ODF reconstruction in Q-ball imaging with solid angle consideration

Authors:
Iman Aganj;Christophe Lenglet;Guillermo Sapiro
Affiliations:
Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN;Department of Electrical and Computer Engineering and Center for Magnetic Resonance Research, University of Minnesota, Minneapolis, MN;Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN
Venue:
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
Year:
2009

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Abstract

Q-ball imaging (QBI) is a high angular resolution diffusion imaging (HARDI) technique which has been proven very successful in resolving multiple intravoxel fiber orientations in MR images. The standard computation of the orientation distribution function (ODF, the probability of diffusion in a given direction) from q-ball uses linear radial projection, neglecting the change in the volume element along the ray, thereby resulting in distributions different from the true ODFs. For instance, they are not normalized or as sharp as expected, and generally require post-processing, such as sharpening or spherical deconvolution. In this paper, we consider the mathematically correct definition of the ODF and derive a closed-form expression for it in QBI. The derived ODF is dimensionless and normalized, and can be efficiently computed from q-ball acquisition protocols. We describe our proposed method and demonstrate its significantly improved performance on artificial data and real HARDI volumes.