Diffusion MRI provides an insight into the microstructural architecture of tissue by observing the restricted and hindered displacement of water molecules undergoing Brownian motion in vivo. By looking at the probability density function p of displacements over a fixed period of time t, inferences can be made about the tissue microstructure. In some regions of the brain, the barriers to diffusion have no preferred orientation, resulting in isotropic diffusion. An example of an isotropic region in the brain are the ventricles which contain cerebrospinal fluid. As there are few barriers to water molecule mobility, water displacement is equally likely in all directions.
Grey matter consists of dense tissue containing many barriers to water mobility, such as cell walls and membranes. However, the barriers in grey matter often have no preferred orientation and so hinder the water displacement equally in all directions. In white matter regions of the brain, water molecules are constrained by organised fibrous structure. Water molecules in white matter (such as the pyramidal tracts and the corpus callosum) move on average further along fibres than across them.
In this paper, we present a new regularized super-resolution method for finding accurate fibre orientations and volume fractions of fibre populations on a sub-voxel scale from a 3D diffusion MRI acquisition in order to distinguish between various fibre configurations such as fanning and bending, and ameliorate partial volume effects. We treat this task as a general inverse problem, which we solve by regularization and optimization, and demonstrate the method on human brain data.