Locally Weighted Regression for Estimating and Smoothing ODF Field Simultaneously

High angular resolution diffusion imaging (HARDI) has become an important tool for resolving neural architecture in regions with complex patterns of fiber crossing. A popular method for estimating the diffusion orientation distribution function (ODF) employs a least square (LS) approach by modeling the raw HARDI data on a spherical harmonic basis. We propose herein a novel approach for reconstruction of ODF fields from raw HARDI data that combines into one step the smoothing of raw HARDI data and the estimation of ODF field using correlated information in a local neighborhood. Based on the most popular method of least square for estimating ODF, we incorporated into it local weights that are determined by a special weighting function, making it a locally weighted linear least square method (LWLLS). The method thus can efficiently perform the smoothing of HARDI data and estimating the ODF field simultaneously. We evaluated the effectiveness of this method using both simulated and real-world HARDI data.