Generalized Autocalibrating Partially Parallel Acquisitions Reconstruction Research Articles

Improved Parallel Magnertic Resonance Imaging reconstruction with Complex Proximal Support Vector Regression

Generalized Auto-calibrating Partially Parallel Acquisitions (GRAPPA) has been widely used to reduce imaging time in Magnetic Resonance Imaging. GRAPPA synthesizes missing data by using a linear interpolation of neighboring measured data over all coils, thus accuracy of the interpolation weights fitting to the auto-calibrating signal data is crucial for the GRAPPA reconstruction. Conventional GRAPPA algorithms fitting the interpolation weights with a least squares solution are sensitive to interpolation window size. MKGRAPPA that estimates the interpolation weights with support vector machine reduces the sensitivity of the k-space reconstruction to interpolation window size, whereas it is computationally expensive. In this study, a robust GRAPPA reconstruction method is proposed that applies an extended proximal support vector regression (PSVR) to fit the interpolation weights with wavelet kernel mapping. Experimental results on in vivo MRI data show that the proposed PSVR-GRAPPA method visually improves overall quality compared to conventional GRAPPA methods, while it has faster reconstruction speed compared to MKGRAPPA.

Exact Calculation of Noise Maps and ${g}$ -Factor in GRAPPA Using a ${k}$ -Space Analysis.

Characterization of the noise distribution in magnetic resonance images has multiple applications, including quality assurance and protocol optimization. Noise characterization is particularly important in the presence of parallel imaging acceleration with multi-coil acquisitions, where the noise distribution can contain severe spatial heterogeneities. If the parallel imaging reconstruction is a linear process, an accurate noise analysis can be carried out by taking into account the correlations between all the samples involved. However, for -space-based techniques such as generalized autocalibrating partially parallel acquisition (GRAPPA), the exact analysis has been considered computationally prohibitive due to the very large size of the noise covariance matrices required to characterize the noise propagation from -space to image space. Previously proposed methods avoid this computational burden by formulating the GRAPPA reconstruction as a pixel-wise linear operation performed in the image space. However, these methods are not exact in the presence of non-uniform sampling of -space (e.g., containing a calibration region). For this reason, in this paper, we develop an accurate characterization of the noise distribution for self-calibrated parallel imaging in the presence of arbitrary Cartesian sampling patterns. By exploiting the symmetries and separability in the noise propagation process, the proposed method is computationally efficient and does not require large matrices. Under the assumption of a fixed reconstruction kernel, this method provides the precise distribution of the noise variance for each coil's image. These coil-by-coil noise maps are subsequently combined according to the coil combination approach used in image reconstruction, and therefore can be applied with both complex coil combination and root-sum-of-squares approaches. In this paper, we present the proposed noise characterization method and compare it to previous techniques using Monte Carlo simulations as well as phantom acquisitions.

Iterative Schemes to Solve Low-Dimensional Calibration Equations in Parallel MR Image Reconstruction with GRAPPA.

GRAPPA (Generalized Autocalibrating Partially Parallel Acquisition) is a widely used parallel MRI reconstruction technique. The processing of data from multichannel receiver coils may increase the storage and computational requirements of GRAPPA reconstruction. Random projection on GRAPPA (RP-GRAPPA) uses random projection (RP) method to overcome the computational overheads of solving large linear equations in the calibration phase of GRAPPA, saving reconstruction time. However, RP-GRAPPA compromises the reconstruction accuracy in case of large reductions in the dimensions of calibration equations. In this paper, we present the implementation of GRAPPA reconstruction method using potential iterative solvers to estimate the reconstruction coefficients from the randomly projected calibration equations. Experimental results show that the proposed methods withstand the reconstruction accuracy (visually and quantitatively) against large reductions in the dimension of linear equations, when compared with RP-GRAPPA reconstruction. Particularly, the proposed method using conjugate gradient for least squares (CGLS) demonstrates more savings in the computational time of GRAPPA, without significant loss in the reconstruction accuracy, when compared with RP-GRAPPA. It is also demonstrated that the proposed method using CGLS complements the channel compression method for reducing the computational complexities associated with higher channel count, thereby resulting in additional memory savings and speedup.

Instrument Variables for Reducing Noise in Parallel MRI Reconstruction.

