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39
Nonuniform Fast Fourier Transforms Using MinMax Interpolation
 IEEE Trans. Signal Process
, 2003
"... The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformlyspaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e.,a nonuniform FT . Several pap ..."
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Cited by 90 (16 self)
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The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformlyspaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e.,a nonuniform FT . Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents an interpolation method for the nonuniform FT that is optimal in the minmax sense of minimizing the worstcase approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the minmax approach provides substantially lower approximation errors than conventional interpolation methods. The minmax criterion is also useful for optimizing the parameters of interpolation kernels such as the KaiserBessel function.
Toeplitzbased iterative image reconstruction for MRI with correction for magnetic field inhomogeneity
 IEEE Trans. Signal Process
, 2005
"... Abstract — In some types of magnetic resonance (MR) imaging, particularly functional brain scans, the conventional Fourier model for the measurements is inaccurate. Magnetic field inhomogeneities, caused by imperfect main fields and by magnetic susceptibility variations, induce distortions in images ..."
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Cited by 20 (4 self)
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Abstract — In some types of magnetic resonance (MR) imaging, particularly functional brain scans, the conventional Fourier model for the measurements is inaccurate. Magnetic field inhomogeneities, caused by imperfect main fields and by magnetic susceptibility variations, induce distortions in images that are reconstructed by conventional Fourier methods. These artifacts hamper the use of functional MR imaging (fMRI) in brain regions near air/tissue interfaces. Recently, iterative methods that combine the conjugate gradient (CG) algorithm with nonuniform FFT (NUFFT) operations have been shown to provide considerably improved image quality relative to the conjugatephase method. However, for nonCartesian kspace trajectories, each CGNUFFT iteration requires numerous kspace interpolations, operations that are computationally expensive and poorly suited to fast hardware implementations. This paper proposes a faster iterative approach to fieldcorrected MR image reconstruction based on the CG algorithm and certain Toeplitz matrices. This CGToeplitz approach requires kspace interpolations only for the initial iteration; thereafter only FFTs are required. Simulation results show that the proposed CGToeplitz approach produces equivalent image quality as the CGNUFFT method with significantly reduced computation time. Index Terms — fMRI imaging, spiral trajectory, magnetic susceptibility, nonCartesian sampling I.
Iterative image reconstruction in MRI with separate magnitude and phase regularization
 In Proc. IEEE Intl. Symp. Biomed. Imag
, 2004
"... Iterative methods for image reconstruction in MRI are useful in several applications, including reconstruction from nonCartesian kspace samples, compensation for magnetic field inhomogeneities, and imaging with multiple receive coils. Existing iterative MR image reconstruction methods are either u ..."
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Cited by 9 (2 self)
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Iterative methods for image reconstruction in MRI are useful in several applications, including reconstruction from nonCartesian kspace samples, compensation for magnetic field inhomogeneities, and imaging with multiple receive coils. Existing iterative MR image reconstruction methods are either unregularized, and therefore sensitive to noise, or have used regularization methods that smooth the complex valued image. These existing methods regularize the real and imaginary components of the image equally. In many MRI applications, including T ∗ 2weighted imaging as used in fMRI BOLD imaging, one expects most of the signal information of interest to be contained in the magnitude of the voxel value, whereas the phase values are expected to vary smoothly spatially. This paper proposes separate regularization of the magnitude and phase components, preserving the spatial resolution of the magnitude component while strongly regularizing the phase component. This leads to a nonconvex regularized leastsquares cost function. We describe a new iterative algorithm that monotonically decreases this cost function. The resulting images have reduced noise relative to conventional regularization methods. 1.
How GPUs can improve the quality of magnetic resonance imaging
 In The First Workshop on General Purpose Processing on Graphics Processing Units
, 2007
"... Abstract — In magnetic resonance imaging (MRI), nonCartesian scan trajectories are advantageous in a wide variety of emerging applications. Advanced reconstruction algorithms that operate directly on nonCartesian scan data using optimality criteria such as leastsquares (LS) can produce significan ..."
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Cited by 9 (3 self)
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Abstract — In magnetic resonance imaging (MRI), nonCartesian scan trajectories are advantageous in a wide variety of emerging applications. Advanced reconstruction algorithms that operate directly on nonCartesian scan data using optimality criteria such as leastsquares (LS) can produce significantly better images than conventional algorithms that apply a fast Fourier transform (FFT) after interpolating the scan data onto a Cartesian grid. However, advanced LS reconstructions require significantly more computation than conventional reconstructions based on the FFT. For example, one LS algorithm requires nearly six hours to reconstruct a single threedimensional image on a modern CPU. Our work demonstrates that this advanced reconstruction can be performed quickly and efficiently on a modern GPU, with the reconstruction of a 64 3 3D image requiring just three minutes, an acceptable latency for key applications. This paper describes how the reconstruction algorithm leverages the resources of the GeForce 8800 GTX (G80) to achieve over 150 GFLOPS in performance. We find that the combination of tiling the data and storing the data in the G80’s constant memory dramatically reduces the algorithm’s required bandwidth to offchip memory. The G80’s special functional units provide substantial acceleration for the trigonometric computations in the algorithm’s inner loops. Finally, experimentdriven code transformations increase the reconstruction’s performance by as much as 60 % to 80%. I.
