

Multimedia Tools and Applications ◽

10.1007/s11042-019-07947-w ◽

2019 ◽

Vol 78 (22) ◽

pp. 31137-31161

Author(s):

Yingmo Jie ◽

Mingchu Li ◽

Cheng Guo ◽

Bin Feng ◽

Tingting Tang

Keyword(s):

Signal Processing ◽

Compressed Sensing ◽

Finite Fields ◽

Vector Spaces ◽

New Construction ◽

Compressed Sensing Matrices ◽

Sensing Matrices

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Deterministic construction of compressed sensing matrices with characters over finite fields

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830918500611 ◽

2018 ◽

Vol 10 (05) ◽

pp. 1850061

Author(s):

Gang Wang ◽

Min-Yao Niu ◽

Fang-Wei Fu

Keyword(s):

Compressed Sensing ◽

Finite Fields ◽

Sampling Technique ◽

Sparse Signals ◽

Sensing Matrix ◽

New Approach ◽

Polynomials Over Finite Fields ◽

Compressed Sensing Matrices ◽

Deterministic Construction ◽

Sensing Matrices

Compressed sensing theory provides a new approach to acquire data as a sampling technique and makes sure that an original sparse signal can be reconstructed from few measurements. The construction of compressed sensing matrices is a central problem in compressed sensing theory. In this paper, the deterministic compressed sensing matrices with characters of finite fields are constructed and the coherence of the matrices are computed. Furthermore, the maximum sparsity of recovering the original sparse signals by using our compressed sensing matrices is obtained. Meanwhile, a comparison is made with the compressed sensing matrices constructed by DeVore based on polynomials over finite fields. In the numerical simulations, our compressed sensing matrix outperforms DeVore’s matrix in the process of recovering original sparse signals.

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