@Article{CSIAM-AM-5-18,
author = {Ge , HuanminChen , Wengu and K. Ng , Michael},
title = {Uniform RIP Bounds for Recovery of Signals with Partial Support Information by Weighted $ℓ_p$-Minimization},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2024},
volume = {5},
number = {1},
pages = {18--57},
abstract = {<p style="text-align: justify;">In this paper, we consider signal recovery in both noiseless and noisy cases
via weighted $ℓ_p \ (0 &lt; p ≤ 1)$ 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 $t&gt;d$ ($d≥1$ 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 $t &gt; 2d$ on the RIP parameter, and include the existing optimal
conditions for the $ℓ_p$-minimization and the weighted $ℓ_1$-minimization as special cases.</p>},
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}
}