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Real phase retrieval from unordered partial frame coefficients

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Abstract

We study the signal recovery from unordered partial phaseless frame coefficients. To this end, we introduce the concepts of m-erasure (almost) phase retrievable frames. We show that with an m-erasure (almost) phase retrievable frame, it is possible to reconstruct (almost) all n-dimensional real signals up to a sign from their arbitrary N − m unordered phaseless frame coefficients, where N stands for the element number of the frame. We give necessary and sufficient conditions for a frame to be m-erasure (almost) phase retrievable. Moreover, we give an explicit construction of such frames based on prime numbers.

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Acknowledgements

The authors thank the referees very much for carefully reading the paper and for elaborate and valuable suggestions.

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Authors and Affiliations

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China

    Fusheng Lv & Wenchang Sun

Authors
  1. Fusheng Lv
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  2. Wenchang Sun
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Correspondence to Wenchang Sun.

Additional information

Communicated by: Gitta Kutyniok

This work was partially supported by the National Natural Science Foundation of China (11371200, 11525104 and 11531013).

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Lv, F., Sun, W. Real phase retrieval from unordered partial frame coefficients. Adv Comput Math 44, 879–896 (2018). https://doi.org/10.1007/s10444-017-9566-4

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  • DOI: https://doi.org/10.1007/s10444-017-9566-4

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