Phase retrieval from multiple FRFT measurements based on nonconvex low-rank minimization

•Multiple fractional Fourier transforms (MFRFT) measurements are applied for phase retrieval (PR) problems. Compared to the mask-based Fourier transform (FT) measurements, MFRFT measurements can avoid the problems related to masks, such as the choice of suitable masks in different applications.•Trun...

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Bibliographic Details
Published in:Signal processing 2022-09, Vol.198, p.108601, Article 108601
Main Authors: Su, Xinhua, Tao, Ran, Li, Yongzhe
Format: Article
Language:English
Subjects:
Fourier transform
Fractional Fourier transform
Low rank
Truncated nuclear norm
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Summary:•Multiple fractional Fourier transforms (MFRFT) measurements are applied for phase retrieval (PR) problems. Compared to the mask-based Fourier transform (FT) measurements, MFRFT measurements can avoid the problems related to masks, such as the choice of suitable masks in different applications.•Truncated nuclear norm regularization (TNNR) is first applied to construct PR model, which can effectively take advantage of the rank apriority, and guarantee that the corresponding optimal process achieves a rank-1 matrix.•TNNR-MFRFT is proposed for retrieval (PR) problems. In addition, the rationality of MFRFT measurements is proved by theoretical explanations and simulated experiments. Through numerical simulations, we also demonstrate that TNNR-MFRFT outperforms current techniques. Phase retrieval (PR) problems aim to recover the phase from intensity measurements and are relevant in many applications such as X-ray crystallography and diffraction imaging. Most existing phase retrieval algorithms apply mask-based Fourier transform (FT) measurements to provide redundant information for signal reconstruction. This gives rise to a series of problems with masks such as the choice of suitable masks. In this work, we prove the rationality of multiple fractional Fourier transform (MFRFT) measurements, which can be applied to replace mask-based FT measurements. In addition, based on the low rank property (rank-1) of the desired matrix, we present a new low-rank model for PR problems using truncated nuclear norm regularization (TNNR), called TNNR-MFRFT. Extensive experiments validate the superiority of our approach over the state-of-the-art algorithms.
ISSN:0165-1684
1872-7557
DOI:10.1016/j.sigpro.2022.108601