Data augmentation in Rician noise model and Bayesian Diffusion Tensor Imaging

TL;DR

This paper introduces a Bayesian data augmentation approach for diffusion tensor imaging that directly models Rician noise, enabling improved estimation of brain white matter tracts from noisy spectral data across all b-values.

Contribution

It presents a novel Bayesian hierarchical model with data augmentation for DTI that directly incorporates Rician noise, improving accuracy over traditional methods.

Findings

Effective modeling of Rician noise in DTI data.

Simultaneous estimation and regularization of tensor fields.

Enhanced reconstruction of white matter tracts.

Abstract

Mapping white matter tracts is an essential step towards understanding brain function. Diffusion Magnetic Resonance Imaging (dMRI) is the only noninvasive technique which can detect in vivo anisotropies in the 3-dimensional diffusion of water molecules, which correspond to nervous fibers in the living brain. In this process, spectral data from the displacement distribution of water molecules is collected by a magnetic resonance scanner. From the statistical point of view, inverting the Fourier transform from such sparse and noisy spectral measurements leads to a non-linear regression problem. Diffusion tensor imaging (DTI) is the simplest modeling approach postulating a Gaussian displacement distribution at each volume element (voxel). Typically the inference is based on a linearized log-normal regression model that can fit the spectral data at low frequencies. However such approximation fails to fit the high frequency measurements which contain information about the details of the displacement distribution but have a low signal to noise ratio. In this paper, we directly work with the Rice noise model and cover the full range of $b$-values. Using data augmentation to represent the likelihood, we reduce the non-linear regression problem to the framework of generalized linear models. Then we construct a Bayesian hierarchical model in order to perform simultaneously estimation and regularization of the tensor field. Finally the Bayesian paradigm is implemented by using Markov chain Monte Carlo.