Estimating Orientation Distribution Functions with Probability Density Constraints and Spatial Regularity

Authors:
Alvina Goh;Christophe Lenglet;Paul M. Thompson;René Vidal
Affiliations:
CIS and Dept. of Biomedical Engineering, Johns Hopkins University,;CMRR and Dept. of Electrical and Computer Engineering, University of Minnesota,;LONI and Dept. of Neurology, University of California at Los Angeles,;CIS and Dept. of Biomedical Engineering, Johns Hopkins University,
Venue:
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part I
Year:
2009

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Abstract

High angular resolution diffusion imaging (HARDI) has become an important magnetic resonance technique for in vivo imaging. Current techniques for estimating the diffusion orientation distribution function (ODF), i.e., the probability density function of water diffusion along any direction, do not enforce the estimated ODF to be nonnegative or to sum up to one. Very often this leads to an estimated ODF which is not a proper probability density function. In addition, current methods do not enforce any spatial regularity of the data. In this paper, we propose an estimation method that naturally constrains the estimated ODF to be a proper probability density function and regularizes this estimate using spatial information. By making use of the spherical harmonic representation, we pose the ODF estimation problem as a convex optimization problem and propose a coordinate descent method that converges to the minimizer of the proposed cost function. We illustrate our approach with experiments on synthetic and real data.