Phaseless Signal Recovery in Infinite Dimensional Spaces Using Structured Modulations
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This paper considers the recovery of continuous signals in infinite dimensional spaces from the magnitude of their frequency samples. It proposes a sampling scheme which involves a combination of oversampling and modulations with complex exponentials. Sufficient conditions are given such that almost every signal with compact support can be reconstructed up to a unimodular constant using only its magnitude samples in the frequency domain. Finally it is shown that an average sampling rate of four times the Nyquist rate is enough to reconstruct almost every time-limited signal.
KeywordsBernstein spaces Interpolation Phase retrieval Sampling Signal reconstruction
Mathematics Subject ClassificationPrimary 30D10 94A20 Secondary 42C15 94A12
This work was partly supported by the German Research Foundation (DFG) under Grant PO 1347/2-1 and BO 1734/22-1.
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