Cross-validation-based kernel support selection for improved GRAPPA reconstruction.

The extended version of the generalized autocalibrating partially parallel acquisition (GRAPPA) technique incorporates multiple lines and multiple columns of measured k-space data to estimate missing data. For a given accelerated dataset, the selection of the measured data points for fitting a missing datum (i.e., the kernel support) that provides optimal reconstruction depends on coil array configuration, noise level in the acquired data, imaging configuration, and number and position of autocalibrating signal lines. In this work, cross-validation is used to select the kernel support that best balances the conflicting demands of fit accuracy and stability in GRAPPA reconstruction. The result is an optimized tradeoff between artifacts and noise. As demonstrated with experimental data, the method improves image reconstruction with GRAPPA. Because the method is simple and applied in postprocessing, it can be used with GRAPPA routinely.     

Improved parallel MR imaging using a coefficient penalized regularization for GRAPPA reconstruction

A novel coefficient penalized regularization method for generalized autocalibrating partially parallel acquisitions (GRAPPA) reconstruction is developed for improving MR image quality. In this method, the fitting coefficients of the source data are weighted with different penalty factors, which are highly dependent upon the relative displacements from the source data to the target data in k‐space. The imaging data from both phantom testing and in vivo MRI experiments demonstrate that the coefficient penalized regularization method in GRAPPA reconstruction is able to reduce noise amplification to a greater degree. Therefore, the method enhances the quality of images significantly when compared to the previous least squares and Tikhonov regularization methods. Magn Reson Med 69:1109–1114, 2013. © 2012 Wiley Periodicals, Inc.     

IIR GRAPPA for parallel MR image reconstruction

Accelerated parallel MRI has advantage in imaging speed, and its image quality has been improved continuously in recent years. This paper introduces a two‐dimensional infinite impulse response model of inverse filter to replace the finite impulse response model currently used in generalized autocalibrating partially parallel acquisitions class image reconstruction methods. The infinite impulse response model better characterizes the correlation of k‐space data points and better approximates the perfect inversion of parallel imaging process, resulting in a novel generalized image reconstruction method for accelerated parallel MRI. This k‐space‐based reconstruction method includes the conventional generalized autocalibrating partially parallel acquisitions class methods as special cases and has a new infinite impulse response data estimation mechanism for effective improvement of image quality. The experiments on in vivo MRI data show that the proposed method significantly reduces reconstruction errors compared with the conventional two‐dimensional generalized autocalibrating partially parallel acquisitions method, particularly at the high acceleration rates. Magn Reson Med, 2010. © 2009 Wiley‐Liss, Inc.     

SPIRiT: Iterative self‐consistent parallel imaging reconstruction from arbitrary k‐space

A new approach to autocalibrating, coil‐by‐coil parallel imaging reconstruction, is presented. It is a generalized reconstruction framework based on self‐consistency. The reconstruction problem is formulated as an optimization that yields the most consistent solution with the calibration and acquisition data. The approach is general and can accurately reconstruct images from arbitrary k‐space sampling patterns. The formulation can flexibly incorporate additional image priors such as off‐resonance correction and regularization terms that appear in compressed sensing. Several iterative strategies to solve the posed reconstruction problem in both image and k‐space domain are presented. These are based on a projection over convex sets and conjugate gradient algorithms. Phantom and in vivo studies demonstrate efficient reconstructions from undersampled Cartesian and spiral trajectories. Reconstructions that include off‐resonance correction and nonlinear ?₁‐wavelet regularization are also demonstrated. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

High-pass GRAPPA: an image support reduction technique for improved partially parallel imaging.

Partially parallel imaging (PPI) is a widely used technique in clinical applications. A limitation of this technique is the strong noise and artifact in the reconstructed images when high reduction factors are used. This work aims to increase the clinical applicability of PPI by improving its performance at high reduction factors. A new concept, image support reduction, is introduced. A systematic filter-design approach for image support reduction is proposed. This approach shows more advantages when used with an important existing PPI technique, GRAPPA. An improved GRAPPA method, high-pass GRAPPA (hp-GRAPPA), was developed based on this approach. The new technique does not involve changing the original GRAPPA kernel and performs reconstruction in almost the same amount of time. Experimentally, it is demonstrated that the reconstructed images using hp-GRAPPA have much lower noise/artifact level than those reconstructed using GRAPPA.     

