We present a new variational framework for recovery of apparent diffusion coefficient (ADC) from High Angular Resolution Diffusion-weighted (HARD) MRI. The model approximates the ADC profiles by a 4th order spherical harmonic series (SHS), whose coefficients are obtained by solving a constrained minimization problem. By minimizing the energy functional, the ADC profiles are estimated and regularized simultaneously across the entire volume. In this model, feature preserving smoothing is achieved by minimizing a non-standard growth functional, and the estimation is based on the original Stejskal-Tanner equation. The antipodal symmetry and positiveness of the ADC are also accommodated into the model. Furthermore, coefficients of the SHS and the variance of ADC profiles from its mean are used to characterize the diffusion anisotropy. The effectiveness of the proposed model is depicted via application to both simulated and HARD MRI human brain data. The characterization of non-Gaussian diffusion based on the proposed model showed consistency with known neuroanatomy.