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Phase retrieval from intensity difference of linear canonical transform

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Abstract

The chirp-modulated shift-invariant space (CMSIS) is of interest in the linear canonical transform (LCT) based sampling theory. In this paper, we investigate the phase retrieval (PR) problem for the causal signals in CMSIS generated by \(\hbox {sinc}\) function. Unlike the traditional PR model, the measurement we use is the intensity difference of the LCT (IDLCT) but not the LCT intensity. The requirement for IDLCT measurement is weaker than that for intensity measurement. Such an IDLCT perspective is motivated by the famous PR model: the transport of intensity equation. It is revealed that the phase retrievability depends on both the LCT parameter matrix and the maximum gap of the target signal. From this, a necessary and sufficient condition for PR is established. Additionally, a sequence of sampling intervals are designed such that the PR can be achieved by the corresponding IDLCT measurements. Numerical simulations are conducted to check the correctness of the main results.

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Acknowledgements

The authors thank the reviewers for their suggestions which improve the presentation of the paper. Youfa Li is partially supported by Natural Science Foundation of China (Nos: 61961003, 61561006, 11501132), Natural Science Foundation of Guangxi (Nos: 2018JJA110110, 2016GXNSFAA380049) and the talent project of Education Department of Guangxi Government for Young-Middle-Aged backbone teachers

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Authors and Affiliations

  1. College of Mathematics and Information Science, Guangxi University, Nanning, China

    Youfa Li, Guangde Wu & Ganji Huang

  2. College of Education, Nanning University, Nanning, China

    Yanfen Huang

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  1. Youfa Li
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  2. Guangde Wu
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  3. Yanfen Huang
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  4. Ganji Huang
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Correspondence to Guangde Wu.

Additional information

Communicated by Dachun Yang.

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Li, Y., Wu, G., Huang, Y. et al. Phase retrieval from intensity difference of linear canonical transform. Banach J. Math. Anal. 18, 3 (2024). https://doi.org/10.1007/s43037-023-00307-9

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