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arXiv · 2502.12417

Point source localisation with unbalanced optimal transport

Tuomo Valkonen
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Abstract

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.

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Tuomo Valkonen. 2025-02-18. Point source localisation with unbalanced optimal transport. https://arxiv.org/abs/2502.12417

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