A Locally Linear Least Squares Method for Simultaneously Smoothing DWI Data and Estimating Diffusion Tensors

Abstract

Magnetic resonance diffusion-weighted imaging (MR-DWI) data usually contain a great deal of noise and a significant number of outlier data points that can undermine the accurate estimation of diffusion tensors (DTs). Raw MR-DWI data therefore usually must undergo substantial preprocessing prior to tensor estimation. This study proposes an approach for the reconstruction of DT fields from MR-DWI data that combines into a single step the regularization of raw MR-DWI data and the optimized estimation of DT fields. The approach uses locally weighted linear least squares (LWLLS) estimation to correlate information within the local neighborhood of each voxel. It incorporates into the linear least squares (LLS) framework a bilateral filter which assigns different weights to neighbor voxels according to their intensities and relative distance. This method efficiently smoothes the MR-DWI data and estimates optimal tensors simultaneously. The performance of the proposed method was compared to that of traditional LLS estimation of tensors using both simulated and real-world human MR-DWI data. Both the simulated and real-world datasets demonstrated that the proposed method greatly outperforms the conventional LLS method and that the simultaneous smoothing of MR-DWI data and tensor estimation performs as well as the separate and sequential execution of these procedures.