Newly deterministic construction of compressed sensing matrices via singular linear spaces over finite fields

2016 ◽  
Vol 34 (1) ◽  
pp. 245-256 ◽  
Author(s):  
Yingmo Jie ◽  
Cheng Guo ◽  
Zhangjie Fu
Keyword(s):  
Compressed Sensing ◽  
Finite Fields ◽  
Linear Spaces ◽  
Compressed Sensing Matrices ◽  
Deterministic Construction ◽  
Singular Linear Spaces ◽  
Sensing Matrices

Deterministic construction of compressed sensing matrices with characters over finite fields

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.

Constructions of compressed sensing matrices based on the subspaces of symplectic space over finite fields

2015 ◽  
Vol 15 (02) ◽  
pp. 1650025 ◽  
Author(s):  
You Gao ◽  
Xiaojuan Zhang
Keyword(s):  
Compressed Sensing ◽  
Finite Fields ◽  
Symplectic Geometry ◽  
Symplectic Space ◽  
The Matrix ◽  
Compressed Sensing Matrices ◽  
Sensing Matrices

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.

Deterministic Construction of Compressed Sensing Matrices from Codes

2017 ◽  
Vol 28 (02) ◽  
pp. 99-109 ◽  
Author(s):  
Xiang Wang ◽  
Fang-Wei Fu
Keyword(s):  
Compressed Sensing ◽  
Linear Codes ◽  
Sampling Theory ◽  
Sparse Sampling ◽  
Sparse Signal ◽  
Sensing Matrix ◽  
Adaptive Measurements ◽  
Compressed Sensing Matrices ◽  
Deterministic Construction ◽  
Sensing Matrices

Compressed sensing is a sparse sampling theory. Compared with the Nyquist-Shannon sampling theory, in compressed sensing one could reconstruct a sparse signal from a few linear and non-adaptive measurements. How to construct a good sensing matrix which captures the full information of a sparse signal is an important problem in compressed sensing. In this paper, we present a new deterministic construction using a linear or nonlinear code, which is a generalization of DeVore’s construction and Li et al.’s construction. By choosing some appropriate linear codes or nonlinear codes, we will construct some good binary sensing matrices which are superior to DeVore’s ones and Li et al.’s ones.

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