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

Eliminating electromagnetic interference for RF shielding-free MRI via k-space convolution: Insights from MR parallel imaging advances

Recent advances in ultra-low field MRI have attracted attention from both academic and industrial MR communities for its potential in democratizing MRI applications. One of the most striking features on those advances is shielding-free imaging by actively sensing and eliminating the electromagnetic interference (EMI). In this study, we review the analytical approaches for EMI estimation/elimination, and investigate their theoretical basis and relations with parallel imaging reconstruction. We provide further understanding of the existing approaches, formulating EMI estimation as convolution in k-space or multiplication in spectrum-space. We further propose to use tailored convolutional kernel to adaptively fit the varying EMI coupling across the acquisition window. These methods were evaluated with both simulation study and human brain imaging. The results show that using tailored convolutional kernel can achieve more robust performance against system and acquisition imperfections.

Diffusion model based on generalized map for accelerated MRI

In recent years, diffusion models have made significant progress in accelerating magnetic resonance imaging. Nevertheless, it still has inherent limitations, such as prolonged iteration times and sluggish convergence rates. In this work, we present a novel generalized map generation model based on mean-reverting SDE, called GM-SDE, to alleviate these shortcomings. Notably, the core idea of GM-SDE is optimizing the initial values of the iterative algorithm. Specifically, the training process of GM-SDE diffuses the original k-space data to an intermediary degraded state with fixed Gaussian noise, while the reconstruction process generates the data by reversing this process. Based on the generalized map, three variants of GM-SDE are proposed to learn k-space data with different structural characteristics to improve the effectiveness of model training. GM-SDE also exhibits flexibility, as it can be integrated with traditional constraints, thereby further enhancing its overall performance. Experimental results showed that the proposed method can reduce reconstruction time and deliver excellent image reconstruction capabilities compared to the complete diffusion-based method.

Using High-Pass Filter to Enhance Scan Specific Learning for MRI Reconstruction without Any Extra Training Data

In accelerated MRI, the robust artificial-neural-network for k-space interpolation (RAKI) method is an attractive learning-based reconstruction that does not require additional training data. This study was focused on obtaining high quality MR images from regular under-sampled multi-coil k-space data using a high-pass filtered RAKI (HP-RAKI) reconstruction without any extra training data. MRI scan from human subjects was under-sampled with a regular pattern using skipped phase encoding and a fully sampled k-space center. A high-pass (HP) filter was applied in k-space to reduce image support to facilitate linear prediction. The HP filtered k-space center was used to train the RAKI network without any extra training data. The unacquired k-space data can be predicted from a trained RAKI network with optimized parameters. Final reconstruction was obtained after performing an inverse HP filtering for the predicted k-space data. This HP-RAKI method can be extended to corresponding residual structure (HP-rRAKI). HP-RAKI was compared with GRAPPA, HP-GRAPPA, RAKI and MW-RAKI algorithms, and HP-rRAKI was compared with corresponding residual extensions, including rRAKI and MW-rRAKI, all qualitatively and quantitatively using visual inspection and such metrics as SSIM and PSNR. HP-RAKI and HP-rRAKI were found to be effective in reconstructing MR images even at high acceleration factors. HP-RAKI and HP-rRAKI compared favorably with other algorithms. Using high-pass filtered central k-space data for training, HP-RAKI offers higher reconstruction quality for regularly under-sampled multi-coil k-space data without any extra training data. It has shown promising capabilities for fast MRI applications, especially those lacking fully sampled training data.

WKGM: weighted k-space generative model for parallel imaging reconstruction

Deep learning based parallel imaging (PI) has made great progress in recent years to accelerate MRI. Nevertheless, it still has some limitations: for example, the robustness and flexibility of existing methods are greatly deficient. In this work, we propose a method to explore the k-space domain learning via robust generative modeling for flexible calibrationless PI reconstruction, coined the weighted k-space generative model (WKGM). Specifically, WKGM is a generalized k-space domain model, where the k-space weighting technology and high-dimensional space augmentation design are efficiently incorporated for score-based generative model training, resulting in good and robust reconstructions. In addition, WKGM is flexible and thus can be synergistically combined with various traditional k-space PI models, which can make full use of the correlation between multi-coil data and realize calibrationless PI. Even though our model was trained on only 500 images, experimental results with varying sampling patterns and acceleration factors demonstrate that WKGM can attain state-of-the-art reconstruction results with the well learned k-space generative prior.

