Diffusion tensor magnetic resonance image regularization

As multi-dimensional complex data become more common, new regularization schemes tailored to those data are needed. In this paper we present a scheme for regularising diffusion tensor magnetic resonance (DT-MR) data, and more generally multi-dimensional data defined by a direction map and one or several magnitude maps. The scheme is divided in two steps. First, a variational method is proposed to restore direction fields with preservation of discontinuities. Its theoretical aspects are presented, as well as its application to the direction field that defines the main orientation of the diffusion tensors. The second step makes use of an anisotropic diffusion process to regularize the magnitude maps. The main idea is that for a range of data it is possible to use the restored direction as a prior to drive the regularization process in a way that preserves discontinuities and respects the local coherence of the magnitude map. We show that anisotropic diffusion is a convenient framework to implement that idea, and define a regularization process for the magnitude maps from our DT-MR data. Both steps are illustated on synthetic and real diffusion tensor magnetic resonance data.