Vectorial total variation regularisation of orientation distribution functions in diffusion weighted MRI

Authors:
Yuyuan Ouyang;Yunmei Chen;Ying Wu
Affiliations:
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA;Department of Mathematics, University of Florida, Gainesville, FL 32611, USA;Center for Advanced Imaging, Evanston Hospital, 2650 Ridge Avenue, Evanston, IL 60201, USA
Venue:
International Journal of Bioinformatics Research and Applications
Year:
2014

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Abstract

We propose a model for simultaneous Orientation Distribution Function ODF reconstruction and regularisation. The ODFs are represented by real spherical harmonic functions, and we propose to solve the spherical harmonic coefficients of the ODFs, with spatial regularisation by minimising the Vectorial Total Variation VTV of the coefficients. The proposed model also incorporates angular regularisation of the ODFs using Laplace-Beltrami operator on the unit sphere. A modified primal-dual hybrid gradient algorithm is applied to solve the model efficiently. The experimental results indicate better directional structures of reconstructed ODFs.