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.     

Non‐Cartesian parallel imaging reconstruction

Non‐Cartesian parallel imaging has played an important role in reducing data acquisition time in MRI. The use of non‐Cartesian trajectories can enable more efficient coverage of k‐space, which can be leveraged to reduce scan times. These trajectories can be undersampled to achieve even faster scan times, but the resulting images may contain aliasing artifacts. Just as Cartesian parallel imaging can be used to reconstruct images from undersampled Cartesian data, non‐Cartesian parallel imaging methods can mitigate aliasing artifacts by using additional spatial encoding information in the form of the nonhomogeneous sensitivities of multi‐coil phased arrays. This review will begin with an overview of non‐Cartesian k‐space trajectories and their sampling properties, followed by an in‐depth discussion of several selected non‐Cartesian parallel imaging algorithms. Three representative non‐Cartesian parallel imaging methods will be described, including Conjugate Gradient SENSE (CG SENSE), non‐Cartesian generalized autocalibrating partially parallel acquisition (GRAPPA), and Iterative Self‐Consistent Parallel Imaging Reconstruction (SPIRiT). After a discussion of these three techniques, several potential promising clinical applications of non‐Cartesian parallel imaging will be covered. J. Magn. Reson. Imaging 2014;40:1022–1040 . © 2014 Wiley Periodicals, Inc.     

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.     

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.     

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.     

Iterative GRAPPA (iGRAPPA) for improved parallel imaging reconstruction.

In this work an iterative reconstruction method based on generalized autocalibrating partially parallel acquisitions (GRAPPA) reconstruction is introduced. In the new method the reconstructed lines are used to reestimate and refine the weights from all the acquired data by applying the GRAPPA procedure iteratively with regularization. Both phantom and in vivo MRI experiments demonstrated that, compared to GRAPPA, the iterative approach reduces parallel imaging artifacts and permits high-quality image reconstruction with a relatively small number of calibration lines and slight changes of GRAPPA weights.     

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.     

Comprehensive quantification of signal‐to‐noise ratio and g‐factor for image‐based and k‐space‐based parallel imaging reconstructions

Parallel imaging reconstructions result in spatially varying noise amplification characterized by the g‐factor, precluding conventional measurements of noise from the final image. A simple Monte Carlo based method is proposed for all linear image reconstruction algorithms, which allows measurement of signal‐to‐noise ratio and g‐factor and is demonstrated for SENSE and GRAPPA reconstructions for accelerated acquisitions that have not previously been amenable to such assessment. Only a simple “prescan” measurement of noise amplitude and correlation in the phased‐array receiver, and a single accelerated image acquisition are required, allowing robust assessment of signal‐to‐noise ratio and g‐factor. The “pseudo multiple replica” method has been rigorously validated in phantoms and in vivo, showing excellent agreement with true multiple replica and analytical methods. This method is universally applicable to the parallel imaging reconstruction techniques used in clinical applications and will allow pixel‐by‐pixel image noise measurements for all parallel imaging strategies, allowing quantitative comparison between arbitrary k‐space trajectories, image reconstruction, or noise conditioning techniques. Magn Reson Med 60:895–907, 2008. © 2008 Wiley‐Liss, Inc.     

High resolution diffusion‐weighted imaging using readout‐segmented echo‐planar imaging,parallel imaging and a two‐dimensional navigator‐based reacquisition

Single‐shot echo‐planar imaging (EPI) is well established as the method of choice for clinical, diffusion‐weighted imaging with MRI because of its low sensitivity to the motion‐induced phase errors that occur during diffusion sensitization of the MR signal. However, the method is prone to artifacts due to susceptibility changes at tissue interfaces and has a limited spatial resolution. The introduction of parallel imaging techniques, such as GRAPPA (GeneRalized Autocalibrating Partially Parallel Acquisitions), has reduced these problems, but there are still significant limitations, particularly at higher field strengths, such as 3 Tesla (T), which are increasingly being used for routine clinical imaging. This study describes how the combination of readout‐segmented EPI and parallel imaging can be used to address these issues by generating high‐resolution, diffusion‐weighted images at 1.5T and 3T with a significant reduction in susceptibility artifact compared with the single‐shot case. The technique uses data from a 2D navigator acquisition to perform a nonlinear phase correction and to control the real‐time reacquisition of unusable data that cannot be corrected. Measurements on healthy volunteers demonstrate that this approach provides a robust correction for motion‐induced phase artifact and allows scan times that are suitable for routine clinical application. Magn Reson Med, 2009. © 2009 Wiley‐Liss, Inc.     

