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Iteratively reweighted algorithm for signals recovery with coherent tight frame
Author(s) -
Bi Ning,
Liang Kaihao
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5091
Subject(s) - mathematics , algorithm , compressed sensing , frame (networking) , hilbert space , equiangular polygon , nyquist–shannon sampling theorem , haar , wavelet , mathematical analysis , computer science , telecommunications , geometry , artificial intelligence , monotone polygon
We consider the problem of compressed sensing with a coherent tight frame and design an iteratively reweighted least squares algorithm to solve it. To analyze the problem, we propose a sufficient null space property under a tight frame (sufficient D‐NSP). We show that, if a measurement matrix A satisfies the sufficient D‐NSP of order s , then an s ‐sparse signal under the tight frame can be exactly recovered. Furthermore, if A satisfies the restricted isometric property with tight frame D of order 2 b s , then it also satisfies the sufficient D‐NSP of order a s with a < b and b sufficiently large. We prove the convergence of the algorithm based on the sufficient D‐NSP and give the upper error bounds. In numerical experiments, we use the discrete cosine transform, discrete Fourier transform, and Haar wavelets to verify the effectiveness of this algorithm. With increasing measurement number, the signal‐to‐noise ratio increases monotonically.