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

Authors: Yuyuan Ouyang; Yunmei Chen; Ying Wu

Addresses: 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

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.

Keywords: diffusion-weighted MRI; magnetic resonance imaging; orientation distribution function; vectorial total variation; primal-dual hybrid gradient; spherical harmonic coefficients; spatial regularisation.

DOI: 10.1504/IJBRA.2014.058781

International Journal of Bioinformatics Research and Applications, 2014 Vol.10 No.1, pp.110 - 127

Published online: 22 Oct 2014 *

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