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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.03807 |
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| _version_ | 1866908860633055232 |
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| author | Chen, Yang Cheng, Cheng |
| author_facet | Chen, Yang Cheng, Cheng |
| contents | Conjugate phase retrieval considers the recovery of a function, up to a unimodular constant and conjugation, from its phaseless measurements. In this paper, we explore the conjugate phase retrieval in a shift-invariant space generated by a Gaussian funciton. First, we show that the modulus function in the Gaussian shift-invariant space can be determined from the phaseless Hermite samples taken on a discrete sampling set. We then show that a function in the shift-invariant space generated by a Gaussian can be uniquely determined, up to a unimodular constant and conjugation, from its phaseless Hermite samples on a discrete set. For the functions with finite coefficient sequences, we provide an explicit reconstruction procedure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03807 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conjugate phase retrieval in shift-invariant spaces generated by a Gaussian Chen, Yang Cheng, Cheng Functional Analysis Conjugate phase retrieval considers the recovery of a function, up to a unimodular constant and conjugation, from its phaseless measurements. In this paper, we explore the conjugate phase retrieval in a shift-invariant space generated by a Gaussian funciton. First, we show that the modulus function in the Gaussian shift-invariant space can be determined from the phaseless Hermite samples taken on a discrete sampling set. We then show that a function in the shift-invariant space generated by a Gaussian can be uniquely determined, up to a unimodular constant and conjugation, from its phaseless Hermite samples on a discrete set. For the functions with finite coefficient sequences, we provide an explicit reconstruction procedure. |
| title | Conjugate phase retrieval in shift-invariant spaces generated by a Gaussian |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2412.03807 |