DT-MRI Images: Estimation, Regularization, and Application

Diffusion-Tensor MRI is a technique allowing the measurement of the water molecule motion in the tissues fibers, by the mean of rendering multiple MRI images under different oriented magnetic fields. This large set of raw data is then further estimated into a volume of diffusion tensors (i.e. 3 × 3 symmetric and positive-definite matrices) that describe through their spectral elements, the diffusivities and the main directions of the tissues fibers. We address two crucial issues encountered for this process : diffusion tensor estimation and regularization. After a review on existing algorithms, we propose alternative variational formalisms that lead to new and improved results, thanks to the introduction of important tensor constraint priors (positivity, symmetry) in the considered schemes. We finally illustrate how our set of techniques can be applied to enhance fiber tracking in the white matter of the brain.