Wasserstein Patch Prior for Image Superresolution

Many recent superresolution methods are based on supervised learning. That means, that they require a large database of pairs of high- and low-resolution images as training data. However, for many applications, acquiring registered pairs of high and low resolution data or even imaging a large area with a high resolution is unrealistic. To overcome this problem, we introduce a Wasserstein patch prior for unsupervised superresolution of two- and three-dimensional images. In addition to the low-resolution observation, our method only requires one, possibly small, reference image which has a similar patch distribution as the high resolution ground truth. This assumption can e.g. be fulfilled when working with texture images or images of homogeneous material microstructures. The proposed regularizer penalizes the Wasserstein-2-distance of the patch distributions within the reconstruction and the reference image at different scales. We demonstrate the performance of the proposed method by applying it to two- and three-dimensional images of materials' microstructures.