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

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

Acceleration Methods for MRI

Acceleration methods are a critical area of research for MRI. Two of the most important acceleration techniques involve parallel imaging and compressed sensing. These advanced signal processing techniques have the potential to drastically reduce scan times and provide radiologists with new information for diagnosing disease. However, many of these new techniques require solving difficult optimization problems, which motivates the development of more advanced algorithms to solve them. In addition, acceleration methods have not reached maturity in some applications, which motivates the development of new models tailored to these applications. This dissertation makes advances in three different areas of accelerations. The first is the development of a new algorithm (called B1-Based, Adaptive Restart, Iterative Soft Thresholding Algorithm or BARISTA), that solves a parallel MRI optimization problem with compressed sensing assumptions. BARISTA is shown to be 2-3 times faster and more robust to parameter selection than current state-of-the-art variable splitting methods. The second contribution is the extension of BARISTA ideas to non-Cartesian trajectories that also leads to a 2-3 times acceleration over previous methods. The third contribution is the development of a new model for functional MRI that enables a 3-4 factor of acceleration of effective temporal resolution in functional MRI scans. Several variations of the new model are proposed, with an ROC curve analysis showing that a combination low-rank/sparsity model giving the best performance in identifying the resting-state motor network.PhDBiomedical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120841/1/mmuckley_1.pd

Under-Sampled Reconstruction Techniques for Accelerated Magnetic Resonance Imaging

Due to physical and biological constraints and requirements on the minimum resolution and SNR, the acquisition time is relatively long in magnetic resonance imaging (MRI). Consequently, a limited number of pulse sequences can be run in a clinical MRI session because of constraints on the total acquisition time due to patient comfort and cost considerations. Therefore, it is strongly desired to reduce the acquisition time without compromising the reconstruction quality. This thesis concerns under-sampled reconstruction techniques for acceleration of MRI acquisitions, i.e., parallel imaging and compressed sensing. While compressed sensing MRI reconstructions are commonly regularized by penalizing the decimated wavelet transform coefficients, it is shown in this thesis that the visual artifacts, associated with the lack of translation-invariance of the wavelet basis in the decimated form, can be avoided by penalizing the undecimated wavelet transform coefficients, i.e., the stationary wavelet transform (SWT). An iterative SWT thresholding algorithm for combined SWT-regularized compressed sensing and parallel imaging reconstruction is presented. Additionally, it is shown that in MRI applications involving multiple sequential acquisitions, e.g., quantitative T1/T2 mapping, the correlation between the successive acquisitions can be incorporated as an additional constraint for joint under-sampled reconstruction, resulting in improved reconstruction performance. While quantitative measures of quality, e.g., reconstruction error with respect to the fully-sampled reference, are commonly used for performance evaluation and comparison of under-sampled reconstructions, this thesis shows that such quantitative measures do not necessarily correlate with the subjective quality of reconstruction as perceived by radiologists and other expert end users. Therefore, unless accompanied by subjective evaluations, quantitative quality measurements/comparisons will be of limited clinical impact. The results of experiments aimed at subjective evaluation/comparison of different under-sampled reconstructions for specific clinical neuroimaging MRI applications are presented in this thesis. One motivation behind the current work was to reduce the acquisition time for relaxation mapping techniques DESPOT1 and DESPOT2. This work also includes a modification to the Driven Equilibrium Single Pulse Observation of T1 with high-speed incorporation of RF field inhomogeneities (DESPOT1-HIFI), resulting in more accurate estimation of T1 values at high strength (3T and higher) magnetic fields

Parallel MR Image Reconstruction Using Augmented Lagrangian Methods

Magnetic resonance image (MRI) reconstruction using SENSitivity Encoding (SENSE) requires regularization to suppress noise and aliasing effects. Edge-preserving and sparsity-based regularization criteria can improve image quality, but they demand computation-intensive nonlinear optimization. In this paper, we present novel methods for regularized MRI reconstruction from undersampled sensitivity encoded data-SENSE-reconstruction-using the augmented Lagrangian (AL) framework for solving large-scale constrained optimization problems. We first formulate regularized SENSE-reconstruction as an unconstrained optimization task and then convert it to a set of (equivalent) constrained problems using variable splitting. We then attack these constrained versions in an AL framework using an alternating minimization method, leading to algorithms that can be implemented easily. The proposed methods are applicable to a general class of regularizers that includes popular edge-preserving (e.g., total-variation) and sparsity-promoting (e.g., -norm of wavelet coefficients) criteria and combinations thereof. Numerical experiments with synthetic and in vivo human data illustrate that the proposed AL algorithms converge faster than both general-purpose optimization algorithms such as nonlinear conjugate gradient (NCG) and state-of-the-art MFISTA.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85846/1/Fessler4.pd

Reconstruction of Self-Sparse 2D NMR Spectra from Undersampled Data in the Indirect Dimension†

Reducing the acquisition time for two-dimensional nuclear magnetic resonance (2D NMR) spectra is important. One way to achieve this goal is reducing the acquired data. In this paper, within the framework of compressed sensing, we proposed to undersample the data in the indirect dimension for a type of self-sparse 2D NMR spectra, that is, only a few meaningful spectral peaks occupy partial locations, while the rest of locations have very small or even no peaks. The spectrum is reconstructed by enforcing its sparsity in an identity matrix domain with ℓp (p = 0.5) norm optimization algorithm. Both theoretical analysis and simulation results show that the proposed method can reduce the reconstruction errors compared with the wavelet-based ℓ1 norm optimization