Vectorial total variation regularisation of orientation distribution functions in diffusion weighted MRI.
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.
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA.
Yuyuan
Y
Ouyang
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA.
Yunmei
Y
Chen
Center for Advanced Imaging, Evanston Hospital, 2650 Ridge Avenue, Evanston, IL 60201, USA.
Ying
Y
Wu
D000465:Algorithms; D001369:Axons / Q000648:ultrastructure*; D001921:Brain / Q000648:ultrastructure*; D003627:Data Interpretation, Statistical; D056324:Diffusion Tensor Imaging / Q000379:methods*; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D009413:Nerve Fibers, Myelinated / Q000648:ultrastructure*; D010363:Pattern Recognition, Automated / Q000379:methods*; D016008:Statistical Distributions
diffusion–weighted MRI; magnetic resonance imaging; orientation distribution function; primal–dual hybrid gradient; spatial regularisation; spherical harmonic coefficients; vectorial total variation