Data augmentation in Rician noise model and Bayesian Diffusion Tensor Imaging

Published on Mar 20, 2014in arXiv: Computation
Dario Gasbarra11
Estimated H-index: 11
,
Jia Liu2
Estimated H-index: 2
,
Juha Railavo2
Estimated H-index: 2
Sources
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 bvalues. 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.
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2005
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References42
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Feb 15, 2012 in PDP (Parallel, Distributed and Network-Based Processing)
#1Moises Hern´ndez (University of Murcia)H-Index: 1
#2Ginés D. Guerrero (University of Murcia)H-Index: 11
Last. Stamatios N. Sotiropoulos (University of Oxford)H-Index: 42
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Diffusion Weighted Magnetic Resonance Imaging (DW-MRI) and tractography approaches are the only tools that can be utilized to estimate structural connections between different brain areas, non-invasively and in-vivo. A first step that is commonly utilized in these techniques includes the estimation of the underlying fibre orientations and their uncertainty in each voxel of the image. A popular method to achieve that is implemented in the FSL software, provided by the FMRIB Centre at University o...
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#1Aurobrata GhoshH-Index: 18
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This paper presents a general and complete (up to degree 4) set of invariants of 3D 4th order tensors with respect to SO3. The invariants to SO3 for the 2nd order diffusion tensor are well known and play a crucial role in deriving important biomarkers for DTI, e.g. MD, FA, RA, etc. But DTI is limited in regions with fiber heterogeneity and DTI biomarkers severely lack specificity. 4th order tensors are both a natural extension to DTI and also form an alternate basis to spherical harmonics for sp...
#1Jelle Veraart (University of Antwerp)H-Index: 32
#2Wim Van Hecke (University of Antwerp)H-Index: 33
Last. Jan Sijbers (University of Antwerp)H-Index: 68
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A computational framework to obtain an accurate quantification of the Gaussian and non-Gaussian component of water molecules’ diffusion through brain tissues with diffusion kurtosis imaging, is presented. The diffusion kurtosis imaging model quantifies the kurtosis, the degree of non-Gaussianity, on a direction dependent basis, constituting a higher order diffusion kurtosis tensor, which is estimated in addition to the well-known diffusion tensor. To reconcile with the physical phenomenon of mol...
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#1Aurobrata GhoshH-Index: 18
Diffusion MRI (dMRI) is a powerful tool for inferring the architecture of the cerebral white matter in-vivo and non-invasively. Based on model assumptions, reconstructed diffusion functions can provide sub-voxel resolution microstructural information of the white matter superior to the resolution of the raw diffusion images. In the commonly used Diffusion Tensor Iumaging (DTIa) the diffusion function is modelled by a second order tensor. However, since it is limited in regions with fiber inhomog...
#1Lieve Lauwers (Vrije Universiteit Brussel)H-Index: 9
#2Kurt BarbéH-Index: 17
Last. Rik PintelonH-Index: 61
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Analyzing functional MRI data is often a hard task due to the fact that these periodic signals are strongly disturbed with noise. In many cases, the signals are buried under the noise and not visible, such that detection is quite impossible. However, it is well known that the amplitude measurements of such disturbed signals follow a Rice distribution which is characterized by two parameters. In this paper, an alternative Bayesian approach is proposed to tackle this two-parameter estimation probl...
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#1Yanhui Liao (CSU: Central South University)H-Index: 24
#2Jinsong Tang (CSU: Central South University)H-Index: 27
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Ketamine abuse has been shown to have a deleterious impact on brain function. However, the precise mechanisms of ketamine dependence-induced pathological change remain poorly understood. Although there is evidence for white matter changes in drug abuse, the presence of white matter abnormalities in chronic ketamine users has not been studied. White matter volumes were measured using in vivo diffusion tensor magnetic resonance imaging data in 41 ketamine-dependent subjects and 44 drug-free health...
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Oct 2, 2009 in MICCAI (Medical Image Computing and Computer-Assisted Intervention)
#1Angelos Barmpoutis (UF: University of Florida)H-Index: 17
#2Baba C. Vemuri (UF: University of Florida)H-Index: 55
Registration of Diffusion-Weighted MR Images (DW-MRI) can be achieved by registering the corresponding 2nd-order Diffusion Tensor Images (DTI). However, it has been shown that higher-order diffusion tensors (e.g. order-4) outperform the traditional DTI in approximating complex fiber structures such as fiber crossings. In this paper we present a novel method for unbiased group-wise non-rigid registration and atlas construction of 4th-order diffusion tensor fields. To the best of our knowledge the...
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#1Haz-Edine Assemlal (CNRS: Centre national de la recherche scientifique)H-Index: 7
#2David Tschumperlé (CNRS: Centre national de la recherche scientifique)H-Index: 19
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We present a method for the estimation of various features of the tissue micro-architecture using the di usion magnetic resonance imaging. The considered features are designed from the displacement probability density function (PDF). The estimation is based on two steps: first the approximation of the signal by a series expansion made of Gaussian-Laguerre and Spherical Harmonics functions; followed by a projection on a finite dimensional space. Besides, we propose to tackle the problem of the ro...
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#1Ian L. Dryden (USC: University of South Carolina)H-Index: 29
#2Alexey Koloydenko (RHUL: Royal Holloway, University of London)H-Index: 14
Last. Diwei ZhouH-Index: 5
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The statistical analysis of covariance matrices occurs in m any important applications, e.g. in diffusion tensor imaging or longitudinal data analysis. We consider the situation where it is of interest to estimate an average covariance matrix, describe its anisotropy and to carry out principal geodesic analysis of covariance matrices. In medical image analysis a particular type of covariance matrix arises in diffusion weighted imaging called a diffusion tensor. The diffusion tensor is a 3 Ă— 3 co...
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#1Cheng Guan Koay (NIH: National Institutes of Health)H-Index: 14
#2Evren Ă–zarslan (NIH: National Institutes of Health)H-Index: 33
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A long-standing problem in magnetic resonance imaging (MRI) is the noise-induced bias in the magnitude signals. This problem is particularly pressing in diffusion MRI at high diffusion-weighting. In this paper, we present a three-stage scheme to solve this problem by transforming noisy nonCentral Chi signals to noisy Gaussian signals. A special case of nonCentral Chi distribution is the Rician distribution. In general, the Gaussian-distributed signals are of interest rather than the Gaussian-der...
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Cited By2
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#1Jia Liu (University of Jyväskylä)H-Index: 2
#2Dario Gasbarra (UH: University of Helsinki)H-Index: 11
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Abstract Diffusion tensor imaging (DTI) is widely used to characterize, in vivo, the white matter of the central nerve system (CNS). This biological tissue contains much anatomic, structural and orientational information of fibers in human brain. Spectral data from the displacement distribution of water molecules located in the brain tissue are collected by a magnetic resonance scanner and acquired in the Fourier domain. After the Fourier inversion, the noise distribution is Gaussian in both rea...
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