SR-HARDI: Spatially Regularizing High Angular Resolution Diffusion Imaging

Shangbang Rao,Joseph G Ibrahim,Jian Cheng,Pew-Thian Yap,Hongtu Zhu

doi:10.1080/10618600.2015.1105750

Abstract

High angular resolution diffusion imaging (HARDI) has recently been of great interest in mapping the orientation of intravoxel 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 article is to propose a penalized multiscale 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-square 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 gray matter) of HARDI. The L1 penalty function is introduced to ensure the sparse solutions of ODFs, while a scaled L1 weighted estimator is calculated to correct the bias introduced by the L1 penalty at each voxel. In PMARM, we integrate the multiscale adaptive regression models, the propagation-separation method, and Lasso (least absolute shrinkage and selection operator) 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. Supplementary materials for this article are available online.

Highlights

Diffusion magnetic resonance imaging is a popular imaging technique for tracking the effective diffusion of water molecules, which is constrained by the surrounding structures, such as nerves or cells, in the human brain in vivo
We have introduced a penalized multiscale adaptive model (PMARM) framework to adaptively reconstruct the orientation distribution function (ODF) across all voxels from high angular resolution diffusion imaging (HARDI) signals
We have shown in the real and simulated data sets that penalized multi-scale adaptive regression model (PMARM) can substantially reduce the noise level, while improving the ODF reconstruction

Summary

Introduction

Diffusion magnetic resonance imaging (dMRI) is a popular imaging technique for tracking the effective diffusion of water molecules, which is constrained by the surrounding structures, such as nerves or cells, in the human brain in vivo. A standard dMRI, diffusion tensor Imaging (DTI), is based on E(q; v) = exp(−buTD(v)u), where b is the diffusion weighting factor associated with q. This yields that p(R; v) is the density of a multivariate Gaussian distribution parametrized by a 3 × 3 covariance matrix D(v), called a diffusion tensor. The principal directions of the diffusion tensors can be used to reconstruct major fiber pathways in regions of the brain and spinal cord with strong whitematter coherence, and it has enabled the mapping of anatomical connections in the central nervous system.

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