K-space and image domain collaborative energy-based model for parallel MRI reconstruction

Decreasing magnetic resonance (MR) image acquisition times can potentially make MR examinations more accessible. Prior arts including the deep learning models have been devoted to solving the problem of long MRI imaging time. Recently, deep generative models have exhibited great potentials in algorithm robustness and usage flexibility. Nevertheless, none of existing schemes can be learned from or employed to the k-space measurement directly. Furthermore, how do the deep generative models work well in hybrid domain is also worth being investigated. In this work, by taking advantage of the deep energy-based models, we propose a k-space and image domain collaborative generative model to comprehensively estimate the MR data from under-sampled measurement. Equipped with parallel and sequential orders, experimental comparisons with the state-of-the-arts demonstrated that they involve less error in reconstruction accuracy and are more stable under different acceleration factors.

Improving accelerated MRI by deep learning with sparsified complex data

PURPOSE

To obtain high-quality accelerated MR images with complex-valued reconstruction from undersampled k-space data.

METHODS

The MRI scans from human subjects were retrospectively undersampled with a regular pattern using skipped phase encoding, leading to ghosts in zero-filling reconstruction. A complex difference transform along the phase-encoding direction was applied in image domain to yield sparsified complex-valued edge maps. These sparse edge maps were used to train a complex-valued U-type convolutional neural network (SCU-Net) for deghosting. A k-space inverse filtering was performed on the predicted deghosted complex edge maps from SCU-Net to obtain final complex images. The SCU-Net was compared with other algorithms including zero-filling, GRAPPA, RAKI, finite difference complex U-type convolutional neural network (FDCU-Net), and CU-Net, both qualitatively and quantitatively, using such metrics as structural similarity index, peak SNR, and normalized mean square error.

RESULTS

The SCU-Net was found to be effective in deghosting aliased edge maps even at high acceleration factors. High-quality complex images were obtained by performing an inverse filtering on deghosted edge maps. The SCU-Net compared favorably with other algorithms.

CONCLUSION

Using sparsified complex data, SCU-Net offers higher reconstruction quality for regularly undersampled k-space data. The proposed method is especially useful for phase-sensitive MRI applications.

Multi-weight respecification of scan-specific learning for parallel imaging

Parallel imaging is widely used in magnetic resonance imaging as an acceleration technology. Traditional linear reconstruction methods in parallel imaging often suffer from noise amplification. Recently, a non-linear robust artificial-neural-network for k-space interpolation (RAKI) exhibits superior noise resilience over other linear methods. However, RAKI performs poorly at high acceleration rates and needs a large number of autocalibration signals as the training samples. In order to tackle these issues, we propose a multi-weight method that implements multiple weighting matrices on the under-sampled data, named MW-RAKI. Enforcing multiple weighted matrices on the measurements can effectively reduce the influence of noise and increase the data constraints. Furthermore, we incorporate the strategy of multiple weighting matrixes into a residual version of RAKI, and form MW-rRAKI. Experimental comparisons with the alternative methods demonstrated noticeably better reconstruction performances, particularly at high acceleration rates. With only 12.5% of the k-space data is available, the PSNR of MW-RAKI and MW-rRAKI is improved by about 3 dB and 4 dB compared to RAKI and rRAKI, respectively.

Group feature selection for enhancing information gain in MRI reconstruction

Magnetic resonance imaging (MRI) has revolutionized the radiology. As a leading medical imaging modality, MRI not only visualizes the structures inside body, but also produces functional imaging. However, due to the slow imaging speed constrained by the MR physics, MRI cost is expensive, and patient may feel not comfortable in a scanner for a long time. Parallel MRI has accelerated the imaging speed through the sub-Nyquist sampling strategy and the missing data are interpolated by the multiple coil data acquired. Kernel learning has been used in the parallel MRI reconstruction to learn the interpolation weights and re-construct the undersampled data. However, noise and aliasing artifacts still exist in the reconstructed image and a large number of auto-calibration signal lines are needed. To further improve the kernel learning-based MRI reconstruction and accelerate the speed, this paper proposes a group feature selection strategy to improve the learning performance and enhance the reconstruction quality. An explicit kernel mapping is used for selecting a subset of features which contribute most to estimate the missing k-space data. The experimental results show that the learning behaviours can be better predicted and therefore the reconstructed image quality is improved.

Improving Nonlinear Interpolation of K-Space Data Using Semi-Supervised Learning and Autoregressive Model

Parallel magnetic resonance imaging (pMRI) accelerates data acquisition by undersampling k-space through an array of receiver coils. Finding accurate relationships between acquired and missing k-space data determines the interpolation performance and reconstruction quality. Autocalibration signals (ACS) are generally used to learn the interpolation coefficients for reconstructing the missing k-space data. Based on the estimation-approximation error analysis in machine learning, increasing training data size can reduce estimation error and therefore enhance generalization ability of the interpolator, but scanning time will be longer if more ACS data are acquired. We propose to augment training data using unacquired and acquired data outside of ACS region through semi-supervised learning idea and autoregressive model. Local neighbor unacquired k-space data can be used for training tasks and reducing the generalization error. Experimental results show that the proposed method outperforms the conventional methods by suppressing noise and aliasing artifacts.

