Bispectrum Unbiasing for Dilation-Invariant Multi-reference Alignment
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909116603039744 |
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| author | Yin, Liping Little, Anna Hirn, Matthew |
| author_facet | Yin, Liping Little, Anna Hirn, Matthew |
| contents | Motivated by modern data applications such as cryo-electron microscopy, the goal of classic multi-reference alignment (MRA) is to recover an unknown signal $f: \mathbb{R} \to \mathbb{R}$ from many observations that have been randomly translated and corrupted by additive noise. We consider a generalization of classic MRA where signals are also corrupted by a random scale change, i.e. dilation. We propose a novel data-driven unbiasing procedure which can recover an unbiased estimator of the bispectrum of the unknown signal, given knowledge of the dilation distribution. Lastly, we invert the recovered bispectrum to achieve full signal recovery, and validate our methodology on a set of synthetic signals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14276 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bispectrum Unbiasing for Dilation-Invariant Multi-reference Alignment Yin, Liping Little, Anna Hirn, Matthew Signal Processing Information Theory Motivated by modern data applications such as cryo-electron microscopy, the goal of classic multi-reference alignment (MRA) is to recover an unknown signal $f: \mathbb{R} \to \mathbb{R}$ from many observations that have been randomly translated and corrupted by additive noise. We consider a generalization of classic MRA where signals are also corrupted by a random scale change, i.e. dilation. We propose a novel data-driven unbiasing procedure which can recover an unbiased estimator of the bispectrum of the unknown signal, given knowledge of the dilation distribution. Lastly, we invert the recovered bispectrum to achieve full signal recovery, and validate our methodology on a set of synthetic signals. |
| title | Bispectrum Unbiasing for Dilation-Invariant Multi-reference Alignment |
| topic | Signal Processing Information Theory |
| url | https://arxiv.org/abs/2402.14276 |