445 research outputs found
Video Compressive Sensing for Dynamic MRI
We present a video compressive sensing framework, termed kt-CSLDS, to
accelerate the image acquisition process of dynamic magnetic resonance imaging
(MRI). We are inspired by a state-of-the-art model for video compressive
sensing that utilizes a linear dynamical system (LDS) to model the motion
manifold. Given compressive measurements, the state sequence of an LDS can be
first estimated using system identification techniques. We then reconstruct the
observation matrix using a joint structured sparsity assumption. In particular,
we minimize an objective function with a mixture of wavelet sparsity and joint
sparsity within the observation matrix. We derive an efficient convex
optimization algorithm through alternating direction method of multipliers
(ADMM), and provide a theoretical guarantee for global convergence. We
demonstrate the performance of our approach for video compressive sensing, in
terms of reconstruction accuracy. We also investigate the impact of various
sampling strategies. We apply this framework to accelerate the acquisition
process of dynamic MRI and show it achieves the best reconstruction accuracy
with the least computational time compared with existing algorithms in the
literature.Comment: 30 pages, 9 figure
Accelerating Magnetic Resonance Parametric Mapping Using Simultaneously Spatial Patch-based and Parametric Group-based Low-rank Tensors (SMART)
Quantitative magnetic resonance (MR) parametric mapping is a promising
approach for characterizing intrinsic tissue-dependent information. However,
long scan time significantly hinders its widespread applications. Recently,
low-rank tensor has been employed and demonstrated good performance in
accelerating MR parametricmapping. In this study, we propose a novel method
that uses spatial patch-based and parametric group-based low rank tensors
simultaneously (SMART) to reconstruct images from highly undersampled k-space
data. The spatial patch-based low-rank tensor exploits the high local and
nonlocal redundancies and similarities between the contrast images in
parametric mapping. The parametric group based low-rank tensor, which
integrates similar exponential behavior of the image signals, is jointly used
to enforce the multidimensional low-rankness in the reconstruction process. In
vivo brain datasets were used to demonstrate the validity of the proposed
method. Experimental results have demonstrated that the proposed method
achieves 11.7-fold and 13.21-fold accelerations in two-dimensional and
three-dimensional acquisitions, respectively, with more accurate reconstructed
images and maps than several state-of-the-art methods. Prospective
reconstruction results further demonstrate the capability of the SMART method
in accelerating MR quantitative imaging.Comment: 15 pages, 12 figure
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
Simultaneous use of Individual and Joint Regularization Terms in Compressive Sensing: Joint Reconstruction of Multi-Channel Multi-Contrast MRI Acquisitions
Purpose: A time-efficient strategy to acquire high-quality multi-contrast
images is to reconstruct undersampled data with joint regularization terms that
leverage common information across contrasts. However, these terms can cause
leakage of uncommon features among contrasts, compromising diagnostic utility.
The goal of this study is to develop a compressive sensing method for
multi-channel multi-contrast magnetic resonance imaging (MRI) that optimally
utilizes shared information while preventing feature leakage.
Theory: Joint regularization terms group sparsity and colour total variation
are used to exploit common features across images while individual sparsity and
total variation are also used to prevent leakage of distinct features across
contrasts. The multi-channel multi-contrast reconstruction problem is solved
via a fast algorithm based on Alternating Direction Method of Multipliers.
Methods: The proposed method is compared against using only individual and
only joint regularization terms in reconstruction. Comparisons were performed
on single-channel simulated and multi-channel in-vivo datasets in terms of
reconstruction quality and neuroradiologist reader scores.
Results: The proposed method demonstrates rapid convergence and improved
image quality for both simulated and in-vivo datasets. Furthermore, while
reconstructions that solely use joint regularization terms are prone to
leakage-of-features, the proposed method reliably avoids leakage via
simultaneous use of joint and individual terms.
Conclusion: The proposed compressive sensing method performs fast
reconstruction of multi-channel multi-contrast MRI data with improved image
quality. It offers reliability against feature leakage in joint
reconstructions, thereby holding great promise for clinical use.Comment: 13 pages, 13 figures. Submitted for possible publicatio
Robust Algorithms for Low-Rank and Sparse Matrix Models
Data in statistical signal processing problems is often inherently matrix-valued, and a natural first step in working with such data is to impose a model with structure that captures the distinctive features of the underlying data. Under the right model, one can design algorithms that can reliably tease weak signals out of highly corrupted data. In this thesis, we study two important classes of matrix structure: low-rankness and sparsity. In particular, we focus on robust principal component analysis (PCA) models that decompose data into the sum of low-rank and sparse (in an appropriate sense) components. Robust PCA models are popular because they are useful models for data in practice and because efficient algorithms exist for solving them.
This thesis focuses on developing new robust PCA algorithms that advance the state-of-the-art in several key respects. First, we develop a theoretical understanding of the effect of outliers on PCA and the extent to which one can reliably reject outliers from corrupted data using thresholding schemes. We apply these insights and other recent results from low-rank matrix estimation to design robust PCA algorithms with improved low-rank models that are well-suited for processing highly corrupted data. On the sparse modeling front, we use sparse signal models like spatial continuity and dictionary learning to develop new methods with important adaptive representational capabilities. We also propose efficient algorithms for implementing our methods, including an extension of our dictionary learning algorithms to the online or sequential data setting. The underlying theme of our work is to combine ideas from low-rank and sparse modeling in novel ways to design robust algorithms that produce accurate reconstructions from highly undersampled or corrupted data. We consider a variety of application domains for our methods, including foreground-background separation, photometric stereo, and inverse problems such as video inpainting and dynamic magnetic resonance imaging.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143925/1/brimoor_1.pd
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