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We present a new variational framework for simultaneous smoothing and estimation of apparent diffusion coefficient (ADC) profiles from High Angular Resolution Diffusion-weighted MRI. The model approximates the ADC profiles at each voxel by a 4th order spherical harmonic series (SHS). The coefficients in SHS are obtained by solving a constrained minimization problem. The smoothing with feature preserved is achieved by minimizing a variable exponent, linear growth functional, and the data constraint is determined by the original Stejskal-Tanner equation.  The antipodal symmetry and positiveness of the ADC are accommodated  in the model. We use these coefficients  and variance of the ADC profiles from its mean to classify the  diffusion in each voxel as isotropic, anisotropic with single  fiber orientation, or two fiber orientations.  The proposed model has been applied to both simulated data and  HARD MRI human brain data . The experiments  demonstrated the effectiveness of our method in estimation and  smoothing of ADC profiles and in enhancement of diffusion anisotropy.  Further characterization of non-Gaussian diffusion based on the proposed  model showed a consistency between our results and known neuroanatomy.

A nonstandard smoothing in reconstruction of apparent diffusion coefficient profiles from diffusion weighted images