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Circuits, Systems, and Signal Processing
Published in:

09-06-2024

Recovery Conditions in Weighted Sparse Phase Retrieval via Weighted \(\ell _q\, (0<q\le 1)\) Minimization

Authors: Haiye Huo, Li Xiao

Published in: Circuits, Systems, and Signal Processing | Issue 9/2024

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Abstract

In this paper, we generalize the conditions for the exact or stable recovery of weighted k-sparse signals in weighted sparse phase retrieval in our previous work [11] from the weighted \(\ell _1\) minimization to the weighted \(\ell _q\, (0<q\le 1)\) minimization in a broad sense. Specifically, we first present that the weighted null space property (WNSP) is a sufficient and necessary condition to guarantee the exact recovery of a weighted k-sparse signal from its noiseless phaseless measurements via the weighted \(\ell _q\, (0<q\le 1)\) minimization in both the real and complex cases. In addition, we establish a general strong weighted restricted isometry property (SWRIP) condition for the stable recovery of a weighted k-sparse signal from its noisy phaseless measurements via the weighted \(\ell _q\, (0<q\le 1)\) minimization in the real case.
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Appendix
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Metadata
Title
Recovery Conditions in Weighted Sparse Phase Retrieval via Weighted Minimization
Authors
Haiye Huo
Li Xiao
Publication date
09-06-2024
Publisher
Springer US
Published in
Circuits, Systems, and Signal Processing / Issue 9/2024
Print ISSN: 0278-081X
Electronic ISSN: 1531-5878
DOI
https://doi.org/10.1007/s00034-024-02735-w

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