TY - JOUR
T1 - New RIP Bounds for Recovery of Sparse Signals With Partial Support Information via Weighted ℓp -Minimization
AU - Ge, Huanmin
AU - Chen, Wengu
AU - Ng, Michael K.
N1 - This work was supported in part by NSF of China under Grant 11871109, Grant 11901037; and Grant 11801509; in part by NSAF of China under Grant U1830107; and in part by the Hong Kong Research Grant Council General Research Fund under Grant 12306616, Grant 12200317, Grant 12300218, and Grant 12300519.
publisher copyright:
© 2020 IEEE.
PY - 2020/1/13
Y1 - 2020/1/13
N2 - In this paper, we consider the recovery of k-sparse signals using the weighted ℓ
p
(0 <; p ≤ 1) minimization when some partial prior information on the
support is available. First, we present a unified analysis of
restricted isometry constant δ
tk
with d <; t ≤ 2d (d ) ≥1 is determined by the prior support information) for sparse signal recovery by the weighted ℓ
p
(0 <; p ≤ 1) minimization in both noiseless and noisy settings. This result fills a vacancy on δ
tk
with t <; 2, compared with previous works on δ
(a+1)k
(a > 1). Second, we provide a sufficient condition on δ
tk
with 1 <; t ≤ 2 for the recovery of sparse signals using the ℓ
p
(0 <; p ≤ 1) minimization, which extends the existing optimal result on δ
2k
in the literature. Last, various numerical examples are presented to demonstrate the better performance of the weighted ℓ
p
(0 <; p ≤ 1) minimization is achieved when the accuracy of prior
information on the support is at least 50%, compared with that of the ℓ
p
(0 <; p ≤1) minimization.
AB - In this paper, we consider the recovery of k-sparse signals using the weighted ℓ
p
(0 <; p ≤ 1) minimization when some partial prior information on the
support is available. First, we present a unified analysis of
restricted isometry constant δ
tk
with d <; t ≤ 2d (d ) ≥1 is determined by the prior support information) for sparse signal recovery by the weighted ℓ
p
(0 <; p ≤ 1) minimization in both noiseless and noisy settings. This result fills a vacancy on δ
tk
with t <; 2, compared with previous works on δ
(a+1)k
(a > 1). Second, we provide a sufficient condition on δ
tk
with 1 <; t ≤ 2 for the recovery of sparse signals using the ℓ
p
(0 <; p ≤ 1) minimization, which extends the existing optimal result on δ
2k
in the literature. Last, various numerical examples are presented to demonstrate the better performance of the weighted ℓ
p
(0 <; p ≤ 1) minimization is achieved when the accuracy of prior
information on the support is at least 50%, compared with that of the ℓ
p
(0 <; p ≤1) minimization.
KW - Adaptive recovery
KW - compressed sensing
KW - restricted isometry property
KW - sparse representation
KW - weighted p minimization
UR - http://www.scopus.com/inward/record.url?scp=85092508807&partnerID=8YFLogxK
U2 - 10.1109/TIT.2020.2966436
DO - 10.1109/TIT.2020.2966436
M3 - Journal article
AN - SCOPUS:85092508807
SN - 0018-9448
VL - 66
SP - 3914
EP - 3928
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 6
ER -