SR-HARDI: Spatially Regularizing High Angular Resolution Diffusion Imaging.

High angular resolution diffusion imaging (HARDI) has recently been of great interest in mapping the orientation of intra-voxel crossing fibers, and such orientation information allows one to infer the connectivity patterns prevalent among different brain regions and possible changes in such connectivity over time for various neurodegenerative and neuropsychiatric diseases. The aim of this paper is to propose a penalized multi-scale adaptive regression model (PMARM) framework to spatially and adaptively infer the orientation distribution function (ODF) of water diffusion in regions with complex fiber configurations. In PMARM, we reformulate the HARDI imaging reconstruction as a weighted regularized least-squares regression (WRLSR) problem. Similarity and distance weights are introduced to account for spatial smoothness of HARDI, while preserving the unknown discontinuities (e.g., edges between white matter and grey matter) of HARDI. The L ₁ penalty function is introduced to ensure the sparse solutions of ODFs, while a scaled L ₁ weighted estimator is calculated to correct the bias introduced by the L ₁ penalty at each voxel. In PMARM, we integrate the multiscale adaptive regression models (Li et al., 2011), the propagation-separation method (Polzehl and Spokoiny, 2000), and Lasso (least absolute shrinkage and selection operator) (Tibshirani, 1996) to adaptively estimate ODFs across voxels. Experimental results indicate that PMARM can reduce the angle detection errors on fiber crossing area and provide more accurate reconstruction than standard voxel-wise methods.