A statistical approach to SENSE regularization with arbitrary k-space trajectories.
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TLDR
This study presents a new method for adaptive regularization using the image and noise statistics, which addresses the blurry edges in Tikhonov regularization and the blocky effects in total variation (TV) regularization.Abstract:
SENSE reconstruction suffers from an ill-conditioning problem, which increasingly lowers the signal-to-noise ratio (SNR) as the reduction factor increases. Ill-conditioning also degrades the convergence behavior of iterative conjugate gradient reconstructions for arbitrary trajectories. Regularization techniques are often used to alleviate the ill-conditioning problem. Based on maximum a posteriori statistical estimation with a Huber Markov random field prior, this study presents a new method for adaptive regularization using the image and noise statistics. The adaptive Huber regularization addresses the blurry edges in Tikhonov regularization and the blocky effects in total variation (TV) regularization. Phantom and in vivo experiments demonstrate improved image quality and convergence speed over both the unregularized conjugate gradient method and Tikhonov regularization method, at no increase in total computation time. Magn Reson Med 60:414 – 421, 2008. © 2008 Wileyread more
Citations
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Journal ArticleDOI
Accelerating SENSE using compressed sensing.
TL;DR: A novel method to combine sensitivity encoding (SENSE), one of the standard methods for parallel MRI, and compressed sensing for rapid MR imaging (SparseMRI), a recently proposed method for applying CS in MR imaging with Cartesian trajectories is proposed.
Journal ArticleDOI
Parallel MR Image Reconstruction Using Augmented Lagrangian Methods
TL;DR: 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 are presented.
Journal ArticleDOI
A Fast Wavelet-Based Reconstruction Method for Magnetic Resonance Imaging
TL;DR: This work exploits the fact that wavelets can represent magnetic resonance images well, with relatively few coefficients, to improve magnetic resonance imaging (MRI) reconstructions from undersampled data with arbitrary k-space trajectories and proposes a variant that combines recent improvements in convex optimization and that can be tuned to a given specific k- space trajectory.
Journal ArticleDOI
Accelerating MR parameter mapping using sparsity-promoting regularization in parametric dimension.
TL;DR: The proposed p‐CS regularization strategy uses smoothness of signal evolution in the parametric dimension within compressed sensing framework (p‐CS) to provide accurate and precise estimation of parametric maps from undersampled data.
Journal ArticleDOI
A wavelet-based regularized reconstruction algorithm for SENSE parallel MRI with applications to neuroimaging☆
TL;DR: A novel method for SENSE-based reconstruction which proceeds with regularization in the complex wavelet domain by promoting sparsity is presented which relies on a fast algorithm that enables the minimization of regularized non-differentiable criteria including more general penalties than a classical ℓ(1) term.
References
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Optimization by Simulated Annealing
TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
PatentDOI
SENSE: Sensitivity Encoding for fast MRI
TL;DR: The problem of image reconstruction from sensitivity encoded data is formulated in a general fashion and solved for arbitrary coil configurations and k‐space sampling patterns and special attention is given to the currently most practical case, namely, sampling a common Cartesian grid with reduced density.
Journal ArticleDOI
Generalized autocalibrating partially parallel acquisitions (GRAPPA).
Mark A. Griswold,Peter M. Jakob,Robin M. Heidemann,Mathias Nittka,Vladimir Jellus,Jianmin Wang,Berthold Kiefer,Axel Haase +7 more
TL;DR: This technique, GeneRalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) is an extension of both the PILS and VD‐AUTO‐SMASH reconstruction techniques and provides unaliased images from each component coil prior to image combination.
Book
An Introduction to Signal Detection and Estimation
TL;DR: Signal Detection in Discrete Time and Signal Estimation in Continuous Time: Elements of Hypothesis Testing and Elements of Parameter Estimation.