918 research outputs found
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
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
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
Accelerated partial separable model using dimension-reduced optimization technique for ultra-fast cardiac MRI
Objective. Imaging dynamic object with high temporal resolution is
challenging in magnetic resonance imaging (MRI). Partial separable (PS) model
was proposed to improve the imaging quality by reducing the degrees of freedom
of the inverse problem. However, PS model still suffers from long acquisition
time and even longer reconstruction time. The main objective of this study is
to accelerate the PS model, shorten the time required for acquisition and
reconstruction, and maintain good image quality simultaneously. Approach. We
proposed to fully exploit the dimension reduction property of the PS model,
which means implementing the optimization algorithm in subspace. We optimized
the data consistency term, and used a Tikhonov regularization term based on the
Frobenius norm of temporal difference. The proposed dimension-reduced
optimization technique was validated in free-running cardiac MRI. We have
performed both retrospective experiments on public dataset and prospective
experiments on in-vivo data. The proposed method was compared with four
competing algorithms based on PS model, and two non-PS model methods. Main
results. The proposed method has robust performance against shortened
acquisition time or suboptimal hyper-parameter settings, and achieves superior
image quality over all other competing algorithms. The proposed method is
20-fold faster than the widely accepted PS+Sparse method, enabling image
reconstruction to be finished in just a few seconds. Significance. Accelerated
PS model has the potential to save much time for clinical dynamic MRI
examination, and is promising for real-time MRI applications.Comment: 23 pages, 11 figures. Accepted as manuscript on Physics in Medicine &
Biolog
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