17,251 research outputs found
Complex diffusion-weighted image estimation via matrix recovery under general noise models
We propose a patch-based singular value shrinkage method for diffusion
magnetic resonance image estimation targeted at low signal to noise ratio and
accelerated acquisitions. It operates on the complex data resulting from a
sensitivity encoding reconstruction, where asymptotically optimal signal
recovery guarantees can be attained by modeling the noise propagation in the
reconstruction and subsequently simulating or calculating the limit singular
value spectrum. Simple strategies are presented to deal with phase
inconsistencies and optimize patch construction. The pertinence of our
contributions is quantitatively validated on synthetic data, an in vivo adult
example, and challenging neonatal and fetal cohorts. Our methodology is
compared with related approaches, which generally operate on magnitude-only
data and use data-based noise level estimation and singular value truncation.
Visual examples are provided to illustrate effectiveness in generating denoised
and debiased diffusion estimates with well preserved spatial and diffusion
detail.Comment: 26 pages, 9 figure
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
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition
Hyperspectral images (HSIs) are often corrupted by a mixture of several types
of noise during the acquisition process, e.g., Gaussian noise, impulse noise,
dead lines, stripes, and many others. Such complex noise could degrade the
quality of the acquired HSIs, limiting the precision of the subsequent
processing. In this paper, we present a novel tensor-based HSI restoration
approach by fully identifying the intrinsic structures of the clean HSI part
and the mixed noise part respectively. Specifically, for the clean HSI part, we
use tensor Tucker decomposition to describe the global correlation among all
bands, and an anisotropic spatial-spectral total variation (SSTV)
regularization to characterize the piecewise smooth structure in both spatial
and spectral domains. For the mixed noise part, we adopt the norm
regularization to detect the sparse noise, including stripes, impulse noise,
and dead pixels. Despite that TV regulariztion has the ability of removing
Gaussian noise, the Frobenius norm term is further used to model heavy Gaussian
noise for some real-world scenarios. Then, we develop an efficient algorithm
for solving the resulting optimization problem by using the augmented Lagrange
multiplier (ALM) method. Finally, extensive experiments on simulated and
real-world noise HSIs are carried out to demonstrate the superiority of the
proposed method over the existing state-of-the-art ones.Comment: 15 pages, 20 figure
Persistent Homology in Sparse Regression and its Application to Brain Morphometry
Sparse systems are usually parameterized by a tuning parameter that
determines the sparsity of the system. How to choose the right tuning parameter
is a fundamental and difficult problem in learning the sparse system. In this
paper, by treating the the tuning parameter as an additional dimension,
persistent homological structures over the parameter space is introduced and
explored. The structures are then further exploited in speeding up the
computation using the proposed soft-thresholding technique. The topological
structures are further used as multivariate features in the tensor-based
morphometry (TBM) in characterizing white matter alterations in children who
have experienced severe early life stress and maltreatment. These analyses
reveal that stress-exposed children exhibit more diffuse anatomical
organization across the whole white matter region.Comment: submitted to IEEE Transactions on Medical Imagin
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