Non-Cartesian data reconstruction using GRAPPA operator gridding (GROG).

A novel approach that uses the concepts of parallel imaging to grid data sampled along a non-Cartesian trajectory using GRAPPA operator gridding (GROG) is described. GROG shifts any acquired data point to its nearest Cartesian location, thereby converting non-Cartesian to Cartesian data. Unlike other parallel imaging methods, GROG synthesizes the net weight for a shift in any direction from a single basis set of weights along the logical k-space directions. Given the vastly reduced size of the basis set, GROG calibration and reconstruction requires fewer operations and less calibration data than other parallel imaging methods for gridding. Instead of calculating and applying a density compensation function (DCF), GROG requires only local averaging, as the reconstructed points fall upon the Cartesian grid. Simulations are performed to demonstrate that the root mean square error (RMSE) values of images gridded with GROG are similar to those for images gridded using the gold-standard convolution gridding. Finally, GROG is compared to the convolution gridding technique using data sampled along radial, spiral, rosette, and BLADE (a.k.a. periodically rotated overlapping parallel lines with enhanced reconstruction [PROPELLER]) trajectories.     

Improved data reconstruction method for GRAPPA.

This paper presents an improved data reconstruction method for generalized autocalibrating partially parallel acquisitions (GRAPPA) using multicolumn multiline interpolation (MCMLI). Both nearest acquired line (ky) neighboring points and column (kx) neighboring points from all components of an array coil were used to reconstruct each missing datum through interpolation. A new fitting scheme was designed to estimate the interpolation weights. Both simulations and in vivo experiments demonstrated that the proposed method yields higher-quality data reconstruction than the original GRAPPA method, especially with high acceleration factors.     

Auto-calibrated parallel spiral imaging.

This work describes an auto-calibrated method for parallel imaging with spiral trajectory. The method is a k-space approach where an interpolation kernel, accounting for coil sensitivity factors, is derived from experimental data and used to interpolate the reduced data set in parallel imaging to estimate the missing k-space data. For the case of spiral imaging, this interpolation kernel is defined along radial directions so that missing spiral interleaves can be estimated directly from neighboring interleaves. This kernel is invariant along the radial direction but varies azimuthally. Therefore, the k-space is divided into angular sectors and sector-specific kernels are used. It is demonstrated experimentally that relatively few sectors are sufficient for accurate reconstruction, allowing for efficient implementation. The interpolation kernels can be derived either from a separate calibration scan or self-calibration data available with a dual-density spiral acquisition. The reconstruction method is implemented with two sampling strategies and experimentally demonstrated to be robust.     

Single‐shot multiecho parallel echo‐planar imaging (EPI) for diffusion tensor imaging (DTI) with improved signal‐to‐noise ratio (SNR) and reduced distortion

In this work, a multiecho parallel echo‐planar imaging (EPI) acquisition strategy is introduced as a way to improve the acquisition efficiency in parallel diffusion tensor imaging (DTI). With the use of an appropriate echo combination strategy, the sequence can provide signal‐to‐noise ratio (SNR) enhancement while maintaining the advantages of parallel EPI. Simulations and in vivo experiments demonstrate that a weighted summation of multiecho images provides a significant gain in SNR over the first echo image. It is experimentally demonstrated that this SNR gain can be utilized to reduce the number of measurements often required to ensure adequate SNR for accurate DTI measures. Furthermore, the multiple echoes can be used to derive a T₂ map, providing additional information that might be useful in some applications. Magn Reson Med 60:1512–1517, 2008. © 2008 Wiley‐Liss, Inc.     

Dynamic autocalibrated parallel imaging using temporal GRAPPA (TGRAPPA).