Generalized autocalibrating partially parallel acquisition (GRAPPA) has been a widely used parallel MRI technique. However, noise deteriorates the reconstructed image when reduction factor increases or even at low reduction factor for some noisy datasets. Noise, initially generated from scanner, propagates noise-related errors during fitting and interpolation procedures of GRAPPA to distort the final reconstructed image quality. The basic idea we proposed to improve GRAPPA is to remove noise from a system identification perspective. In this paper, we first analyze the GRAPPA noise problem from a noisy input-output system perspective; then, a new framework based on errors-in-variables (EIV) model is developed for analyzing noise generation mechanism in GRAPPA and designing a concrete method—instrument variables (IV) GRAPPA to remove noise. The proposed EIV framework provides possibilities that noiseless GRAPPA reconstruction could be achieved by existing methods that solve EIV problem other than IV method. Experimental results show that the proposed reconstruction algorithm can better remove the noise compared to the conventional GRAPPA, as validated with both of phantom and in vivo brain data.

Empirical mode decomposition based GRAPPA reconstruction algorithm for parallel MRI

This paper presents a zero-assisted bivariate empirical mode decomposition (bEMD) based generalized autocalibrating partially parallel acquisitions (GRAPPA) for improved reconstruction of magnetic resonance images. Each line in the readout direction of the zero filled sub-sampled k-space is decomposed into intrinsic mode functions (IMFs) using bEMD to obtain multiple EMD domain k-spaces constructed from the respective IMFs of each line. GRAPPA reconstruction is then performed on these EMD domain k-spaces to calculate the missing lines of the sub-sampled k-spaces. These fully reconstructed EMD domain k-spaces are combined together to obtain the final reconstructed k-space of the desired object. The results of experimental tests using phantom, human brain and spine data demonstrate that the proposed EMD domain GRAPPA reconstruction method can result in better image quality than that of the conventional GRAPPA. It is also shown that the proposed approach can be incorporated with other k-space based reconstruction algorithms, e.g. iterative and nonlinear GRAPPA, for further reduction of reconstruction artifacts, in particular, at higher acceleration factor.

Improvement of temporal signal-to-noise ratio of GRAPPA accelerated echo planar imaging using a FLASH based calibration scan.

To demonstrate that the temporal signal-to-noise ratio (SNR) of generalized autocalibrating partially parallel acquisitions (GRAPPA) accelerated echo planar imaging (EPI) can be enhanced and made more spatially uniform by using a fast low angle shot (FLASH) based calibration scan. EPI of a phantom and human brains were acquired at 3 Tesla without and with GRAPPA acceleration factor of 2. The GRAPPA accelerated data were reconstructed using calibration scans acquired with EPI and FLASH acquisition schemes. The increase in temporal signal fluctuation due to GRAPPA reconstruction was quantified and compared. Simulated g-factor maps were also created for different calibration scans. GRAPPA accelerated phantom data exhibited areas with high g values when using the EPI based calibration for reconstruction. The g-factor maps were uniform when using the FLASH calibration scan. g was greater than 1.1 in 74% of pixels in 64 × 64 data reconstructed with the EPI calibration compared with only 15% when using the FLASH calibration scan. Human data also showed abnormally high g regions when using the EPI calibration but not when using the FLASH calibration scan. Use of the FLASH calibration scan increased the whole brain temporal SNR by ∼12% without affecting the image quality. Experimental observations were confirmed by simulations. A calibration scan based on a FLASH acquisition scheme can be used to improve the temporal SNR of GRAPPA accelerated EPI time series. Magn Reson Med 75:2362-2371, 2016. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.

GRAPPA reconstruction with spatially varying calibration of self-constraint.

To develop and evaluate a novel method of generalized auto-calibrating partially parallel acquisition (GRAPPA) with spatially varying calibration of self-constraint for parallel magnetic resonance imaging (MRI) reconstruction. The conventional GRAPPA independently estimates each missing sample with adjacent acquired data over multiple coils, thereby ignoring correlations inside missing data. Self-constrained methods can exploit correlations inside missing data by imposing linear dependence within full neighborhood kernels and showing improved reconstruction compared with GRAPPA. However, self-constraint kernels are currently calibrated by using auto-calibration signals. Thus, they may be suboptimal for reconstructing outer k-space because of spatially varying correlations. This study proposes a novel GRAPPA method with separate self-constraints (SSC-GRAPPA). In this method, the spatially varying self-constraint coefficients are adaptively calibrated by separately exploiting correlations inside missing and acquired data in the outer k-space. Both phantom and in vivo imaging experiments were conducted with retrospective undersampling to evaluate the performance of the proposed method. Compared with GRAPPA and self-constrained GRAPPA, the proposed SSC-GRAPPA generates images with reduced artifacts and noise. The proposed method provides an effective and efficient approach to improve parallel MRI reconstruction, and has potential to benefit routine clinical practice in the future.

