Estimation, Smoothing, and Charaterization of Appranet Diffusion 
Coefficient Profiles from High Angular Resolution DWI


Abstract:
We present a new variational framework for simultaneous smoothing and 
estimation of the apparent diffusion coefficient (ADC) profiles from high 
angular resolution Diffusion-Weighted (HARD) MRI. Our model approximates 
the ADC profiles at each voxel by a 4th order spherical harmonic series (SHS).
The coefficients of the SHS at each voxel are obtained by solving a 
constrained variational problem. The energy function for this problem consists
of two parts. One part is the $L^{p(x)}$ norm of the gradients of these 
coefficients, where $p(x)$ is designed such that the regularization preserves 
relevant features in these coefficients. The other part is the data fidelity 
term, which is based on the original Stejskal-tanner equation instead of its 
linearzed version usually employed in literature.
The antipodal symmetry and positiveness of the ADC are  accommodated in the 
model and constraint. We use these coefficients and the variance of the ADC 
profile against its mean to classify the diffusion at each voxel as isotropic,
single fiber, and two fibers. 

The proposed model has been applied to simulated  and HARD data from normal 
human brains. The experimental results showed the effectiveness of the model 
in the estimation of  ADC profiles and the enhancement of anisotropy of the 
diffusion. The characterization of non-Gaussian diffusion from the proposed 
method is consistent with the known fiber anatomy.