Current parallel imaging techniques for accelerated imaging require a fully encoded reference data set to estimate the spatial coil sensitivity information needed for reconstruction. In dynamic parallel imaging a time-interleaved acquisition scheme can be used, which eliminates the need for separately acquiring additional reference data, since the signal from directly adjacent time frames can be merged to build a set of fully encoded full-resolution reference data for coil calibration. In this work, we demonstrate that a time-interleaved sampling scheme, in combination with autocalibrated GRAPPA (referred to as TGRAPPA), allows one to easily update the coil weights for the GRAPPA algorithm dynamically, thereby improving the acquisition efficiency. This method may update coil sensitivity estimates frame by frame, thereby tracking changes in relative coil sensitivities that may occur during the data acquisition.     

Comparison of parallel acquisition techniques generalized autocalibrating partially parallel acquisitions (GRAPPA) and modified sensitivity encoding (mSENSE) in functional MRI (fMRI) at 3T

PURPOSE: To evaluate the parallel acquisition techniques, generalized autocalibrating partially parallel acquisitions (GRAPPA) and modified sensitivity encoding (mSENSE), and determine imaging parameters maximizing sensitivity toward functional activation at 3T. MATERIALS AND METHODS: A total of eight imaging protocols with different parallel imaging techniques (GRAPPA and mSENSE) and reduction factors (R = 1, 2, 3) were compared at different matrix sizes (64 and 128) with respect to temporal noise characteristics, artifact behavior, and sensitivity toward functional activation. RESULTS: Echo planar imaging (EPI) with GRAPPA and a reduction factor of 2 revealed similar image quality and sensitivity than full k-space EPI. A higher incidence of artifacts and a marked sensitivity loss occurred at R = 3. Even though the same eight-channel head coil was used for signal detection in all experiments, GRAPPA generally showed more benign patterns of spatially-varying noise amplification, and mSENSE was also more susceptible to residual unfolding artifacts than GRAPPA. CONCLUSION: At 3T and a reduction factor of 2, parallel imaging can be used with only little penalty with regard to sensitivity. With our implementation and coil setup the performance of GRAPPA was clearly superior to mSENSE. Thus, it seems advisable to pay special attention to the employed parallel imaging method and its implementation.     

Using GRAPPA to improve autocalibrated coil sensitivity estimation for the SENSE family of parallel imaging reconstruction algorithms

Two strategies are widely used in parallel MRI to reconstruct subsampled multicoil image data. SENSE and related methods employ explicit receiver coil spatial response estimates to reconstruct an image. In contrast, coil‐by‐coil methods such as GRAPPA leverage correlations among the acquired multicoil data to reconstruct missing k‐space lines. In self‐referenced scenarios, both methods employ Nyquist‐rate low‐frequency k‐space data to identify the reconstruction parameters. Because GRAPPA does not require explicit coil sensitivities estimates, it needs considerably fewer autocalibration signals than SENSE. However, SENSE methods allow greater opportunity to control reconstruction quality though regularization and thus may outperform GRAPPA in some imaging scenarios. Here, we employ GRAPPA to improve self‐referenced coil sensitivity estimation in SENSE and related methods using very few auto‐calibration signals. This enables one to leverage each methods' inherent strength and produce high quality self‐referenced SENSE reconstructions. Magn Reson Med 60:462–467, 2008. © 2008 Wiley‐Liss, Inc.     

Fast method for 1D non-cartesian parallel imaging using GRAPPA.

