GROUND TRUTH FREE DENOISING BY OPTIMAL TRANSPORT

Abstract

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 realworld 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.