Sufficient conditions on stable reconstruction of weighted problem

Abstract

In this paper, two new sufficient conditions on stable recovery of the weighted signals via the weighted minimization are proposed based upon the weighted robust null space property (NSP) and the weighted restricted isometry property (RIP), respectively. Moreover, it is shown that the weighted RIP, as a stronger condition to estimate reconstruction errors, implies the weighted robust NSP.

Keywords:

• Weighted robust null space
• weighted restricted isometry property
• stable recovery
• weighted minimization

2010 Mathematics Subject Classifications:

• 68W25
• 49N45

Acknowledgments

This project is supported by the National Natural Science Foundation of China (No. 62071262) and K. C. Wong Magna Fund in Ningbo University.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This project is supported by the National Natural Science Foundation of China (No. 62071262) and K. C. Wong Magna Fund in Ningbo University.