910 research outputs found
Accelerated Cardiac Diffusion Tensor Imaging Using Joint Low-Rank and Sparsity Constraints
Objective: The purpose of this manuscript is to accelerate cardiac diffusion
tensor imaging (CDTI) by integrating low-rankness and compressed sensing.
Methods: Diffusion-weighted images exhibit both transform sparsity and
low-rankness. These properties can jointly be exploited to accelerate CDTI,
especially when a phase map is applied to correct for the phase inconsistency
across diffusion directions, thereby enhancing low-rankness. The proposed
method is evaluated both ex vivo and in vivo, and is compared to methods using
either a low-rank or sparsity constraint alone. Results: Compared to using a
low-rank or sparsity constraint alone, the proposed method preserves more
accurate helix angle features, the transmural continuum across the myocardium
wall, and mean diffusivity at higher acceleration, while yielding significantly
lower bias and higher intraclass correlation coefficient. Conclusion:
Low-rankness and compressed sensing together facilitate acceleration for both
ex vivo and in vivo CDTI, improving reconstruction accuracy compared to
employing either constraint alone. Significance: Compared to previous methods
for accelerating CDTI, the proposed method has the potential to reach higher
acceleration while preserving myofiber architecture features which may allow
more spatial coverage, higher spatial resolution and shorter temporal footprint
in the future.Comment: 11 pages, 16 figures, published on IEEE Transactions on Biomedical
Engineerin
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
Low-rank and sparse reconstruction in dynamic magnetic resonance imaging via proximal splitting methods
Dynamic magnetic resonance imaging (MRI) consists of collecting multiple MR images in time, resulting in a spatio-temporal signal. However, MRI intrinsically suffers from long acquisition times due to various constraints. This limits the full potential of dynamic MR imaging, such as obtaining high spatial and temporal resolutions which are crucial to observe dynamic phenomena. This dissertation addresses the problem of the reconstruction of dynamic MR images from a limited amount of samples arising from a nuclear magnetic resonance experiment. The term limited can be explained by the approach taken in this thesis to speed up scan time, which is based on violating the Nyquist criterion by skipping measurements that would be normally acquired in a standard MRI procedure. The resulting problem can be classified in the general framework of linear ill-posed inverse problems. This thesis shows how low-dimensional signal models, specifically lowrank and sparsity, can help in the reconstruction of dynamic images from partial measurements. The use of these models are justified by significant developments in signal recovery techniques from partial data that have emerged in recent years in signal processing. The major contributions of this thesis are the development and characterisation of fast and efficient computational tools using convex low-rank and sparse constraints via proximal gradient methods, the development and characterisation of a novel joint reconstruction–separation method via the low-rank plus sparse matrix decomposition technique, and the development and characterisation of low-rank based recovery methods in the context of dynamic parallel MRI. Finally, an additional contribution of this thesis is to formulate the various MR image reconstruction problems in the context of convex optimisation to develop algorithms based on proximal splitting methods
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
Low-rank Tensor Assisted K-space Generative Model for Parallel Imaging Reconstruction
Although recent deep learning methods, especially generative models, have
shown good performance in fast magnetic resonance imaging, there is still much
room for improvement in high-dimensional generation. Considering that internal
dimensions in score-based generative models have a critical impact on
estimating the gradient of the data distribution, we present a new idea,
low-rank tensor assisted k-space generative model (LR-KGM), for parallel
imaging reconstruction. This means that we transform original prior information
into high-dimensional prior information for learning. More specifically, the
multi-channel data is constructed into a large Hankel matrix and the matrix is
subsequently folded into tensor for prior learning. In the testing phase, the
low-rank rotation strategy is utilized to impose low-rank constraints on tensor
output of the generative network. Furthermore, we alternately use traditional
generative iterations and low-rank high-dimensional tensor iterations for
reconstruction. Experimental comparisons with the state-of-the-arts
demonstrated that the proposed LR-KGM method achieved better performance
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
Structured low-rank methods for robust 3D multi-shot EPI
Magnetic resonance imaging (MRI) has inherently slow acquisition speed, and Echo-Planar Imaging (EPI), as an efficient acquisition scheme, has been widely used in functional magnetic resonance imaging (fMRI) where an image series with high temporal resolution is needed to measure neuronal activity. Recently, 3D multi-shot EPI which samples data from an entire 3D volume with repeated shots has been drawing growing interest for fMRI with its high isotropic spatial resolution, particularly at ultra-high fields. However, compared to single-shot EPI, multi-shot EPI is sensitive to any inter-shot instabilities, e.g., subject movement and even physiologically induced field fluctuations. These inter-shot inconsistencies can greatly negate the theoretical benefits of 3D multi-shot EPI over conventional 2D multi-slice acquisitions.
Structured low-rank image reconstruction which regularises under-sampled image reconstruction by exploiting the linear dependencies in MRI data has been successfully demonstrated in a variety of applications. In this thesis, a structured low-rank reconstruction method is optimised for 3D multi-shot EPI imaging together with a dedicated sampling pattern termed seg-CAIPI, in order to enhance the robustness to physiological fluctuations and improve the temporal stability of 3D multi-shot EPI for fMRI at 7T. Moreover, a motion compensated structured low-rank reconstruction framework is also presented for robust 3D multi-shot EPI which further takes into account inter-shot instabilities due to bulk motion. Lastly, this thesis also investigates into the improvement of structured low-rank reconstruction from an algorithmic perspective and presents the locally structured low-rank reconstruction scheme
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