This dissertation introduces a transport-based framework for unpaired image restoration using Unbalanced Optimal Transport. The approach reformulates restoration as learning a transport map between the distributions of noisy measurements and clean target signals using a modified UOT formulation that reflects the statistical structure of real measurement processes. A theoretical analysis establishes the existence and uniqueness of the resulting transport map under this modified formulation. Experiments across diverse restoration tasks show that the framework achieves superior performance compared to prior methods. This work demonstrates that unbalanced transport theory provides a principled and effective foundation for addressing real-world unpaired image restoration problems.

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