Abstract

The Nonlocal Data and Smoothness (NDS) filtering frame- work for greyvalue images has been recently proposed by Mr?zek et al. This model for image denoising unifies M-smoothing and bilateral fil- tering, and several well-known nonlinear filters from the literature be- come particular cases. In this article we extend this model to so-called matrix fields. These data appear, for example, in diffusion tensor mag- netic resonance imaging (DT-MRI). Our matrix-valued NDS framework includes earlier filters developped for DT-MRI data, for instance, the affine-invariant and the log-Euclidean regularisation of matrix fields. Ex- periments performed with synthetic matrix fields and real DT-MRI data showed excellent performance with respect to restoration quality as well as speed of convergence.