Uniform RIP Bounds for Recovery of Signals with Partial Support Information by Weighted $ℓ_p$-Minimization

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

Huanmin Ge

Wengu Chen

Michael K. Ng

  1. 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]