Parameter estimation and geometric fiber reconstruction from MR diffusion tensor images of the brain

The goal for the proposed project is to investigate mathematical and computational aspects of each step in the chain of DTI processing - from data acquisition to final reconstruction of gross fiber geometry in individual brains. We think this is a good project for a PhD candidate because it involves a succession of well-defined problem types (noise filtering; non-rigid spatial alignment of diffusion weighted image components; robust numerical estimation of a 3x3 diffusion tensor at each voxel; construction of a (smooth) 3-D vector field of principal diffusion directions; tissue segmentation from scalar maps of local diffusion anisotropy together with 3-D anatomical image data to constrain fiber tracking; geometric reconstruction and visualization of fiber bundles expressing brain connectivity). All these are essential parts of the overall goal, and must be solved satisfactory to provide a robust and practically useful tool in clinical medicine and in biomedical and neurocognitive research.