Estimation of non-negative ODFs using the eigenvalue distribution of spherical functions

Authors:
Evan Schwab;Bijan Afsari;René Vidal
Affiliations:
Center for Imaging Science, Johns Hopkins University;Center for Imaging Science, Johns Hopkins University;Center for Imaging Science, Johns Hopkins University
Venue:
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Year:
2012

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Abstract

Current methods in high angular resolution diffusion imaging (HARDI) estimate the probability density function of water diffusion as a continuous-valued orientation distribution function (ODF) on the sphere. However, such methods could produce an ODF with negative values, because they enforce non-negativity only at finitely many directions. In this paper, we propose to enforce non-negativity on the continuous domain by enforcing the positive semi-definiteness of Toeplitz-like matrices constructed from the spherical harmonic representation of the ODF. We study the distribution of the eigenvalues of these matrices and use it to derive an iterative semi-definite program that enforces non-negativity on the continuous domain. We illustrate the performance of our method and compare it to the state-of-the-art with experiments on synthetic and real data.