Uniform RIP Bounds for Recovery of Signals with Partial Support Information by Weighted $ℓ_p$-Minimization
Year: 2024
Author: Huanmin Ge, Wengu Chen, Michael K. Ng
CSIAM Transactions on Applied Mathematics, Vol. 5 (2024), Iss. 1 : pp. 18–57
Abstract
In this paper, we consider signal recovery in both noiseless and noisy cases via weighted $ℓ_p \ (0 < p ≤ 1)$ minimization when some partial support information on the signals is available. The uniform sufficient condition based on restricted isometry property (RIP) of order $tk$ for any given constant $t>d$ ($d≥1$ is determined by the prior support information) guarantees the recovery of all $k$-sparse signals with partial support information. The new uniform RIP conditions extend the state-of-the-art results for weighted $ℓ_p$-minimization in the literature to a complete regime, which fill the gap for any given constant $t > 2d$ on the RIP parameter, and include the existing optimal conditions for the $ℓ_p$-minimization and the weighted $ℓ_1$-minimization as special cases.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2022-0016
CSIAM Transactions on Applied Mathematics, Vol. 5 (2024), Iss. 1 : pp. 18–57
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 40
Keywords: Compressed sensing weighted $ℓ_p$ minimization stable recovery restricted isometry property.
Author Details
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Uniform RIP analysis for the ℓp-ωℓq minimization
Ge, Huanmin
Xie, Yujia
Chen, Wengu
Journal of Computational and Applied Mathematics, Vol. 451 (2024), Iss. P.116100
https://doi.org/10.1016/j.cam.2024.116100 [Citations: 0]