MRI with non-Cartesian sampling schemes can offer inherent advantages. Radial acquisitions are known to be very robust, even in the case of vast undersampling. This is also true for 1D non-Cartesian MRI, in which the center of k-space is oversampled or at least sampled at the Nyquist rate. There are two main reasons for the more relaxed foldover artifact behavior: First, due to the oversampling of the center, high-energy foldover artifacts originating from the center of k-space are avoided. Second, due to the non-equidistant sampling of k-space, the corresponding field of view (FOV) is no longer well defined. As a result, foldover artifacts are blurred over a broad range and appear less severe. The more relaxed foldover artifact behavior and the densely sampled central k-space make trajectories of this type an ideal complement to autocalibrated parallel MRI (pMRI) techniques, such as generalized autocalibrating partially parallel acquisitions (GRAPPA). Although pMRI can benefit from non-Cartesian trajectories, this combination has not yet entered routine clinical use. One of the main reasons for this is the need for long reconstruction times due to the complex calculations necessary for non-Cartesian pMRI. In this work it is shown that one can significantly reduce the complexity of the calculations by exploiting a few specific properties of k-space-based pMRI.     

Zigzag sampling for improved parallel imaging

Conventional Cartesian parallel MRI methods are limited to the sensitivity variations provided by the underlying receiver coil array in the dimension in which the data reduction is carried out, namely, the phase‐encoding directions. However, in this work an acquisition strategy is presented that takes advantage of sensitivity variations in the readout direction, thus improving the parallel imaging reconstruction process. This is achieved by employing rapidly oscillating phase‐encoding gradients during the actual readout. The benefit of this approach is demonstrated in vivo using various zigzag‐shaped gradient trajectory designs. It is shown that zigzag type sampling, in analogy to CAIPIRINHA, modifies the appearance of aliasing in 2D and 3D imaging, thereby utilizing additional sensitivity variations in the readout direction directly resulting in improved parallel imaging reconstruction performance. Magn Reson Med 60:474–478, 2008. © 2008 Wiley‐Liss, Inc.     

Direct parallel image reconstructions for spiral trajectories using GRAPPA.

The use of spiral trajectories is an efficient way to cover a desired k-space partition in magnetic resonance imaging (MRI). Compared to conventional Cartesian k-space sampling, it allows faster acquisitions and results in a slight reduction of the high gradient demand in fast dynamic scans, such as in functional MRI (fMRI). However, spiral images are more susceptible to off-resonance effects that cause blurring artifacts and distortions of the point-spread function (PSF), and thereby degrade the image quality. Since off-resonance effects scale with the readout duration, the respective artifacts can be reduced by shortening the readout trajectory. Multishot experiments represent one approach to reduce these artifacts in spiral imaging, but result in longer scan times and potentially increased flow and motion artifacts. Parallel imaging methods are another promising approach to improve image quality through an increase in the acquisition speed. However, non-Cartesian parallel image reconstructions are known to be computationally time-consuming, which is prohibitive for clinical applications. In this study a new and fast approach for parallel image reconstructions for spiral imaging based on the generalized autocalibrating partially parallel acquisitions (GRAPPA) methodology is presented. With this approach the computational burden is reduced such that it becomes comparable to that needed in accelerated Cartesian procedures. The respective spiral images with two- to eightfold acceleration clearly benefit from the advantages of parallel imaging, such as enabling parallel MRI single-shot spiral imaging with the off-resonance behavior of multishot acquisitions.     

Comparison of reconstruction accuracy and efficiency among autocalibrating data‐driven parallel imaging methods

The class of autocalibrating “data‐driven” parallel imaging (PI) methods has gained attention in recent years due to its ability to achieve high quality reconstructions even under challenging imaging conditions. The aim of this work was to perform a formal comparative study of various data‐driven reconstruction techniques to evaluate their relative merits for certain imaging applications. A total of five different reconstruction methods are presented within a consistent theoretical framework and experimentally compared in terms of the specific measures of reconstruction accuracy and efficiency using one‐dimensional (1D)‐accelerated Cartesian datasets. It is shown that by treating the reconstruction process as two discrete phases, a calibration phase and a synthesis phase, the reconstruction pathway can be tailored to exploit the computational advantages available in certain data domains. A new “split‐domain” reconstruction method is presented that performs the calibration phase in k‐space (k_x, k_y) and the synthesis phase in a hybrid (x, k_y) space, enabling highly accurate 2D neighborhood reconstructions to be performed more efficiently than previously possible with conventional techniques. This analysis may help guide the selection of PI methods for a given imaging task to achieve high reconstruction accuracy at minimal computational expense. Magn Reson Med 59:382–395, 2008. © 2008 Wiley‐Liss, Inc.     

