Workshop on Bioimaging II / PDEs, Fri, 23 Nov, 2007
Speaker: David Tschumperle
Abstract
We address the problem of processing high-angular resolution diffusion MRI images(also known as HARDI datasets). This kind of medical images allows to retrieve the water molecule diffusion in tissues, and indirectly gives valuable clues about the overall structure of the fibers map in the white matter of the brain.
In a first part, we focus on the classical 2nd-order tensor model and propose different variational formulations to estimate, regularize and visualize diffusion tensor maps, using PDE flows constrained on the natural tensor space.
In a second part, we consider model-free diffusion profiles (ODF), expressed as a set of spherical harmonics coefficients. We propose to estimate the ODFs volume directly from the raw HARDI data by minimizing a nonlinear energy functional which considers the MRI noise model as well as introduces regularity constraints on the estimated diffusion field. Both estimation methods are performed by a set of multi-valued partial differential equations
composed of both robust estimation and discontinuity-preserving regularization terms. Throughout the talk, we illustrate the role of the constraints introduced in these PDE flows, with real and synthetic MRI diffusion datasets.
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
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