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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.21022 |
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| _version_ | 1866913760997801984 |
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| author | Casper, W. Riley Orozco, Bobby |
| author_facet | Casper, W. Riley Orozco, Bobby |
| contents | The higher-order autocorrelations of integer-valued or rational-valued gridded data sets appear naturally in X-ray crystallography, and have applications in computer vision systems, correlation tomography, correlation spectroscopy, and pattern recognition. In this paper, we consider the problem of reconstructing a gridded data set from its higher-order autocorrelations. We describe an explicit reconstruction algorithm, and prove that the autocorrelations up to order 3r + 3 are always sufficient to determine the data up to translation, where r is the dimension of the grid. We also provide examples of rational-valued gridded data sets which are not determined by their autocorrelations up to order 3r + 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21022 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reconstructing Gridded Data from Higher Autocorrelations Casper, W. Riley Orozco, Bobby Computer Vision and Pattern Recognition Group Theory Data Analysis, Statistics and Probability 20K01, 68T45, 68T10 The higher-order autocorrelations of integer-valued or rational-valued gridded data sets appear naturally in X-ray crystallography, and have applications in computer vision systems, correlation tomography, correlation spectroscopy, and pattern recognition. In this paper, we consider the problem of reconstructing a gridded data set from its higher-order autocorrelations. We describe an explicit reconstruction algorithm, and prove that the autocorrelations up to order 3r + 3 are always sufficient to determine the data up to translation, where r is the dimension of the grid. We also provide examples of rational-valued gridded data sets which are not determined by their autocorrelations up to order 3r + 2. |
| title | Reconstructing Gridded Data from Higher Autocorrelations |
| topic | Computer Vision and Pattern Recognition Group Theory Data Analysis, Statistics and Probability 20K01, 68T45, 68T10 |
| url | https://arxiv.org/abs/2503.21022 |