Optimal Transport for Unsupervised Denoising Learning

TL;DR

This paper introduces a novel unsupervised denoising criterion based on optimal transport theory, which effectively preserves signal information and achieves high perceptual quality without prior noise model assumptions.

Contribution

It proposes an optimal transport-based criterion for unsupervised denoising that matches the solution of the constrained formulation and works well across various real-world noisy data.

Findings

Achieves near-supervised PSNR on synthetic and real data.

Outperforms supervised methods in perceptual quality and PSNR on microscopy images.

Excels in complex noise scenarios like raw depth images.

Abstract

Recently, much progress has been made in unsupervised denoising learning. However, existing methods more or less rely on some assumptions on the signal and/or degradation model, which limits their practical performance. How to construct an optimal criterion for unsupervised denoising learning without any prior knowledge on the degradation model is still an open question. Toward answering this question, this work proposes a criterion for unsupervised denoising learning based on the optimal transport theory. This criterion has favorable properties, e.g., approximately maximal preservation of the information of the signal, whilst achieving perceptual reconstruction. Furthermore, though a relaxed unconstrained formulation is used in practical implementation, we prove that the relaxed formulation in theory has the same solution as the original constrained formulation. Experiments on synthetic and real-world data, including realistic photographic, microscopy, depth, and raw depth images, demonstrate that the proposed method even compares favorably with supervised methods, e.g., approaching the PSNR of supervised methods while having better perceptual quality. Particularly, for spatially correlated noise and realistic microscopy images, the proposed method not only achieves better perceptual quality but also has higher PSNR than supervised methods. Besides, it shows remarkable superiority in harsh practical conditions with complex noise, e.g., raw depth images. Code is available at https://github.com/wangweiSJTU/OTUR.