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- Title
Estimation of q for ℓq-minimization in signal recovery with tight frame.
- Authors
Liang, Kaihao; Zhang, Chaolong; Zhang, Wenfeng
- Abstract
This study aims to reconstruct signals that are sparse with a tight frame from undersampled data by using the ℓ q -minimization method. This problem can be cast as a ℓ q -minimization problem with a tight frame subjected to an undersampled measurement with a known noise bound. We proved that if the measurement matrix satisfies the restricted isometry property with δ 2 s ≤ 1 / 2 , there exists a value q 0 such that for any q ∈ (0 , q 0 ] , any signal that is s-sparse with a tight frame can be robustly recovered to the true signal. We estimated q 0 as q 0 = 2 / 3 in the case of δ 2 s ≤ 1 / 2 and discussed that the value of q 0 can be much higher. We also showed that when δ 2 s ≤ 0.3317 , for any q ∈ (0 , 1 ] , robust recovery for signals via ℓ q -minimization holds, which is consistent with the case of ℓ q -minimization without a tight frame.
- Subjects
RESTRICTED isometry property; NOISE measurement
- Publication
Journal of Inequalities & Applications, 2023, Vol 2023, Issue 1, p1
- ISSN
1025-5834
- Publication type
Article
- DOI
10.1186/s13660-023-03068-z