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SparsityPromoting Calibration for GRAPPA Accelerated Parallel MRI Reconstruction
"... Abstract—The amount of calibration data needed to produce images of adequate quality can prevent autocalibrating parallel imaging reconstruction methods like generalized autocalibrating partially parallel acquisitions (GRAPPA) from achieving a high total acceleration factor. To improve the quality ..."
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Abstract—The amount of calibration data needed to produce images of adequate quality can prevent autocalibrating parallel imaging reconstruction methods like generalized autocalibrating partially parallel acquisitions (GRAPPA) from achieving a high total acceleration factor. To improve the quality of calibration when the number of autocalibration signal (ACS) lines is restricted, we propose a sparsitypromoting regularized calibration method that finds a GRAPPA kernel consistent with the ACS fit equations that yields jointly sparse reconstructed coil channel images. Several experiments evaluate the performance of the proposed method relative to unregularized and existing regularized calibration methods for both lowquality and underdetermined fits from the ACS lines. These experiments demonstrate that the proposed method, like other regularization methods, is capable of mitigating noise amplification, and in addition, the proposed method is particularly effective at minimizing coherent aliasing artifacts caused by poor kernel calibration in real data. Using the proposed method, we can increase the total achievable acceleration while reducing degradation of the reconstructed image better than existing regularized calibration methods. Index Terms—Compressed sensing, image reconstruction, magnetic resonance imaging, parallel imaging. I.
discrimination in the ACS lines1
"... 1Improving GRAPPA reconstruction by frequency ..."
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1A review on statistical noise models for Magnetic Resonance Imaging1
"... Many image processing applications within MRI are grounded on stochastic methods based on the prior knowledge on the statistics of noise. The ubiquitous Gaussian model provides a poor fitting for mediumlow SNRs, yielding to the use of Rician statistics: the noise in MRI has been traditionally model ..."
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Many image processing applications within MRI are grounded on stochastic methods based on the prior knowledge on the statistics of noise. The ubiquitous Gaussian model provides a poor fitting for mediumlow SNRs, yielding to the use of Rician statistics: the noise in MRI has been traditionally modeled as a stationary process governed by a Rician distribution with constant noise power at each voxel. Modern MRI systems turn this model questionable, making it necessary to develop into more complex patterns. We aim at comprehensively reviewing the main statistical rationales and formulations for the noise in MRI lately found in the literature. We attend to three different criteria: the firstorder, voxelwise probability law, the possible spatial variability of the parameters of such distribution, and the possible noise interdependences between neighboring voxels. Several applications using statistical methods are overviewed, discussing the implications each of the models has on them. Finally, we explore the applicability of the surveyed models to some MRI protocols commonly used. Whereas many parallel and nonparallel acquisitions like GRAPPA and SENSE may be fitted into one of the existing models, other nonlinear reconstruction procedures are lacking a proper noise characterization.
Parallel Magnetic Resonance Imaging as Approximation in a Reproducing Kernel Hilbert Space
, 2014
"... In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (kspace), typically by timeconsuming linebyline scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data using multiple receivers (parallel imaging), and by using more ..."
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In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (kspace), typically by timeconsuming linebyline scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data using multiple receivers (parallel imaging), and by using more efficient nonCartesian sampling schemes. To understand and design kspace sampling patterns, a theoretical framework is needed to analyze how well arbitrary sampling patterns reconstruct unsampled kspace using receive coil information. As shown here, reconstruction from samples at arbitrary locations can be understood as approximation of vectorvalued functions from the acquired samples and formulated using a Reproducing Kernel Hilbert Space (RKHS) with a matrixvalued kernel defined by the spatial sensitivities of the receive coils. This establishes a formal connection between approximation theory and parallel imaging. Theoretical tools from approximation theory can then be used to understand reconstruction in kspace and to extend the analysis of the effects of samples selection beyond the traditional imagedomain gfactor noise analysis to both noise amplification and approximation errors in kspace. This is demonstrated with numerical examples.