Title: UOTIP: Unbalanced Optimal Transport Map for Unpaired Inverse Problems
Primary area: generative models
Keywords: Optimal transport, Unbalanced optimal transport, Inverse problem

Abstract: We address the problem of unpaired image inverse problems, where only independent sets of noisy measurements and clean target signals are available. 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. Moreover, with a quadratic cost formulation, our model effectively handles linear inverse problems with unknown corruption operators. Our experiments show that our model achieves state-of-the-art performance on unpaired image inverse problem benchmarks, across linear (super-resolution and Gaussian deblurring) and nonlinear (high dynamic range reconstruction and nonlinear deblurring) inverse problems.

TL;DR: We propose a novel approach for unpaired image inverse problems based on Unbalanced Optimal Transport (UOT).