STABLE AND ROBUST RECOVERY OF APPROXIMATELY k-SPARSE SIGNALS WITH PARTIAL SUPPORT INFORMATION IN NOISE SETTINGS VIA WEIGHTED ￡P (0 < p < 1)

作者：Du, Biao; Wan, Anhua^*

来源：Journal of Computational Mathematics, 2023, 41(6): 1137-1170.

DOI：10.4208/jcm.2207-m2022-0058

• Signal recovery
• weighted $p minimization
• Approximately k-sparse signal
• Noise setting
• Reconstruction error bound
• Restricted isometry property

In the existing work, the recovery of strictly k -sparse signals with partial support information was derived in the $2 bounded noise setting. In this paper, the recovery of approximately k -sparse signals with partial support information in two noise settings is investigated via weighted $p(0 < p <= 1) minimization method. The restricted isometry constant (RIC) condition delta tk < 1 2 - p eta p 1 +1 on the measurement matrix for some t is an element of [1+ 2-p 2+p sigma, 2] is proved to be sufficient to guarantee the stable and robust recovery of signals under sparsity defect in noisy cases. Herein, sigma is an element of [0, 1] is a parameter related to the prior support information of the original signal, and eta >= 0 is determined by p, t and sigma. The new results not only improve the recent work in [17], but also include the optimal results by weighted $1 minimization or by standard $p minimization as special cases.

• 单位
  中山大学