750 research outputs found
Spherical deconvolution of multichannel diffusion MRI data with non-Gaussian noise models and spatial regularization
Spherical deconvolution (SD) methods are widely used to estimate the
intra-voxel white-matter fiber orientations from diffusion MRI data. However,
while some of these methods assume a zero-mean Gaussian distribution for the
underlying noise, its real distribution is known to be non-Gaussian and to
depend on the methodology used to combine multichannel signals. Indeed, the two
prevailing methods for multichannel signal combination lead to Rician and
noncentral Chi noise distributions. Here we develop a Robust and Unbiased
Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with
realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to
Rician and noncentral Chi likelihood models. To quantify the benefits of using
proper noise models, RUMBA-SD was compared with dRL-SD, a well-established
method based on the RL algorithm for Gaussian noise. Another aim of the study
was to quantify the impact of including a total variation (TV) spatial
regularization term in the estimation framework. To do this, we developed TV
spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The
evaluation was performed by comparing various quality metrics on 132
three-dimensional synthetic phantoms involving different inter-fiber angles and
volume fractions, which were contaminated with noise mimicking patterns
generated by data processing in multichannel scanners. The results demonstrate
that the inclusion of proper likelihood models leads to an increased ability to
resolve fiber crossings with smaller inter-fiber angles and to better detect
non-dominant fibers. The inclusion of TV regularization dramatically improved
the resolution power of both techniques. The above findings were also verified
in brain data
Bayesian uncertainty quantification in linear models for diffusion MRI
Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue
microstructure. By fitting a model to the dMRI signal it is possible to derive
various quantitative features. Several of the most popular dMRI signal models
are expansions in an appropriately chosen basis, where the coefficients are
determined using some variation of least-squares. However, such approaches lack
any notion of uncertainty, which could be valuable in e.g. group analyses. In
this work, we use a probabilistic interpretation of linear least-squares
methods to recast popular dMRI models as Bayesian ones. This makes it possible
to quantify the uncertainty of any derived quantity. In particular, for
quantities that are affine functions of the coefficients, the posterior
distribution can be expressed in closed-form. We simulated measurements from
single- and double-tensor models where the correct values of several quantities
are known, to validate that the theoretically derived quantiles agree with
those observed empirically. We included results from residual bootstrap for
comparison and found good agreement. The validation employed several different
models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI)
and Constrained Spherical Deconvolution (CSD). We also used in vivo data to
visualize maps of quantitative features and corresponding uncertainties, and to
show how our approach can be used in a group analysis to downweight subjects
with high uncertainty. In summary, we convert successful linear models for dMRI
signal estimation to probabilistic models, capable of accurate uncertainty
quantification.Comment: Added results from a group analysis and a comparison with residual
bootstra
Left-Invariant Diffusion on the Motion Group in terms of the Irreducible Representations of SO(3)
In this work we study the formulation of convection/diffusion equations on
the 3D motion group SE(3) in terms of the irreducible representations of SO(3).
Therefore, the left-invariant vector-fields on SE(3) are expressed as linear
operators, that are differential forms in the translation coordinate and
algebraic in the rotation. In the context of 3D image processing this approach
avoids the explicit discretization of SO(3) or , respectively. This is
particular important for SO(3), where a direct discretization is infeasible due
to the enormous memory consumption. We show two applications of the framework:
one in the context of diffusion-weighted magnetic resonance imaging and one in
the context of object detection
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 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
-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.Comment: 37 pages, 3 figure
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