Functional Multi-Reference Alignment via Deconvolution
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917506859401216 |
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| author | Al-Ghattas, Omar Little, Anna Sanz-Alonso, Daniel Sweeney, Mikhail |
| author_facet | Al-Ghattas, Omar Little, Anna Sanz-Alonso, Daniel Sweeney, Mikhail |
| contents | This paper studies the multi-reference alignment (MRA) problem of estimating a signal function from shifted, noisy observations. Our functional formulation reveals a new connection between MRA and deconvolution: the signal can be estimated from second-order statistics via Kotlarski's formula, an important identification result in deconvolution with replicated measurements. To design our MRA algorithms, we extend Kotlarski's formula to general dimension and study the estimation of signals with vanishing Fourier transform, thus also contributing to the deconvolution literature. We validate our deconvolution approach to MRA through both theory and numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12201 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functional Multi-Reference Alignment via Deconvolution Al-Ghattas, Omar Little, Anna Sanz-Alonso, Daniel Sweeney, Mikhail Information Theory Signal Processing Statistics Theory This paper studies the multi-reference alignment (MRA) problem of estimating a signal function from shifted, noisy observations. Our functional formulation reveals a new connection between MRA and deconvolution: the signal can be estimated from second-order statistics via Kotlarski's formula, an important identification result in deconvolution with replicated measurements. To design our MRA algorithms, we extend Kotlarski's formula to general dimension and study the estimation of signals with vanishing Fourier transform, thus also contributing to the deconvolution literature. We validate our deconvolution approach to MRA through both theory and numerical experiments. |
| title | Functional Multi-Reference Alignment via Deconvolution |
| topic | Information Theory Signal Processing Statistics Theory |
| url | https://arxiv.org/abs/2506.12201 |