UOTIP: Unbalanced Optimal Transport Map for Unpaired Inverse Problems

2026-05-20

AI Summary

This work addresses unpaired image inverse problems, where only unpaired noisy measurements and clean target signals are available, by proposing a reconstruction method grounded in unbalanced optimal transport (UOT). The approach introduces a likelihood-guided quadratic cost function and relaxes marginal constraints, yielding a transport map that is theoretically guaranteed to exist and be unique. This formulation enhances robustness and generalization across multi-level noise, class imbalance, and diverse noise types. Empirical evaluations demonstrate that the proposed method achieves state-of-the-art performance on multiple benchmarks encompassing both linear and nonlinear unpaired image inverse problems.

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.

Problem

• unpaired inverse problems
• image reconstruction
• noisy measurements
• clean target signals
• unbalanced optimal transport

Innovation

• Unbalanced Optimal Transport
• Unpaired Inverse Problems
• Transport Map
• Likelihood-based Cost
• Twist Condition