Quantitative myocardial perfusion imaging using different autocalibrated parallel acquisition techniques

PURPOSE: To compare three different autocalibrated parallel acquisition techniques (PAT) for quantitative and semiquantitative myocardial perfusion imaging. MATERIALS AND METHODS: Seven healthy volunteers underwent myocardial first-pass perfusion imaging at rest using an SR-TrueFISP pulse sequence without PAT and while using GRAPPA, mSENSE, and TSENSE. signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), normalized upslopes (NUS), and myocardial blood flow (MBF) were calculated. Artifacts, image noise, and overall image quality were qualitatively assessed. Furthermore, the relation between signal intensity (SI) and contrast medium (CM) concentration was determined in phantoms. RESULTS: Using PAT the linear range of the SR-TrueFISP sequence was increased about 40%. All three PAT methods introduced significant loss in SNR and CNR. GRAPPA yielded slightly better values then mSENSE and TSENSE. Both SENSE techniques introduced significantly residual aliasing artifacts. Image noise was increased with all three PAT methods. However, overall image quality was reduced only with mSENSE. Even though GRAPPA yielded smaller NUS values than non-PAT, mSENSE, and TSENSE, no differences were found in MBF between all applied techniques. CONCLUSION: Quantitative and semiquantitative myocardial perfusion imaging can benefit from PAT due to shorter acquisition times and increased linearity of the pulse sequence. GRAPPA and TSENSE turned out to be well suited for quantitative myocardial perfusion imaging.     

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.     

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. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

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.     

2D partially parallel imaging with k-space surrounding neighbors-based data reconstruction.

Partially parallel imaging (PPI) achieves imaging acceleration by replacing partial phase encoding (PE) with the spatially localized sensitivity encoding of a receiver surface coil array. Further accelerations can be achieved through 2D PPI along two PE directions in 3D MRI. This paper is to explore the k-space-based PPI acquisition and reconstruction strategies for 3D MRI. A surrounding neighbors-based autocalibrating PPI (SNAPPI) was first presented by generalizing the 2D multicolumn multiline interpolation method. Several 2D PPI reconstruction methods were then provided by applying SNAPPI to recover the partially skipped k-space data along two PE directions separately or nonseparately, in k-space or in the hybrid k and image space. An optimal 2D PPI sampling-based reconstruction approach was also presented for applying PPI along certain spatial direction along which the array coil has not sufficient sensitivity variation for a valid PPI reconstruction. Both simulated and in vivo 2D PPI data were used to evaluate the proposed methods.     

Increasing efficiency of parallel imaging for 2D multislice acquisitions

Parallel imaging algorithms require precise knowledge about the spatial sensitivity variation of the receiver coils to reconstruct images with full field of view (FOV) from undersampled Fourier encoded data. Sensitivity information must either be given a priori, or estimated from calibration data acquired along with the actual image data. In this study, two approaches are presented, which require very little or no additional data at all for calibration in two‐dimensional multislice acquisitions. Instead of additional data, information from spatially adjacent slices is used to estimate coil sensitivity information, thereby increasing the efficiency of parallel imaging. The proposed approaches rely on the assumption that over a small range of slices, coil sensitivities vary smoothly in slice direction. Both methods are implemented as variants of the GRAPPA algorithm. For a given effective acceleration, superior image quality is achieved compared to the conventional GRAPPA method. For the latter calibration lines for coil weight computation must be acquired in addition to the undersampled k‐spaces for coil weight computation, thus requiring higher k‐space undersampling, that is, a higher reduction factor to achieve the same effective acceleration. The proposed methods are particularly suitable to speed up parallel imaging for clinical applications where the reduction factor is limited to two or three. Magn Reson Med 2009 © 2009 Wiley‐Liss, Inc.     

Generalized GRAPPA operators for wider spiral bands: Rapid self‐calibrated parallel reconstruction for variable density spiral MRI

A rapid and self‐calibrated parallel imaging reconstruction method is proposed for undersampled variable density spiral datasets. A set of generalized GRAPPA for wider readout line operators are used to expand each acquired spiral line into a wider spiral band, therefore fulfilling Nyquist sampling criterion throughout the k‐space. The calibration of generalized GRAPPA for wider readout line operators is performed using the fully sampled central k‐space region. The resulting generalized GRAPPA for wider readout line operator weights are adaptively regularized to minimize the error in the newly‐generated data at different k‐space locations. Simulation and experimental results demonstrate that the technique can be used either to achieve a significant acceleration and/or to reduce off‐resonance artifacts due to a shorten readout duration. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.