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

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

Construction of compressed sensing matrices for signal processing

2018 ◽  
Vol 77 (23) ◽  
pp. 30551-30574 ◽  
Author(s):  
Yingmo Jie ◽  
Cheng Guo ◽  
Mingchu Li ◽  
Bin Feng
Keyword(s):  
Signal Processing ◽  
Compressed Sensing ◽  
Compressed Sensing Matrices ◽  
Sensing Matrices

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 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.

Optimized Structural Compressed Sensing Matrices for Speech Compression

2018 ◽  
Vol 66 (6) ◽  
pp. 756-771
Author(s):  
Yuvraj V Parkale ◽  
Sanjay L Nalbalwar
Keyword(s):  
Compressed Sensing ◽  
Speech Compression ◽  
Compressed Sensing Matrices ◽  
Sensing Matrices

Toeplitz-Structured Compressed Sensing Matrices

2007 ◽  
Author(s):  
Waheed U. Bajwa ◽  
Jarvis D. Haupt ◽  
Gil M. Raz ◽  
Stephen J. Wright ◽  
Robert D. Nowak
Keyword(s):  
Compressed Sensing ◽  
Compressed Sensing Matrices ◽  
Sensing Matrices
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