Nonlinear filtering of magnetic resonance tomograms by geometry-driven diffusion

The paper deals with a nonuniform diffusion filtering of magnetic resonance (MR) tomograms. Alternative digital schemes for discrete implementation of the nonuniform diffusion equations are analyzed and tested. A novel locally adaptive conductance for the geometry-driven diffusion (GDD) filtering is proposed. It is based on a measure of the neighborhood unhomogeneity adopted from the optimal orientation detection of linear symmetry. The algorithm performance is evaluated on the basis of pseudoartificial 2D MR brain phantom and using the signal-to-noise ratio, as well as HC measure, developed for image discrimination characterization. Three filtering methods are applied to MR images acquired by the fast 3D FLASH sequence. The results obtained are quantitatively and visually compared and discussed.