Abstract:We investigate unpaired image inverse problems, a challenging setting where only independent, non-paired sets of noisy measurements and clean target signals are available for training. We propose a novel inverse problem solver based on Unbalanced Optimal Transport, called Unbalanced Optimal Transport Map for Inverse Problems (UOTIP). Our method formulates the reconstruction task, predicting clean target signals from noisy measurements, as learning a UOT Map from noisy measurement distribution to clean signal distribution by incorporating a likelihood-based cost function. By relaxing the exact marginal constraint, the UOT framework provides key advantages to our model: robustness to multi-level observation noise, adaptability to class imbalance between noisy and clean datasets, and generalizability to diverse noise-type scenarios. Furthermore, we theoretically demonstrate that incorporating a quadratic cost term ensures the existence and uniqueness of the transport map by satisfying the twist condition, even for ill-posed inverse problems. Our experiments demonstrate that UOTIP achieves state-of-the-art performance on unpaired image inverse problem benchmarks, across linear and nonlinear inverse problems.
| Comments: | Accepted at ICML 2026 |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.21094 [cs.LG] |
| (or arXiv:2605.21094v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.21094 arXiv-issued DOI via DataCite (pending registration) |
From: Jaewoong Choi [view email]
[v1]
Wed, 20 May 2026 12:25:26 UTC (8,781 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。