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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2009.05029 |
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| _version_ | 1866917392082272256 |
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| author | Alaifari, Rima Bartolucci, Francesca Wellershoff, Matthias |
| author_facet | Alaifari, Rima Bartolucci, Francesca Wellershoff, Matthias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_05029 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Phase retrieval of bandlimited functions for the wavelet transform Alaifari, Rima Bartolucci, Francesca Wellershoff, Matthias Functional Analysis 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. |
| title | Phase retrieval of bandlimited functions for the wavelet transform |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2009.05029 |