Ground truth free denoising by optimal transport
Sören Dittmer, Carola‐Bibiane Schönlieb, Peter Maaß, Zentrum fr Technomathematik. FB 3 Mathematik und Informatik, Universität Bremen Postfach 330 440, 28344 Bremen, Germany · Numerical Algebra Control and Optimization · 2022
This paper proposes a new training strategy for a denoiser removing (additive) independent noise, with only as readily available data as possible and no further assumptions on the data nor noise. While every real-world measurement contains some noise, it seems that this problem remains unsolved for settings where clean data samples are lacking. We propose a pushforward operator formulation of an ideal denoiser and a corresponding GAN setup for training a denoiser ground truth free. The GAN trains solely on samples of noisy data and noise. In a series of denoising experiments in 1D and 2D, we demonstrate our training strategy's performance, which significantly improves the state-of-the-art of unsupervised denoising. Moreover, for some non-Gaussian noise, the method compares favorably even to naive supervised denoising.