Self-calibrated interpolation of non-Cartesian data with GRAPPA in parallel imaging

PURPOSE

To develop a non-Cartesian k-space reconstruction method using self-calibrated region-specific interpolation kernels for highly accelerated acquisitions.

METHODS

In conventional non-Cartesian GRAPPA with through-time GRAPPA (TT-GRAPPA), the use of region-specific interpolation kernels has demonstrated improved reconstruction quality in dynamic imaging for highly accelerated acquisitions. However, TT-GRAPPA requires the acquisition of a large number of separate calibration scans. To reduce the overall imaging time, we propose Self-calibrated Interpolation of Non-Cartesian data with GRAPPA (SING) to self-calibrate region-specific interpolation kernels from dynamic undersampled measurements. The SING method synthesizes calibration data to adapt to the distinct shape of each region-specific interpolation kernel geometry, and uses a novel local k-space regularization through an extension of TT-GRAPPA. This calibration approach is used to reconstruct non-Cartesian images at high acceleration rates while mitigating noise amplification. The reconstruction quality of SING is compared with conjugate-gradient SENSE and TT-GRAPPA in numerical phantoms and in vivo cine data sets.

RESULTS

In both numerical phantom and in vivo cine data sets, SING offers visually and quantitatively similar reconstruction quality to TT-GRAPPA, and provides improved reconstruction quality over conjugate-gradient SENSE. Furthermore, temporal fidelity in SING and TT-GRAPPA is similar for the same acceleration rates. G-factor evaluation over the heart shows that SING and TT-GRAPPA provide similar noise amplification at moderate and high rates.

CONCLUSION

The proposed SING reconstruction enables significant improvement of acquisition efficiency for calibration data, while matching the reconstruction performance of TT-GRAPPA.

HF-SENSE: an improved partially parallel imaging using a high-pass filter

Background

One of the major limitations of MRI is its slow acquisition speed. To accelerate data acquisition, partially parallel imaging (PPI) methods have been widely used in clinical applications such as sensitivity encoding (SENSE) and generalized autocalibrating partially parallel acquisitions (GRAPPA). SENSE is a popular image-domain partially parallel imaging method, which suffers from residual aliasing artifacts when the reduction factor goes higher. Undersampling the k-space data and then reconstruct images with artificial sparsity is an efficient way to accelerate data acquisition. By exploiting artificial sparsity with a high-pass filter, an improved SENSE method is proposed in this work, termed high-pass filtered SENSE (HF-SENSE).

Methods

First, a high-pass filter was applied to the raw k-space data, the result of which was used as the inputs of sensitivity estimation and undersampling process. Second, the adaptive array coil combination method was adopted to calculate sensitivity maps on a block-by-block basis. Third, Tikhonov regularized SENSE was then used to reconstruct magnetic resonance images. Fourth, the reconstructed images were transformed into k-space data, which was filtered with the corresponding inverse filter.

Results

Both simulation and in vivo experiments demonstrate that HF-SENSE method significantly reduces noise level of the reconstructed images compared with SENSE. Furthermore, it is found that HF-SENSE can achieve lower normalized root-mean-square error value than SENSE.

Conclusions

The proposed method explores artificial sparsity with a high-pass filter. Experiments demonstrate that the proposed HF-SENSE method can improve the image quality of SENSE reconstruction. The high-pass filter parameters can be predefined. With this image reconstruction method, high acceleration factors can be achieved, which will improve the clinical applicability of SENSE.

This retrospective study (HF-SENSE: an improved partially parallel imaging using a high-pass filter) was approved by Institute Review Board of 2nd Affiliated Hospital of Zhejiang University (ethical approval number 2018–314). Participant for all images have informed consent that he knew the risks and agreed to participate in the research.

Improved k-t PCA Algorithm Using Artificial Sparsity in Dynamic MRI

The k-t principal component analysis (k-t PCA) is an effective approach for high spatiotemporal resolution dynamic magnetic resonance (MR) imaging. However, it suffers from larger residual aliasing artifacts and noise amplification when the reduction factor goes higher. To further enhance the performance of this technique, we propose a new method called sparse k-t PCA that combines the k-t PCA algorithm with an artificial sparsity constraint. It is a self-calibrated procedure that is based on the traditional k-t PCA method by further eliminating the reconstruction error derived from complex subtraction of the sampled k-t space from the original reconstructed k-t space. The proposed method is tested through both simulations and in vivo datasets with different reduction factors. Compared to the standard k-t PCA algorithm, the sparse k-t PCA can improve the normalized root-mean-square error performance and the accuracy of temporal resolution. It is thus useful for rapid dynamic MR imaging.

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.

