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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 (CS). In this paper, the deterministic constructions of compressed sensing matrices based on affine singular linear space over finite fields are presented and a comparison is made with the compressed sensing matrices constructed by DeVore based on polynomials over finite fields. By choosing appropriate parameters, our sparse compressed sensing matrices are superior to the DeVore's matrices. Then we use a new formulation of support recovery to recover the support sets of signals with sparsity no more than *k* on account of binary compressed sensing matrices satisfying disjunct and inclusive properties.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E101-A No.11 pp.1957-1963

- Publication Date
- 2018/11/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E101.A.1957

- Type of Manuscript
- LETTER

- Category
- Coding Theory

Gang WANG

Nankai University

Min-Yao NIU

Civil Aviation University of China

Jian GAO

Shandong University of Technology

Fang-Wei FU

Nankai University

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Gang WANG, Min-Yao NIU, Jian GAO, Fang-Wei FU, "Deterministic Constructions of Compressed Sensing Matrices Based on Affine Singular Linear Space over Finite Fields" in IEICE TRANSACTIONS on Fundamentals,
vol. E101-A, no. 11, pp. 1957-1963, November 2018, doi: 10.1587/transfun.E101.A.1957.

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 (CS). In this paper, the deterministic constructions of compressed sensing matrices based on affine singular linear space over finite fields are presented and a comparison is made with the compressed sensing matrices constructed by DeVore based on polynomials over finite fields. By choosing appropriate parameters, our sparse compressed sensing matrices are superior to the DeVore's matrices. Then we use a new formulation of support recovery to recover the support sets of signals with sparsity no more than *k* on account of binary compressed sensing matrices satisfying disjunct and inclusive properties.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.1957/_p

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@ARTICLE{e101-a_11_1957,

author={Gang WANG, Min-Yao NIU, Jian GAO, Fang-Wei FU, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Deterministic Constructions of Compressed Sensing Matrices Based on Affine Singular Linear Space over Finite Fields},

year={2018},

volume={E101-A},

number={11},

pages={1957-1963},

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 (CS). In this paper, the deterministic constructions of compressed sensing matrices based on affine singular linear space over finite fields are presented and a comparison is made with the compressed sensing matrices constructed by DeVore based on polynomials over finite fields. By choosing appropriate parameters, our sparse compressed sensing matrices are superior to the DeVore's matrices. Then we use a new formulation of support recovery to recover the support sets of signals with sparsity no more than *k* on account of binary compressed sensing matrices satisfying disjunct and inclusive properties.},

keywords={},

doi={10.1587/transfun.E101.A.1957},

ISSN={1745-1337},

month={November},}

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TY - JOUR

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

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1957

EP - 1963

AU - Gang WANG

AU - Min-Yao NIU

AU - Jian GAO

AU - Fang-Wei FU

PY - 2018

DO - 10.1587/transfun.E101.A.1957

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E101-A

IS - 11

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - November 2018

AB - 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 (CS). In this paper, the deterministic constructions of compressed sensing matrices based on affine singular linear space over finite fields are presented and a comparison is made with the compressed sensing matrices constructed by DeVore based on polynomials over finite fields. By choosing appropriate parameters, our sparse compressed sensing matrices are superior to the DeVore's matrices. Then we use a new formulation of support recovery to recover the support sets of signals with sparsity no more than *k* on account of binary compressed sensing matrices satisfying disjunct and inclusive properties.

ER -