Phase retrieval of bandlimited functions for the wavelet transform
Abstract
We study the recovery of square-integrable signals from the absolute values of their wavelet transforms, also called wavelet phase retrieval. We present a new uniqueness result for wavelet phase retrieval. To be precise, we show that any wavelet with finitely many vanishing moments allows for the unique recovery of real-valued bandlimited signals up to global sign. Additionally, we present the first uniqueness result for sampled wavelet phase retrieval in which the underlying wavelets are allowed to be complex-valued and we present a uniqueness result for phase retrieval from sampled Cauchy wavelet transform measurements.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2020
- DOI:
- 10.48550/arXiv.2009.05029
- arXiv:
- arXiv:2009.05029
- Bibcode:
- 2020arXiv200905029A
- Keywords:
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- Mathematics - Functional Analysis
- E-Print:
- 18 pages