Fast GRAPPA reconstruction with random projection.

To address the issue of computational complexity in generalized autocalibrating partially parallel acquisition (GRAPPA) when several calibration data are used. GRAPPA requires fully sampled data for accurate calibration with increasing data needed for higher reduction factors to maintain accuracy, which leads to longer computational time, especially in a three-dimensional (3D) setting and with higher channel count coils. Channel reduction methods have been developed to address this issue when massive array coils are used. In this study, the complexity problem was addressed from a different prospective. Instead of compressing to fewer channels, we propose the use of random projections to reduce the dimension of the linear equation in the calibration phase. The equivalence before and after the reduction is supported by the Johnson-Lindenstrauss lemma. The proposed random projection method can be integrated with channel reduction sequentially for even higher computational efficiency. Experimental results show that GRAPPA with random projection can achieve comparable image quality with much less computational time when compared with conventional GRAPPA without random projection. The proposed random projection method is able to reduce the computational time of GRAPPA, especially in a 3D setting, without compromising the image quality, or to improve the reconstruction quality by allowing more data for calibration when the computational time is a limiting factor. Magn Reson Med 74:71-80, 2015. © 2014 Wiley Periodicals, Inc.

Robust GRAPPA reconstruction using sparse multi-kernel learning with least squares support vector regression

Accuracy of interpolation coefficients fitting to the auto-calibrating signal data is crucial for k-space-based parallel reconstruction. Both conventional generalized autocalibrating partially parallel acquisitions (GRAPPA) reconstruction that utilizes linear interpolation function and nonlinear GRAPPA (NLGRAPPA) reconstruction with polynomial kernel function are sensitive to interpolation window and often cannot consistently produce good results for overall acceleration factors. In this study, sparse multi-kernel learning is conducted within the framework of least squares support vector regression to fit interpolation coefficients as well as to reconstruct images robustly under different subsampling patterns and coil datasets. The kernel combination weights and interpolation coefficients are adaptively determined by efficient semi-infinite linear programming techniques. Experimental results on phantom and in vivo data indicate that the proposed method can automatically achieve an optimized compromise between noise suppression and residual artifacts for various sampling schemes. Compared with NLGRAPPA, our method is significantly less sensitive to the interpolation window and kernel parameters.

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.

Denoising sparse images from GRAPPA using the nullspace method

To accelerate magnetic resonance imaging using uniformly undersampled (nonrandom) parallel imaging beyond what is achievable with generalized autocalibrating partially parallel acquisitions (GRAPPA) alone, the DEnoising of Sparse Images from GRAPPA using the Nullspace method is developed. The trade-off between denoising and smoothing the GRAPPA solution is studied for different levels of acceleration. Several brain images reconstructed from uniformly undersampled k-space data using DEnoising of Sparse Images from GRAPPA using the Nullspace method are compared against reconstructions using existing methods in terms of difference images (a qualitative measure), peak-signal-to-noise ratio, and noise amplification (g-factors) as measured using the pseudo-multiple replica method. Effects of smoothing, including contrast loss, are studied in synthetic phantom data. In the experiments presented, the contrast loss and spatial resolution are competitive with existing methods. Results for several brain images demonstrate significant improvements over GRAPPA at high acceleration factors in denoising performance with limited blurring or smoothing artifacts. In addition, the measured g-factors suggest that DEnoising of Sparse Images from GRAPPA using the Nullspace method mitigates noise amplification better than both GRAPPA and L1 iterative self-consistent parallel imaging reconstruction (the latter limited here by uniform undersampling).

New trajectory for image reconstruction based on GRAPPA

The sampling trajectory of traditional GRAPPA(generalized auto-calibrating partially parallel acquisitions) has some problems,such as bad reconstruction image,and long data scanning time.A new trajectory for GRAPPA reconstruction called 3D sampling trajectory was proposed.This method not only undersampled in phase encoding direction,but also in frequency encoding direction and coil direction.The missing data were calculated by a 3D kernel.Brain imaging experiment of real brain data demonstrates that this new trajectory and 3D kernel can make use of coil spatial sensitivity information effectively,improve quality of reconstruction image and reduce time of data scanning.In a word,3D sampling trajectory is an effective method.

