Ground truth free denoising by optimal transport

This paper proposes a new training strategy for a denoiser re-moving (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 push -forward operator formulation of an ideal denoiser and a corresponding GAN setup for training a denoiser ground truth free. The GAN trains solely on sam-ples 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.