Optimal Transport Based Unsupervised Restoration Learning Exploiting Degradation Sparsity

Optimal transport (OT) has recently been shown as a promising criterion for unsupervised restoration when no explicit prior model is available. Despite its theoretical appeal, OT still significantly falls short of supervised methods on challenging tasks such as super-resolution, deraining, and dehazing. In this paper, we propose a \emph{sparsity-aware optimal transport} (SOT) framework to bridge this gap by leveraging a key observation: the degradations in these tasks exhibit distinct sparsity in the frequency domain. Incorporating this sparsity prior into OT can significantly reduce the ambiguity of the inverse mapping for restoration and substantially boost performance. We provide analysis to show exploiting degradation sparsity benefits unsupervised restoration learning. Extensive experiments on real-world super-resolution, deraining, and dehazing demonstrate that SOT offers notable performance gains over standard OT, while achieving superior perceptual quality compared to existing supervised and unsupervised methods. In particular, SOT consistently outperforms existing unsupervised methods across all three tasks and narrows the performance gap to supervised counterparts.