Analysis & Applied Math

Denoising – the removal of noise from measurements – is a fundamental inverse problem across the experimental sciences. One aims to find the denoised data that, once passed through the noise model, best matches the measured data under a chosen loss function.

In this talk, we present recent work concerning a Wasserstein loss. We establish sharp conditions for the existence and uniqueness of optimizers, answering open questions of Li et al. regarding well-posedness for a class of noise models. We then develop a provably convergent generalized Sinkhorn algorithm to compute approximate optimizers. Numerical experiments show that our optimal transport approach offers robust, accurate performance compared to Richardson-Lucy deconvolution for Kullback-Leibler loss, the dominant method in particle physics applications.

Joint work with K. Craig and B. Nachman.