UOTIP learns an unbalanced optimal transport map from noisy to clean distributions for unpaired inverse problems, incorporating a likelihood cost and proving existence/uniqueness via quadratic cost satisfying the twist condition.
arXiv preprint arXiv:2410.02628 , year=
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The paper establishes existence, uniqueness up to equivalence, and stability for inverse optimal transport with Bregman regularization under cost-matrix assumptions, and gives an efficient BCD algorithm with linear convergence and element-wise Newton updates for quadratic penalties.
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UOTIP: Unbalanced Optimal Transport Map for Unpaired Inverse Problems
UOTIP learns an unbalanced optimal transport map from noisy to clean distributions for unpaired inverse problems, incorporating a likelihood cost and proving existence/uniqueness via quadratic cost satisfying the twist condition.
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Well-Posedness and Efficient Algorithms for Inverse Optimal Transport with Bregman Regularization
The paper establishes existence, uniqueness up to equivalence, and stability for inverse optimal transport with Bregman regularization under cost-matrix assumptions, and gives an efficient BCD algorithm with linear convergence and element-wise Newton updates for quadratic penalties.