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Fast Algorithms for Image Reconstruction with Application to Partially Parallel MR Imaging
"... This paper presents two fast algorithms for total variationbased image reconstruction in partially parallel magnetic resonance imaging (PPI) where the inversion matrix is large and illconditioned. These algorithms utilize variable splitting techniques to decouple the original problem into more eas ..."
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This paper presents two fast algorithms for total variationbased image reconstruction in partially parallel magnetic resonance imaging (PPI) where the inversion matrix is large and illconditioned. These algorithms utilize variable splitting techniques to decouple the original problem into more easily solved subproblems. The first method reduces the image reconstruction problem to an unconstrained minimization problem, which is solved by an alternating proximal minimization algorithm. One phase of the algorithm solves a total variation (TV) denoising problem, and second phase solves an illconditioned linear system. Linear and sublinear convergence results are given, and an implementation based on a primaldual hybrid gradient (PDHG) scheme for the TV problem and a BarzilaiBorwein scheme for the linear inversion is proposed. The second algorithm exploits the special structure of the PPI reconstruction problem by decomposing it into one subproblem involving Fourier transforms and another subproblem that can be treated by the PDHG scheme. Numerical results and comparisons with recently developed methods indicate the efficiency of the proposed algorithms. Key words. Image reconstruction, Variable splitting, TV denoising, Nonlinear optimization 1
High Resolution Projection Reconstruction MR Imaging using FOCUSS
"... This paper is concerned about high resolution reconstruction of projection reconstruction MR imaging from angular undersampled kspace data. A similar problem has been recently addressed in the framework of compressed sensing theory. Unlike the existing algorithms used in compressed sensing theory, ..."
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This paper is concerned about high resolution reconstruction of projection reconstruction MR imaging from angular undersampled kspace data. A similar problem has been recently addressed in the framework of compressed sensing theory. Unlike the existing algorithms used in compressed sensing theory, this paper employs the FOCal Underdetermined System Solver(FOCUSS), which was originally designed for EEG and MEG source localization to obtain sparse solution by successively solving quadratic optimization. We show that FOCUSS is very effective for the projection reconstruction MRI, because the medical images are usually sparse in image domain, and the center region of the undersampled radial kspace data still provides a meaningful low resolution image, which is essential for the convergence of FOCUSS. We applied FOCUSS for projection reconstruction MR imaging using single coil. Extensive experiments confirms that high resolution reconstruction with virtually free of angular aliasing artifacts can be obtained from severely undersampled kspace data.
A Maximum Likelihood Approach to Parallel Imaging With Coil Sensitivity Noise
 IEEE TRANSACTIONS ON MEDICAL IMAGING
"... Parallel imaging is a powerful technique to speed up Magnetic Resonance (MR) image acquisition via multiple coils. Both the received signal of each coil and its sensitivity map, which describes its spatial response, are needed during reconstruction. Widely used schemes such as SENSE assume that sens ..."
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Parallel imaging is a powerful technique to speed up Magnetic Resonance (MR) image acquisition via multiple coils. Both the received signal of each coil and its sensitivity map, which describes its spatial response, are needed during reconstruction. Widely used schemes such as SENSE assume that sensitivity maps of the coils are noiseless while the only errors are due to a noisy signal. In practice, however sensitivity maps are subject to a wide variety of errors. At first glance, sensitivity noise appears to result in an errorsinvariables problem of the kind that is typically solved using Total Least Squares (TLS). However, existing TLS algorithms are inappropriate for the specific type of block structure that arises in parallel imaging. In this paper we take a maximum likelihood approach to the problem of parallel imaging in the presence of independent Gaussian sensitivity noise. This results in a quasiquadratic objective function, which can be efficiently minimized. Experimental evidence suggests substantial gains over conventional SENSE, especially in nonideal imaging conditions like low SNR, high gfactors, large acceleration and misaligned sensitivity maps.
NOISEADAPTIVE ANISOTROPIC DIFFUSION FILTERING OF MRI IMAGES RECONSTRUCTED BY SENSE (SENSITIVITY ENCODING) METHOD
"... SENSE (SENSitivity Encoding) imaging provides significant acquisition speedups in MRI. The main drawback of the method is that it generates images that have increased and spatially nonuniform noise levels and, hence, will often require retrospective filtering. In this paper, we show that standard an ..."