NoiseAdaptive Nonlinear Diffusion Filtering of MR Images With Spatially Varying Noise Levels
 Magnetic Resonance in Medicine
, 2004
"... Anisotropic diffusion filtering is widely used for MR image enhancement. However, the anisotropic filter is nonoptimal for MR images with spatially varying noise levels, such as images reconstructed from sensitivityencoded data and intensity inhomogeneitycorrected images. In this work, a new metho ..."
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Cited by 8 (0 self)
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Anisotropic diffusion filtering is widely used for MR image enhancement. However, the anisotropic filter is nonoptimal for MR images with spatially varying noise levels, such as images reconstructed from sensitivityencoded data and intensity inhomogeneitycorrected images. In this work, a new method for filtering MR images with spatially varying noise levels is presented. In the new method, a priori information regarding the image noise level spatial distribution is utilized for the local adjustment of the anisotropic diffusion filter. Our new method was validated and compared with the standard filter on simulated and real MRI data. The noiseadaptive method was demonstrated to outperform the standard anisotropic diffusion filter in both image error reduction and image signaltonoise ratio (SNR) improvement. The method was also applied to inhomogeneitycorrected and sensitivity encoding (SENSE) images.
Joint estimation of image and coil sensitivities in parallel MRI
 In Proc. IEEE Intl. Symp. Biomed. Imag
, 2006
"... Spiral MRI has received increasing attention due to its reduced T ∗2decay and robustness against bulk physiologic motion. In parallel imaging, spiral trajectories are especially of great interest due to their inherent selfcalibration capabilities, which is especially useful for dynamic imaging ..."
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Cited by 3 (0 self)
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Spiral MRI has received increasing attention due to its reduced T ∗2decay and robustness against bulk physiologic motion. In parallel imaging, spiral trajectories are especially of great interest due to their inherent selfcalibration capabilities, which is especially useful for dynamic imaging applications such as fMRI and cardiac imaging. The existing selfcalibration techniques for spiral use the kspace center data that are sampled densely in the accelerated acquisition for coil sensitivity estimation. There exists a tradeoff in choosing the radius of the center data: it must be sufficiently large to contain all major spatial frequencies of coil sensitivity, but not too large to cause significant aliasing artifacts due to undersampling below Nyquist rate as the trajectory moves away from the center kspace. To address this tradeoff, we generalize the JSENSE approach, which has demonstrated success in Cartesian case, to spiral trajectory. Specifically, the method jointly estimates the coil sensitivities and reconstructs the desired image through cross validations so that the sensitivities are estimated from the full data recovered by SENSE instead of the center kspace data only, thereby increasing high frequency information without introducing aliasing artifacts. We use experimental results to show the proposed method improves sensitivities, which leads to a more accurate SENSE reconstruction. 1.
Fast, iterative image reconstruction for MRI in the presence of field inhomogeneities
 IEEE Trans. Med. Imaging
, 2003
"... Abstract—In magnetic resonance imaging, magnetic field inhomogeneities cause distortions in images that are reconstructed by conventional fast Fourier trasform (FFT) methods. Several noniterative image reconstruction methods are used currently to compensate for field inhomogeneities, but these metho ..."
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Cited by 2 (1 self)
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Abstract—In magnetic resonance imaging, magnetic field inhomogeneities cause distortions in images that are reconstructed by conventional fast Fourier trasform (FFT) methods. Several noniterative image reconstruction methods are used currently to compensate for field inhomogeneities, but these methods assume that the field map that characterizes the offresonance frequencies is spatially smooth. Recently, iterative methods have been proposed that can circumvent this assumption and provide improved compensation for offresonance effects. However, straightforward implementations of such iterative methods suffer from inconveniently long computation times. This paper describes a tool for accelerating iterative reconstruction of fieldcorrected MR images: a novel timesegmented approximation to the MR signal equation. We use a min–max formulation to derive the temporal interpolator. Speedups of around 60 were achieved by combining this temporal interpolator with a nonuniform fast Fourier transform with normalized root mean squared approximation errors of 0.07%. The proposed method provides fast, accurate, fieldcorrected image reconstruction even when the field map is not smooth. Index Terms—Field inhomogeneity correction, image reconstruction, iterative methods, magnetic resonance imaging, temporal interpolation, time segmentation. I.
High Performance Computers
, 1991
"... ACM, (2008). This is the author’s version of the work. It is posted here by permission of ACM for your personal use. Not for ..."
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ACM, (2008). This is the author’s version of the work. It is posted here by permission of ACM for your personal use. Not for
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