Optimized parallel imaging for dynamic PC‐MRI with multidirectional velocity encoding

Phase contrast MRI with multidirectional velocity encoding requires multiple acquisitions of the same k-space lines to encode the underlying velocities, which can considerably lengthen the total scan time. To reduce scan time, parallel imaging is often applied. In dynamic phase contrast MRI using standard generalized autocalibrating partially parallel acquisitions (GRAPPA), several central k-spaces for autocalibration of the reconstruction (autocalibrating signal lines (ACS)) are typically acquired, separately for each velocity direction and each cardiac timeframe, for calculating the reconstruction weights. To further accelerate data acquisition, we developed two methods, which calculated weights with a substantially reduced number of ACSl lines. The effects on image quality and flow quantification were compared to fully sampled data, standard GRAPPA, and time-interleaved sampling scheme in combination with generalized autocalibrating partially parallel acquisitions (TGRAPPA). The results show that the two proposed methods can clearly improve scan efficiency while maintaining image quality and accuracy of measured flow or myocardial tissue velocities. Compared to TGRAPPA, the proposed methods were more accurate in evaluating flow velocity. In conclusion, the proposed reconstruction strategies are promising for dynamic multidirectionally encoded acquisitions and can easily be implemented using the standard GRAPPA reconstruction algorithm.

General formulation for quantitative G‐factor calculation in GRAPPA reconstructions

In this work a theoretical description for practical quantitative estimation of the noise enhancement in generalized autocalibrating partially parallel acquisitions (GRAPPA) reconstructions, equivalent to the geometry (g)-factor in sensitivity encoding for fast MRI (SENSE) reconstructions, is described. The GRAPPA g-factor is derived directly from the GRAPPA reconstruction weights. The procedure presented here also allows the calculation of quantitative g-factor maps for both the uncombined and combined accelerated GRAPPA images. This enables, for example, a fast comparison between the performances of various GRAPPA reconstruction kernels or SENSE reconstructions. The applicability of this approach is validated on phantom studies and demonstrated using in vivo images for 1D and 2D parallel imaging.

Data consistency criterion for selecting parameters for k-space-based reconstruction in parallel imaging

k-space-based reconstruction in parallel imaging depends on the reconstruction kernel setting, including its support. An optimal choice of the kernel depends on the calibration data, coil geometry and signal-to-noise ratio, as well as the criterion used. In this work, data consistency, imposed by the shift invariance requirement of the kernel, is introduced as a goodness measure of k-space-based reconstruction in parallel imaging and demonstrated. Data consistency error (DCE) is calculated as the sum of squared difference between the acquired signals and their estimates obtained based on the interpolation of the estimated missing data. A resemblance between DCE and the mean square error in the reconstructed image was found, demonstrating DCE's potential as a metric for comparing or choosing reconstructions. When used for selecting the kernel support for generalized autocalibrating partially parallel acquisition (GRAPPA) reconstruction and the set of frames for calibration as well as the kernel support in temporal GRAPPA reconstruction, DCE led to improved images over existing methods. Data consistency error is efficient to evaluate, robust for selecting reconstruction parameters and suitable for characterizing and optimizing k-space-based reconstruction in parallel imaging.

Robust GRAPPA reconstruction and its evaluation with the perceptual difference model

To develop and optimize a new modification of GRAPPA (generalized autocalibrating partially parallel acquisitions) MR reconstruction algorithm named "Robust GRAPPA." In Robust GRAPPA, k-space data points were weighted before the reconstruction. Small or zero weights were assigned to "outliers" in k-space. We implemented a Slow Robust GRAPPA method, which iteratively reweighted the k-space data. It was compared to an ad hoc Fast Robust GRAPPA method, which eliminated (assigned zero weights to) a fixed percentage of k-space "outliers" following an initial estimation procedure. In comprehensive experiments the new algorithms were evaluated using the perceptual difference model (PDM), whereby image quality was quantitatively compared to the reference image. Independent variables included algorithm type, total reduction factor, outlier ratio, center filling options, and noise across multiple image datasets, providing 10,800 test images for evaluation. The Fast Robust GRAPPA method gave results very similar to Slow Robust GRAPPA, and showed significant improvements as compared to regular GRAPPA. Fast Robust GRAPPA added little computation time compared with regular GRAPPA. Robust GRAPPA was proposed and proved useful for improving the reconstructed image quality. PDM was helpful in designing and optimizing the MR reconstruction algorithms.