Parallel MRI with extended and averaged GRAPPA kernels (PEAK-GRAPPA): optimized spatiotemporal dynamic imaging

Purpose

To evaluate an optimized k‐t‐space related reconstruction method for dynamic magnetic resonance imaging (MRI), a method called PEAK‐GRAPPA (Parallel MRI with Extended and Averaged GRAPPA Kernels) is presented which is based on an extended spatiotemporal GRAPPA kernel in combination with temporal averaging of coil weights.

Materials and Methods

The PEAK‐GRAPPA kernel consists of a uniform geometry with several spatial and temporal source points from acquired k‐space lines and several target points from missing k‐space lines. In order to improve the quality of coil weight estimation sets of coil weights are averaged over the temporal dimension.

Results

The kernel geometry leads to strongly decreased reconstruction times compared to the recently introduced k‐t‐GRAPPA using different kernel geometries with only one target point per kernel to fit. Improved results were obtained in terms of the root mean square error and the signal‐to‐noise ratio as demonstrated by in vivo cardiac imaging.

Conclusion

Using a uniform kernel geometry for weight estimation with the properties of uncorrelated noise of different acquired timeframes, optimized results were achieved in terms of error level, signal‐to‐noise ratio, and reconstruction time. J. Magn. Reson. Imaging 2008;28:1226–1232. © 2008 Wiley‐Liss, Inc.     

Discrepancy-based adaptive regularization for GRAPPA reconstruction

PURPOSE: To develop a novel regularization method for GRAPPA by which the regularization parameters can be optimally and adaptively chosen. MATERIALS AND METHODS: In the fit procedures in GRAPPA, the discrepancy principle, which chooses the regularization parameter based on a priori information about the noise level in the autocalibrating signals (ACS), is used with the truncated singular value decomposition (TSVD) regularization and the Tikhonov regularization, and its performance is compared with the singular value (SV) threshold method and the L-curve method, respectively by axial and sagittal head imaging experiments. RESULTS: In both axial and sagittal reconstructions, normal GRAPPA reconstruction results exhibit a relatively high level of noise. With discrepancy-based choices of parameters, regularization can improve the signal-to-noise ratio (SNR) with only a very modest increase in aliasing artifacts. The L-curve method in all of the reconstructions leads to overregularization, which causes severe residual aliasing artifacts. The 10% SV threshold method yields good overall image quality in the axial case, but in the sagittal case it also leads to an obvious increase in aliasing artifacts. CONCLUSION: Neither a fixed SV threshold nor the L-curve are robust means of choosing the appropriate parameters in GRAPPA reconstruction. However, with the discrepancy-based parameter-choice strategy, adaptively regularized GRAPPA can be used to automatically choose nearly optimal parameters for reconstruction and achieve an excellent compromise between SNR and artifacts.     

Nonlinear GRAPPA: a kernel approach to parallel MRI reconstruction

GRAPPA linearly combines the undersampled k-space signals to estimate the missing k-space signals where the coefficients are obtained by fitting to some auto-calibration signals (ACS) sampled with Nyquist rate based on the shift-invariant property. At high acceleration factors, GRAPPA reconstruction can suffer from a high level of noise even with a large number of auto-calibration signals. In this work, we propose a nonlinear method to improve GRAPPA. The method is based on the so-called kernel method which is widely used in machine learning. Specifically, the undersampled k-space signals are mapped through a nonlinear transform to a high-dimensional feature space, and then linearly combined to reconstruct the missing k-space data. The linear combination coefficients are also obtained through fitting to the ACS data but in the new feature space. The procedure is equivalent to adding many virtual channels in reconstruction. A polynomial kernel with explicit mapping functions is investigated in this work. Experimental results using phantom and in vivo data demonstrate that the proposed nonlinear GRAPPA method can significantly improve the reconstruction quality over GRAPPA and its state-of-the-art derivatives.