WPPNets and WPPFlows: The Power of Wasserstein Patch Priors for Superresolution

TL;DR

This paper introduces WPPNets, a novel neural network approach leveraging Wasserstein patch priors for efficient image superresolution, with added uncertainty quantification via normalizing flows, outperforming traditional methods.

Contribution

It proposes an unsupervised learning framework for superresolution using Wasserstein patch priors with CNNs and normalizing flows, improving efficiency and uncertainty estimation.

Findings

WPPNets achieve high-quality superresolution across various image classes.

The method is computationally efficient once trained.

Uncertainty quantification is effectively integrated.

Abstract

Exploiting image patches instead of whole images have proved to be a powerful approach to tackle various problems in image processing. Recently, Wasserstein patch priors (WPP), which are based on the comparison of the patch distributions of the unknown image and a reference image, were successfully used as data-driven regularizers in the variational formulation of superresolution. However, for each input image, this approach requires the solution of a non-convex minimization problem which is computationally costly. In this paper, we propose to learn two kind of neural networks in an unsupervised way based on WPP loss functions. First, we show how convolutional neural networks (CNNs) can be incorporated. Once the network, called WPPNet, is learned, it can be very efficiently applied to any input image. Second, we incorporate conditional normalizing flows to provide a tool for uncertainty quantification. Numerical examples demonstrate the very good performance of WPPNets for superresolution in various image classes even if the forward operator is known only approximately.