Diffusion tensor regularization with metric double integrals

Abstract In this paper, we propose a variational regularization method for denoising and inpainting of diffusion tensor magnetic resonance images. We consider these images as manifold-valued Sobolev functions, i.e. in an infinite dimensional setting, which are defined appropriately. The functionals double integrals, equivalent to semi-norms the Euclidean setting. extend analysis [14] concerning stability convergence methods by uniqueness result, apply them processing, validate our model numerical examples with synthetic real data.