The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformly-spaced 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 min-max sense of minimizing the worst-case approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the min-max approach provides substantially lower approximation errors than conventional interpolation methods. The min-max criterion is also useful for optimizing the parameters of interpolation kernels such as the Kaiser-Bessel function.

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 non-Cartesian k-space trajectories, each CG-NUFFT iteration requires numerous k-space interpolations, operations that are computationally expensive and poorly suited to fast hardware implementations. This paper proposes a faster iterative approach to field-corrected MR image reconstruction based on the CG algorithm and certain Toeplitz matrices. This CG-Toeplitz approach requires k-space interpolations only for the initial iteration; thereafter only FFTs are required. Simulation results show that the proposed CG-Toeplitz approach produces equivalent image quality as the CG-NUFFT method with significantly reduced computation time. Index Terms — fMRI imaging, spiral trajectory, magnetic susceptibility, non-Cartesian sampling I.

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 sensitivity-encoded data and intensity inhomogeneity-corrected 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 noise-adaptive method was demonstrated to outperform the standard anisotropic diffusion filter in both image error reduction and image signal-to-noise ratio (SNR) improvement. The method was also applied to inhomogeneity-corrected and sensitivity encoding (SENSE) images.

Abstract — In magnetic resonance imaging (MRI), non-Cartesian scan trajectories are advantageous in a wide variety of emerging applications. Advanced reconstruction algorithms that operate directly on non-Cartesian scan data using optimality criteria such as least-squares (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 three-dimensional 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 off-chip memory. The G80’s special functional units provide substantial acceleration for the trigonometric computations in the algorithm’s inner loops. Finally, experiment-driven code transformations increase the reconstruction’s performance by as much as 60 % to 80%. I.

Abstract not found

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 off-resonance frequencies is spatially smooth. Recently, iterative methods have been proposed that can circumvent this assumption and provide improved compensation for off-resonance effects. However, straightforward implementations of such iterative methods suffer from inconveniently long computation times. This paper describes a tool for accelerating iterative reconstruction of field-corrected MR images: a novel time-segmented 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, field-corrected 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.

This thesis describes a number of algorithms related to the acquisition, reconstruc-tion and post-processing of Magnetic Resonance data. The basic theme underlying each of these algorithms is the use of a unified systems approach to exploit infor-mation redundancy available in MR imaging. There are three basic contributions. The first concerns the development of a new motion correction algorithm for Time-Resolved MR Angiography. Motion artifacts in angiography data are very difficult to remove without affecting vascular evolution. Our algorithm uses suc-cessive POCS iterations to remove unwanted artifacts without degrading quality. Double-blind testing has indicated significant improvement over angiograms cre-ated manually by experienced radiologist. In summary, our method seeks to exploit temporal redundancy to remove motion artifacts. The second contribution is our recent work on Parallel MR imaging in presence of sensitivity errors using a Maximum Likelihood technique. It can be shown that standard phased array reconstruction using popular parallel imaging methods is inappropriate in presence of errors in measuring sensitivity maps of coils. Since

This paper is concerned about high resolution reconstruction of projection reconstruction MR imaging from angular under-sampled k-space 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 under-sampled radial k-space 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 under-sampled k-space data.

Abstract not found

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 errors-in-variables 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 quasi-quadratic objective function, which can be efficiently minimized. Experimental evidence suggests substantial gains over conventional SENSE, especially in non-ideal imaging conditions like low SNR, high g-factors, large acceleration and misaligned sensitivity maps.