Journal
SIGNAL PROCESSING
Volume 153, Issue -, Pages 83-94Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.sigpro.2018.06.027
Keywords
Compressed sensing; restricted isometry property; Weighted l(1) minimization
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Funding
- NSF of China [11371183, 61403036]
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In this paper we study the recovery conditions of weighted l(1) minimization for signal reconstruction from incomplete linear measurements when partial prior support information is available. We obtain that a high order RIP condition can guarantee stable and robust recovery of signals in bounded l(2) and Dantzig selector noise settings. Meanwhile, we not only prove that the sufficient recovery condition of weighted l(1 )minimization method is weaker than that of standard l(1) minimization method, but also prove that weighted l(1) minimization method provides better upper bounds on the reconstruction error in terms of the measurement noise and the compressibility of the signal, provided that the accuracy of prior support estimate is at least 50%. Furthermore, the condition is proved sharp. (C) 2018 Elsevier B.V. All rights reserved.
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