New bounds for RIC in compressed sensing
New bounds for RIC in compressed sensing
This paper gives new bounds for restricted isometry constant (RIC) in compressed sensing. Let Φ be an m×n real matrix and k be a positive integer with k⩽n. The main results of this paper show that if the restricted isometry constant of Φ satisfies δ 8ak <1 and
δk+ak<32−1+(4a+3)2−8−−−−−−−−−−√8a
for a>38, then k-sparse solution can be recovered exactly via l 1 minimization in the noiseless case. In particular, when a=1,1.5,2 and 3, we have δ 2k <0.5746 and δ 8k <1, or δ 2.5k <0.7046 and δ 12k <1, or δ 3k <0.7731 and δ 16k <1 or δ 4k <0.8445 and δ 24k <1.
227-237
Zhou, Shenglong
d183edc9-a9f6-4b07-a140-a82213dbd8c3
Kong, LingChen
ef079edd-14ad-4793-b2a5-0fd261b3b711
Xiu, Naihua
8b5770f7-ae35-4dbe-884a-02fb4ea27bee
25 April 2013
Zhou, Shenglong
d183edc9-a9f6-4b07-a140-a82213dbd8c3
Kong, LingChen
ef079edd-14ad-4793-b2a5-0fd261b3b711
Xiu, Naihua
8b5770f7-ae35-4dbe-884a-02fb4ea27bee
Zhou, Shenglong, Kong, LingChen and Xiu, Naihua
(2013)
New bounds for RIC in compressed sensing.
Journal of the Operations Research Society of China, 1 (2), .
(doi:10.1007/s40305-013-0013-z).
Abstract
This paper gives new bounds for restricted isometry constant (RIC) in compressed sensing. Let Φ be an m×n real matrix and k be a positive integer with k⩽n. The main results of this paper show that if the restricted isometry constant of Φ satisfies δ 8ak <1 and
δk+ak<32−1+(4a+3)2−8−−−−−−−−−−√8a
for a>38, then k-sparse solution can be recovered exactly via l 1 minimization in the noiseless case. In particular, when a=1,1.5,2 and 3, we have δ 2k <0.5746 and δ 8k <1, or δ 2.5k <0.7046 and δ 12k <1, or δ 3k <0.7731 and δ 16k <1 or δ 4k <0.8445 and δ 24k <1.
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Published date: 25 April 2013
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Local EPrints ID: 442087
URI: http://eprints.soton.ac.uk/id/eprint/442087
ISSN: 2194-668X
PURE UUID: 3e42f06e-86e8-488a-b5ad-55ce0818bc2c
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Date deposited: 07 Jul 2020 16:48
Last modified: 16 Mar 2024 08:32
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Author:
Shenglong Zhou
Author:
LingChen Kong
Author:
Naihua Xiu
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