CSIAM Trans. Appl. Math., 5 (2024), pp. 18-57.
Published online: 2024-02
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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.
}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.SO-2022-0016}, url = {http://global-sci.org/intro/article_detail/csiam-am/22919.html} }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.