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arXiv · 2009.05029

Phase retrieval of bandlimited functions for the wavelet transform

Rima Alaifari·Francesca Bartolucci·Matthias Wellershoff
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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.

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Rima Alaifari, Francesca Bartolucci, Matthias Wellershoff. 2021-11-05. Phase retrieval of bandlimited functions for the wavelet transform. https://doi.org/10.1016/j.acha.2023.01.002

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