ISUM: Inverse Problem Solver via Unbalanced Optimal Transport Map

Solving unpaired inverse problems is critical in many applications where paired noisy measurements and clean targets are unavailable. We propose a novel approach for unpaired image inverse problems based on Unbalanced Optimal Transport (UOT). Our method formulates reconstruction as learning a transport map from noisy measurements to clean images, leveraging a likelihood-based cost function. By relaxing the strict marginal-matching constraint via UOT, our model enhances its robustness to multi-level observation noise. Moreover, under a quadratic cost function, our model effectively addresses linear inverse problems with unknown corruption operators. Our experiments demonstrate that our model achieves state-of-the-art performance on both linear (Gaussian deblurring and super-resolution) and nonlinear (high dynamic range reconstruction and nonlinear deblurring) image inverse problems.