Point source localisation with unbalanced optimal transport
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916619150688256 |
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| author | Valkonen, Tuomo |
| author_facet | Valkonen, Tuomo |
| contents | Replacing the quadratic proximal penalty familiar from Hilbert spaces by an unbalanced optimal transport distance, we develop forward-backward type optimisation methods in spaces of Radon measures. We avoid the actual computation of the optimal transport distances through the use of transport three-plans and the rough concept of transport subdifferentials. The resulting algorithm has a step similar to the sliding heuristics previously introduced for conditional gradient methods, however, now non-heuristically derived from the geometry of the space. We demonstrate the improved numerical performance of the approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12417 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Point source localisation with unbalanced optimal transport Valkonen, Tuomo Optimization and Control Replacing the quadratic proximal penalty familiar from Hilbert spaces by an unbalanced optimal transport distance, we develop forward-backward type optimisation methods in spaces of Radon measures. We avoid the actual computation of the optimal transport distances through the use of transport three-plans and the rough concept of transport subdifferentials. The resulting algorithm has a step similar to the sliding heuristics previously introduced for conditional gradient methods, however, now non-heuristically derived from the geometry of the space. We demonstrate the improved numerical performance of the approach. |
| title | Point source localisation with unbalanced optimal transport |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2502.12417 |