A Generic Neighbourhood Filtering Framework for Matrix Fields

The Nonlocal Data and Smoothness (NDS) filtering framework for greyvalue images has been recently proposed by Mrázek et al. This model for image denoising unifies M-smoothing and bilateral filtering, and several well-known nonlinear filters from the literature become particular cases. In this article we extend this model to so-called matrix fields. These data appear, for example, in diffusion tensor magnetic 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. Experiments performed with synthetic matrix fields and real DT-MRI data showed excellent performance with respect to restoration quality as well as speed of convergence.