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SENSE (SENSitivity Encoding) imaging provides significant acquisition speedups in MRI. The main drawback of the method is that it generates images that have increased and spatially nonuniform noise levels and, hence, will often require retrospective filtering. In this paper, we show that standard anisotropic diffusion filtering, while being an effective technique for edgepreserving denoising of images with uniform noise levels, is often nonoptimal for SENSEreconstructed data. We have developed a modification of this filter for SENSE images using a robust statistical analysis of the anisotropic diffusion process. The new method utilizes the image noise matrix that is available from the SENSE reconstruction to automatically adjust filtering parameters with local noise levels. The effectiveness of the method and its advantage over standard anisotropic diffusion filtering for SENSE images were demonstrated with phantom and patient MRI data. 1.
doi:10.1155/2008/297089 Research Article Random Volumetric MRI Trajectories via Genetic Algorithms
"... A pseudorandom, velocityinsensitive, volumetric kspace sampling trajectory is designed for use with balanced steadystate magnetic resonance imaging. Individual arcs are designed independently and do not fit together in the way that multishot spiral, radial or echoplanar trajectories do. Previous ..."
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A pseudorandom, velocityinsensitive, volumetric kspace sampling trajectory is designed for use with balanced steadystate magnetic resonance imaging. Individual arcs are designed independently and do not fit together in the way that multishot spiral, radial or echoplanar trajectories do. Previously, it was shown that secondorder cone optimization problems can be defined for each arc independent of the others, that nulling of zeroth and higher moments can be encoded as constraints, and that individual arcs can be optimized in seconds. For use in steadystate imaging, sampling duty cycles are predicted to exceed 95 percent. Using such pseudorandom trajectories, aliasing caused by undersampling manifests itself as incoherent noise. In this paper, a genetic algorithm (GA) is formulated and numerically evaluated. A large set of arcs is designed using previous methods, and the GA choses particular fit subsets of a given size, corresponding to a desired acquisition time. Numerical simulations of 1 second acquisitions show good detail and acceptable noise for largevolume imaging with 32 coils. Copyright © 2008 A. T. Curtis and C. K. Anand. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.
DOI 10.1155/IJBI/2006/49378 Progressive Magnetic Resonance Image Reconstruction Based on Iterative Solution of a Sparse Linear System
, 2005
"... Image reconstruction from nonuniformly sampled spatial frequency domain data is an important problem that arises in computed imaging. Current reconstruction techniques suffer from limitations in their model and implementation. In this paper, we present a new reconstruction method that is based on so ..."
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Image reconstruction from nonuniformly sampled spatial frequency domain data is an important problem that arises in computed imaging. Current reconstruction techniques suffer from limitations in their model and implementation. In this paper, we present a new reconstruction method that is based on solving a system of linear equations using an efficient iterative approach. Image pixel intensities are related to the measured frequency domain data through a set of linear equations. Although the system matrix is too dense and large to solve by direct inversion in practice, a simple orthogonal transformation to the rows of this matrix is applied to convert the matrix into a sparse one up to a certain chosen level of energy preservation. The transformed system is subsequently solved using the conjugate gradient method. This method is applied to reconstruct images of a numerical phantom as well as magnetic resonance images from experimental spiral imaging data. The results support the theory and demonstrate that the computational load of this method is similar to that of standard gridding, illustrating its practical utility. Copyright © 2006 Yasser M. Kadah et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.
a pseudorandom, noncartesian sampling scheme
"... One important topic in Magnetic Resonance Imaging (MRI) is a desire for faster and more efficient scanning, with an elimination, or at least minimization, of artifacts in the resulting image. Reducing patient discomfort, increasing scanner throughput, difficulties in imaging dynamic elements (cardio ..."
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One important topic in Magnetic Resonance Imaging (MRI) is a desire for faster and more efficient scanning, with an elimination, or at least minimization, of artifacts in the resulting image. Reducing patient discomfort, increasing scanner throughput, difficulties in imaging dynamic elements (cardiovascular system), and minimization of movement artifacts motivate faster scan times. To this end, more complicated and mathematically intense sampling strategies have been developed which either undersample or ignore portions of kspace. These missing samples manifest themselves as specific artifacts indicative of the sampling strategy and the amount of undersampling. Durga uses pseudorandom, volumetric and velocity insensitive kspace trajectories, which are derived from secondorder cone optimization problems [2]. Undersampling a random trajectory results in artifacts which resemble incoherent noise [19] instead of aliased images. Velocity insensitive trajectories do not require rewinders to balance first or higher order moments.