MVIRT, a toolbox for manifold-valued image restoration

In many real life application measured data takes its values on Riemannian manifolds. For the special case of the Euclidean space this setting includes the classical grayscale and color images. Like these classical images, manifold-valued data might suffer from measurement errors in form of noise or missing data. In this paper we present the manifold-valued image restoration toolbox (MVIRT) that provides implementations of classical image processing tasks. Based on recent developments in variational methods for manifold-valued image processing methods, like total variation regularization, the toolbox provides easy access to work with these algorithms. The toolbox is implemented in Matlab, open source, and easily extendible, e.g. with own manifolds, noise models or further algorithms. This paper introduces the main mathematical methods as well as numerical examples.