Variational approaches to the estimation, regularizatinn and segmentation of diffusion tensor images

Diffusion magnetic resonance imaging probes and quantifies the anisotropic diffusion of water molecules in biological tissues, making it possible to non-invasively infer the architecture of the underlying structure. In this chapter, we present a set of new techniques for the robust estimation and regularization of diffusion tensor images (DTI) as well as a novel statistical framework for the segmentation of cerebral white matter structures from this type of dataset. Numerical experiments conducted on real diffusion weighted MRI illustrate the techniques and exhibit promising results.