Adaptive Weighted Total Variation boosted by learning techniques in few-view tomographic imaging
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866929679712124928 |
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| author | Morotti, Elena Evangelista, Davide Sebastiani, Andrea Piccolomini, Elena Loli |
| author_facet | Morotti, Elena Evangelista, Davide Sebastiani, Andrea Piccolomini, Elena Loli |
| contents | This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate approximation of the true image (or its gradient magnitude) through a neural network. Our approach operates without requiring prior knowledge of the noise intensity in the data and avoids the iterative recomputation of weights. Additionally, the paper includes a theoretical analysis of the proposed method, establishing its validity as a regularization approach. This framework integrates advanced neural network capabilities within a regularization context, thereby making the results of the networks interpretable. The results are promising as they enable high-quality reconstructions from limited-view tomographic measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09845 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive Weighted Total Variation boosted by learning techniques in few-view tomographic imaging Morotti, Elena Evangelista, Davide Sebastiani, Andrea Piccolomini, Elena Loli Numerical Analysis Optimization and Control This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate approximation of the true image (or its gradient magnitude) through a neural network. Our approach operates without requiring prior knowledge of the noise intensity in the data and avoids the iterative recomputation of weights. Additionally, the paper includes a theoretical analysis of the proposed method, establishing its validity as a regularization approach. This framework integrates advanced neural network capabilities within a regularization context, thereby making the results of the networks interpretable. The results are promising as they enable high-quality reconstructions from limited-view tomographic measurements. |
| title | Adaptive Weighted Total Variation boosted by learning techniques in few-view tomographic imaging |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2501.09845 |