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