Convolutional dynamical sampling and some new results
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913417208528896 |
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| author | Huang, Longxiu Neuman, A. Martina Tang, Sui Xie, Yuying |
| author_facet | Huang, Longxiu Neuman, A. Martina Tang, Sui Xie, Yuying |
| contents | In this work, we explore the dynamical sampling problem on $\ell^2(\mathbb{Z})$ driven by a convolution operator defined by a convolution kernel. This problem is inspired by the need to recover a bandlimited heat diffusion field from space-time samples and its discrete analogue. In this book chapter, we review recent results in the finite-dimensional case and extend these findings to the infinite-dimensional case, focusing on the study of the density of space-time sampling sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15122 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convolutional dynamical sampling and some new results Huang, Longxiu Neuman, A. Martina Tang, Sui Xie, Yuying Information Theory In this work, we explore the dynamical sampling problem on $\ell^2(\mathbb{Z})$ driven by a convolution operator defined by a convolution kernel. This problem is inspired by the need to recover a bandlimited heat diffusion field from space-time samples and its discrete analogue. In this book chapter, we review recent results in the finite-dimensional case and extend these findings to the infinite-dimensional case, focusing on the study of the density of space-time sampling sets. |
| title | Convolutional dynamical sampling and some new results |
| topic | Information Theory |
| url | https://arxiv.org/abs/2406.15122 |