4,064 research outputs found
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
Evaluating the accuracy of diffusion MRI models in white matter
Models of diffusion MRI within a voxel are useful for making inferences about
the properties of the tissue and inferring fiber orientation distribution used
by tractography algorithms. A useful model must fit the data accurately.
However, evaluations of model-accuracy of some of the models that are commonly
used in analyzing human white matter have not been published before. Here, we
evaluate model-accuracy of the two main classes of diffusion MRI models. The
diffusion tensor model (DTM) summarizes diffusion as a 3-dimensional Gaussian
distribution. Sparse fascicle models (SFM) summarize the signal as a linear sum
of signals originating from a collection of fascicles oriented in different
directions. We use cross-validation to assess model-accuracy at different
gradient amplitudes (b-values) throughout the white matter. Specifically, we
fit each model to all the white matter voxels in one data set and then use the
model to predict a second, independent data set. This is the first evaluation
of model-accuracy of these models. In most of the white matter the DTM predicts
the data more accurately than test-retest reliability; SFM model-accuracy is
higher than test-retest reliability and also higher than the DTM, particularly
for measurements with (a) a b-value above 1000 in locations containing fiber
crossings, and (b) in the regions of the brain surrounding the optic
radiations. The SFM also has better parameter-validity: it more accurately
estimates the fiber orientation distribution function (fODF) in each voxel,
which is useful for fiber tracking
Robust Depth Linear Error Decomposition with Double Total Variation and Nuclear Norm for Dynamic MRI Reconstruction
Compressed Sensing (CS) significantly speeds up Magnetic Resonance Image
(MRI) processing and achieves accurate MRI reconstruction from under-sampled
k-space data. According to the current research, there are still several
problems with dynamic MRI k-space reconstruction based on CS. 1) There are
differences between the Fourier domain and the Image domain, and the
differences between MRI processing of different domains need to be considered.
2) As three-dimensional data, dynamic MRI has its spatial-temporal
characteristics, which need to calculate the difference and consistency of
surface textures while preserving structural integrity and uniqueness. 3)
Dynamic MRI reconstruction is time-consuming and computationally
resource-dependent. In this paper, we propose a novel robust low-rank dynamic
MRI reconstruction optimization model via highly under-sampled and Discrete
Fourier Transform (DFT) called the Robust Depth Linear Error Decomposition
Model (RDLEDM). Our method mainly includes linear decomposition, double Total
Variation (TV), and double Nuclear Norm (NN) regularizations. By adding linear
image domain error analysis, the noise is reduced after under-sampled and DFT
processing, and the anti-interference ability of the algorithm is enhanced.
Double TV and NN regularizations can utilize both spatial-temporal
characteristics and explore the complementary relationship between different
dimensions in dynamic MRI sequences. In addition, Due to the non-smoothness and
non-convexity of TV and NN terms, it is difficult to optimize the unified
objective model. To address this issue, we utilize a fast algorithm by solving
a primal-dual form of the original problem. Compared with five state-of-the-art
methods, extensive experiments on dynamic MRI data demonstrate the superior
performance of the proposed method in terms of both reconstruction accuracy and
time complexity
Structured Sparsity: Discrete and Convex approaches
Compressive sensing (CS) exploits sparsity to recover sparse or compressible
signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity
is also used to enhance interpretability in machine learning and statistics
applications: While the ambient dimension is vast in modern data analysis
problems, the relevant information therein typically resides in a much lower
dimensional space. However, many solutions proposed nowadays do not leverage
the true underlying structure. Recent results in CS extend the simple sparsity
idea to more sophisticated {\em structured} sparsity models, which describe the
interdependency between the nonzero components of a signal, allowing to
increase the interpretability of the results and lead to better recovery
performance. In order to better understand the impact of structured sparsity,
in this chapter we analyze the connections between the discrete models and
their convex relaxations, highlighting their relative advantages. We start with
the general group sparse model and then elaborate on two important special
cases: the dispersive and the hierarchical models. For each, we present the
models in their discrete nature, discuss how to solve the ensuing discrete
problems and then describe convex relaxations. We also consider more general
structures as defined by set functions and present their convex proxies.
Further, we discuss efficient optimization solutions for structured sparsity
problems and illustrate structured sparsity in action via three applications.Comment: 30 pages, 18 figure
Image Restoration Using Joint Statistical Modeling in Space-Transform Domain
This paper presents a novel strategy for high-fidelity image restoration by
characterizing both local smoothness and nonlocal self-similarity of natural
images in a unified statistical manner. The main contributions are three-folds.
First, from the perspective of image statistics, a joint statistical modeling
(JSM) in an adaptive hybrid space-transform domain is established, which offers
a powerful mechanism of combining local smoothness and nonlocal self-similarity
simultaneously to ensure a more reliable and robust estimation. Second, a new
form of minimization functional for solving image inverse problem is formulated
using JSM under regularization-based framework. Finally, in order to make JSM
tractable and robust, a new Split-Bregman based algorithm is developed to
efficiently solve the above severely underdetermined inverse problem associated
with theoretical proof of convergence. Extensive experiments on image
inpainting, image deblurring and mixed Gaussian plus salt-and-pepper noise
removal applications verify the effectiveness of the proposed algorithm.Comment: 14 pages, 18 figures, 7 Tables, to be published in IEEE Transactions
on Circuits System and Video Technology (TCSVT). High resolution pdf version
and Code can be found at: http://idm.pku.edu.cn/staff/zhangjian/IRJSM
7T-guided super-resolution of 3T MRI
High-resolution MR images can depict rich details of brain anatomical structures and show subtle changes in longitudinal data. 7T MRI scanners can acquire MR images with higher resolution and better tissue contrast than the routine 3T MRI scanners. However, 7T MRI scanners are currently more expensive and less available in clinical and research centers. To this end, we propose a method to generate super-resolution 3T MRI that resembles 7T MRI, which is called as 7T-like MR image in this paper
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