New Conditions on Stable Recovery of Weighted Sparse Signals via Weighted l1 Minimization

作者：Huo, Haiye; Sun, Wenchang^*; Xiao, Li

来源：Circuits, Systems, and Signal Processing, 2018, 37(7): 2866-2883.

DOI：10.1007/s00034-017-0691-6

• Compressed sensing
• Null space property
• Restricted isometry property
• Weighted l(1) minimization
• Weighted sparsity

A problem of recovering weighted sparse signals via weighted minimization has recently drawn considerable attention with application to function interpolation. The weighted robust null space property (NSP) of order s and the weighted restricted isometry property (RIP) with the weighted 3s-RIP constant have been proposed and proved to be sufficient conditions for guaranteeing stable recovery of weighted s-sparse signals. In this paper, we propose two new sufficient conditions, i.e., the weighted -robust NSP of order s and the weighted RIP with . Different from the existing results, the weighted -robust NSP of order s is more general and weaker than the weighted robust NSP of order s, and the weighted RIP is characterized by instead of . Accordingly, the reconstruction error estimations based on the newly proposed recovery conditions are also derived, respectively. Moreover, we demonstrate that the weighted RIP with small implies the weighted -robust NSP of order s.

• 出版日期2018-7
• 单位南开大学; 南昌大学