Data augmentation in Rician noise model and Bayesian Diffusion Tensor Imaging

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 livi...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2014-03
Main Authors: Gasbarra, Dario, Liu, Jia, Railavo, Juha
Format: Article
Language:English
Subjects:
Bayesian analysis
Brain
Computer simulation
Data augmentation
Diffusion
Displacement
Fourier transforms
In vivo methods and tests
Linearization
Magnetic resonance imaging
Mapping
Markov analysis
Markov chains
Mathematical analysis
Noise
Normal distribution
Regression models
Regularization
Signal to noise ratio
Spectra
Statistical analysis
Statistical models
Tensors
Water chemistry
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422