Fiber Enhancement in Diffusion-Weighted MRI

Diffusion-Weighted MRI (DW-MRI) measures local water diffusion in biological tissue, which reflects the underlying fiber structure. In order to enhance the fiber structure in the DW-MRI data we consider both (convection-)diffusions and Hamilton-Jacobi equations (erosions) on the space R o S of 3D-positions and orientations, embedded as a quotient in the group SE(3) of 3D-rigid body movements. These leftinvariant evolutions are expressed in the frame of left-invariant vector fields on SE(3), which serves as a moving frame of reference attached to fiber fragments. The linear (convection-)diffusions are solved by a convolution with the corresponding Green’s function, whereas the HamiltonJacobi equations are solved by a morphological convolution with the corresponding Green’s function. Furthermore, we combine dilation and diffusion in pseudo-linear scale spaces on R o S. All methods are tested on DTI-images of the brain. These experiments indicate that our techniques are useful to deal with both the problem of limited angular resolution of DTI and the problem of spurious, non-aligned crossings in HARDI.