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.

Fast High-Spatial-Resolution MRI of the Ankle with Parallel Imaging Using GRAPPA at 3 T

The purpose of our study was to compare an autocalibrating parallel imaging technique at 3 T with standard acquisitions at 3 and 1.5 T for small-field-of-view imaging of the ankle. MRI of the ankle was performed in three fresh human cadaver specimens and three healthy volunteers. Axial and sagittal T1-weighted, axial fat-saturated T2-weighted, and coronal intermediate-weighted fast spin-echo sequences, as well as a fat-saturated spoiled gradient-echo sequence, were acquired at 1.5 and 3 T. At 3 T, reduced data sets were reconstructed using a generalized autocalibrating partially parallel acquisition (GRAPPA) technique, with a scan time reduction of approximately 44%. All images were assessed by two radiologists independently concerning image quality. The signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) were measured in every data set. In the cadaver specimens, macroscopic findings after dissection served as a reference for the pathologic evaluation. SNR and CNR in the GRAPPA images were comparable to the standard acquisition at 3 T. The image quality was rated significantly higher at 3 T with both normal and parallel acquisition compared with 1.5 T. There was no significant difference in ligament and cartilage visualization or in image quality between standard and GRAPPA reconstruction at 3 T. Ankle abnormalities were better seen at 3 T than at 1.5 T for both normal and parallel acquisitions. Using higher field strength combined with parallel technique, MR images of the ankle were obtained with excellent diagnostic quality and a scan time reduction of about 44%. In addition, parallel imaging can provide more flexibility in protocol design.

High-Field Magnetic Resonance Imaging With Reduced Field/Tissue RF Artefacts—A Modeling Study Using Hybrid MoM/FEM and FDTD Technique

Due to complex field/tissue interactions, high-field magnetic resonance (MR) images suffer significant image distortions that result in compromised diagnostic quality. A new method that attempts to remove these distortions is proposed in this paper and is based on the use of transceiver-phased arrays. The proposed system uses, in the examples presented herein, a shielded four-element transceive-phased array head coil and involves performing two separate scans of the same slice with each scan using different excitations during transmission. By optimizing the amplitudes and phases for each scan, antipodal signal profiles can be obtained, and by combining both the images together, the image distortion can be reduced several fold. A combined hybrid method of moments (MoM)/finite element method (FEM) and finite-difference time-domain (FDTD) technique is proposed and used to elucidate the concept of the new method and to accurately evaluate the electromagnetic field (EMF) in a human head model. In addition, the proposed method is used in conjunction with the generalized auto-calibrating partially parallel acquisitions (GRAPPA) reconstruction technique to enable rapid imaging of the two scans. Simulation results reported herein for 11-T (470-MHz) brain imaging applications show that the new method with GRAPPA reconstruction theoretically results in improved image quality and that the proposed combined hybrid MoM/FEM and FDTD technique is suitable for high-field magnetic resonance imaging (MRI) numerical analysis

Accelerated volumetric MRI with a SENSE/GRAPPA combination

To combine the specific advantages of the generalized autocalibrating partially parallel acquisitions (GRAPPA) technique and sensitivity encoding (SENSE) with two-dimensional (2D) undersampling. By splitting the 2D reconstruction process into multiple one-dimensional (1D) reconstructions, the normal 1D GRAPPA method can be used for image reconstruction. Due to this data-handling process, a GRAPPA reconstruction is performed along the phase-encoding (PE) direction and effectively a SENSE reconstruction is performed along the partition-encoding (PAE) direction. In vivo experiments demonstrate the successful implementation of the SENSE/GRAPPA combination. Experimental results with up to 9.6-fold acceleration using a prototype 32-channel receiver head coil array are presented. The proposed SENSE/GRAPPA combination for 3D imaging allows the GRAPPA method to be applied in combination with 2D undersampling. Because the SENSE/GRAPPA combination is not based on knowledge of spatial coil sensitivities, it should be the method of choice whenever it is difficult to extract the sensitivity information.