IEICE TRANSACTIONS on Fundamentals
New Restricted Isometry Condition Using Null Space Constant for Compressed Sensing
Summary :
It has been widely recognized that in compressed sensing, many restricted isometry property (RIP) conditions can be easily obtained by using the null space property (NSP) with its null space constant (NSC) 0<θ≤1 to construct a contradicted method for sparse signal recovery. However, the traditional NSP with θ=1 will lead to conservative RIP conditions. In this paper, we extend the NSP with 0<θ<1 to a scale NSP, which uses a factor τ to scale down all vectors belonged to the Null space of a sensing matrix. Following the popular proof procedure and using the scale NSP, we establish more relaxed RIP conditions with the scale factor τ, which guarantee the bounded approximation recovery of all sparse signals in the bounded noisy through the constrained l1 minimization. An application verifies the advantages of the scale factor in the number of measurements.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E105-A No.12 pp.1591-1603
- Publication Date
- 2022/12/01
- Publicized
- 2022/06/20
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2021EAP1175
- Type of Manuscript
- PAPER
- Category
- Information Theory
Authors
Haiyang ZOU
China West Normal University
Wengang ZHAO
Southwest University of Science and Technology
Keyword
Latest Issue
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Haiyang ZOU, Wengang ZHAO, "New Restricted Isometry Condition Using Null Space Constant for Compressed Sensing" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 12, pp. 1591-1603, December 2022, doi: 10.1587/transfun.2021EAP1175.
Abstract: It has been widely recognized that in compressed sensing, many restricted isometry property (RIP) conditions can be easily obtained by using the null space property (NSP) with its null space constant (NSC) 0<θ≤1 to construct a contradicted method for sparse signal recovery. However, the traditional NSP with θ=1 will lead to conservative RIP conditions. In this paper, we extend the NSP with 0<θ<1 to a scale NSP, which uses a factor τ to scale down all vectors belonged to the Null space of a sensing matrix. Following the popular proof procedure and using the scale NSP, we establish more relaxed RIP conditions with the scale factor τ, which guarantee the bounded approximation recovery of all sparse signals in the bounded noisy through the constrained l1 minimization. An application verifies the advantages of the scale factor in the number of measurements.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAP1175/_p
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@ARTICLE{e105-a_12_1591,
author={Haiyang ZOU, Wengang ZHAO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={New Restricted Isometry Condition Using Null Space Constant for Compressed Sensing},
year={2022},
volume={E105-A},
number={12},
pages={1591-1603},
abstract={It has been widely recognized that in compressed sensing, many restricted isometry property (RIP) conditions can be easily obtained by using the null space property (NSP) with its null space constant (NSC) 0<θ≤1 to construct a contradicted method for sparse signal recovery. However, the traditional NSP with θ=1 will lead to conservative RIP conditions. In this paper, we extend the NSP with 0<θ<1 to a scale NSP, which uses a factor τ to scale down all vectors belonged to the Null space of a sensing matrix. Following the popular proof procedure and using the scale NSP, we establish more relaxed RIP conditions with the scale factor τ, which guarantee the bounded approximation recovery of all sparse signals in the bounded noisy through the constrained l1 minimization. An application verifies the advantages of the scale factor in the number of measurements.},
keywords={},
doi={10.1587/transfun.2021EAP1175},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - New Restricted Isometry Condition Using Null Space Constant for Compressed Sensing
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1591
EP - 1603
AU - Haiyang ZOU
AU - Wengang ZHAO
PY - 2022
DO - 10.1587/transfun.2021EAP1175
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2022
AB - It has been widely recognized that in compressed sensing, many restricted isometry property (RIP) conditions can be easily obtained by using the null space property (NSP) with its null space constant (NSC) 0<θ≤1 to construct a contradicted method for sparse signal recovery. However, the traditional NSP with θ=1 will lead to conservative RIP conditions. In this paper, we extend the NSP with 0<θ<1 to a scale NSP, which uses a factor τ to scale down all vectors belonged to the Null space of a sensing matrix. Following the popular proof procedure and using the scale NSP, we establish more relaxed RIP conditions with the scale factor τ, which guarantee the bounded approximation recovery of all sparse signals in the bounded noisy through the constrained l1 minimization. An application verifies the advantages of the scale factor in the number of measurements.
ER -
English
