TY - JOUR
T1 - Uniform RIP Bounds for Recovery of Signals with Partial Support Information by Weighted $ℓ_p$-Minimization
AU - Ge , Huanmin
AU - Chen , Wengu
AU - K. Ng , Michael
JO - CSIAM Transactions on Applied Mathematics
VL - 1
SP - 18
EP - 57
PY - 2024
DA - 2024/02
SN - 5
DO - http://doi.org/10.4208/csiam-am.SO-2022-0016
UR - https://global-sci.org/intro/article_detail/csiam-am/22919.html
KW - Compressed sensing, weighted $ℓ_p$ minimization, stable recovery, restricted isometry property.
AB - <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>