TY - JOUR
T1 - Uniform RIP Bounds for Recovery of Signals with Partial Support Information by Weighted ℓp-Minimization
AU - Ge, Huanmin
AU - Chen, Wengu
AU - Ng, Michael K.
N1 - This work was supported by the NSF of China (Grant Nos. 12371094, 12271050, 11871109), by the Beijing Natural Science Foundation (Grant No. 1232020), by the CAEP Foundation (Grant No. CX20200027), by the Foundation of National Key Laboratory of Computational Physics (Grant No. 6142A05230503) and by the HKRGC GRF (Grant Nos. 17201020, 17300021), HKRGC CRF C1013-21GF and C7004-21GF, and Joint NSFC and RGC N-HKU769/21.
Publisher Copyright:
© 2024 Global Science Press. All rights reserved.
PY - 2024/3
Y1 - 2024/3
N2 - In this paper, we consider signal recovery in both noiseless and noisy cases via weighted ℓp (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 ℓp-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 ℓp-minimization and the weighted ℓ1-minimization as special cases.
AB - In this paper, we consider signal recovery in both noiseless and noisy cases via weighted ℓp (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 ℓp-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 ℓp-minimization and the weighted ℓ1-minimization as special cases.
KW - Compressed sensing
KW - restricted isometry property
KW - stable recovery
KW - weighted ℓ minimization
UR - http://www.scopus.com/inward/record.url?scp=85187663142&partnerID=8YFLogxK
UR - https://global-sci.com/article/91011/uniform-rip-bounds-for-recovery-of-signals-with-partial-support-information-by-weighted-p-minimization
U2 - 10.4208/csiam-am.SO-2022-0016
DO - 10.4208/csiam-am.SO-2022-0016
M3 - Journal article
AN - SCOPUS:85187663142
SN - 2708-0560
VL - 5
SP - 18
EP - 57
JO - CSIAM Transactions on Applied Mathematics
JF - CSIAM Transactions on Applied Mathematics
IS - 1
ER -