Improving GRAPPA reconstruction by frequency discrimination in the ACS lines

PURPOSE

GRAPPA is a well-known parallel imaging method that recovers the MR magnitude image from aliasing by using a weighted interpolation of the data in k-space. To estimate the optimal reconstruction weights, GRAPPA uses a band along the center of the k-space where the signal is sampled at the Nyquist rate, the so-called autocalibrated (ACS) lines. However, while the subsampled lines usually belong to the medium- to high-frequency areas of the spectrum, the ACS lines include the low-frequency areas around the DC component. The use for estimation and reconstruction of areas of the k-space with very different features may negatively affect the final reconstruction quality. We propose a simple, yet powerful method to eliminate reconstruction artifacts, based on the discrimination of the low-frequency spectrum.

METHODS

The proposal to improve the estimation of the weights lays on a proper selection of the coefficients within the ACS lines, which advises discarding those points around the DC component. A simple approach is the elimination of a square window in the center of the k-space, although more developed approaches can be used.

RESULTS

The method is tested using real multiple-coil MRI acquisitions. We empirically show this approach achieves great enhancement rates, while keeping the same complexity of the original GRAPPA and reducing the g-factor. The reconstruction is even more accurate when combined with other reconstruction methods. Improvement rates of 35% are achieved for 32 ACS and acceleration rate of 3.

CONCLUSIONS

The method proposed highly improves the accuracy of the GRAPPA coefficients and therefore the final image reconstruction. The method is fully compatible with the original GRAPPA formulation and with other optimization methods proposed in literature, and it can be easily implemented into the commercial scanning software.

STEP: Self-supporting tailored k-space estimation for parallel imaging reconstruction

PURPOSE

A new subspace-based iterative reconstruction method, termed Self-supporting Tailored k-space Estimation for Parallel imaging reconstruction (STEP), is presented and evaluated in comparison to the existing autocalibrating method SPIRiT and calibrationless method SAKE.

THEORY AND METHODS

In STEP, two tailored schemes including k-space partition and basis selection are proposed to promote spatially variant signal subspace and incorporated into a self-supporting structured low rank model to enforce properties of locality, sparsity, and rank deficiency, which can be formulated into a constrained optimization problem and solved by an iterative algorithm. Simulated and in vivo datasets were used to investigate the performance of STEP in terms of overall image quality and detail structure preservation.

RESULTS

The advantage of STEP on image quality is demonstrated by retrospectively undersampled multichannel Cartesian data with various patterns. Compared with SPIRiT and SAKE, STEP can provide more accurate reconstruction images with less residual aliasing artifacts and reduced noise amplification in simulation and in vivo experiments. In addition, STEP has the capability of combining compressed sensing with arbitrary sampling trajectory.

CONCLUSION

Using k-space partition and basis selection can further improve the performance of parallel imaging reconstruction with or without calibration signals.

GRAPPA reconstruction with spatially varying calibration of self-constraint

PURPOSE

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.

THEORY AND METHODS

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.

RESULTS

Compared with GRAPPA and self-constrained GRAPPA, the proposed SSC-GRAPPA generates images with reduced artifacts and noise.

CONCLUSION

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.

Error decomposition for parallel imaging reconstruction using modulation-domain representation of undersampled data

This paper presents a quantitative approach to evaluating and optimizing parallel imaging reconstruction for a clinical requirement. By introducing a "modulation domain representation" for undersampled data, the presented approach decomposes parallel imaging reconstruction error into multiple error components that can be grouped into three categories: image fidelity error, residue aliasing artifacts, and amplified noise. It is experimentally found that these error components have different image-space patterns that compromise imaging quality in different fashions. An error function may be defined as the weighted summation of these error components. By choosing a set of weighting coefficients that can quantify desirable image quality, parallel imaging may be optimized for a clinical requirement. It is found that error decomposition model may improve clinical utility of parallel imaging, providing an application-oriented approach to clinical parallel imaging.

Incorporating reference in parallel imaging and compressed sensing

PURPOSE

To develop a new compressed sensing parallel imaging technique called READ-PICS that can effectively incorporate prior information from a reference scan for MR image reconstruction from highly undersampled multichannel measurements.

METHODS

READ-PICS incorporates information from a high-spatial-resolution reference prior using the generalized series model, to achieve increased image sparsity and mitigated noise amplification simultaneously. To further improve the ill-conditioning of the parallel imaging system, an annular area in the central residual k-space is used for calibration. Additionally, the mixed L1-L2 norm of the coefficients from the prior component and residual component is used to enforce joint sparsity.

RESULTS

The evaluations on parametric imaging and multiscan experiment demonstrate superior performance of READ-PICS in terms of detail preservation and noise suppression compared to state-of-the-art technique, L1-Iterative self-consistent parallel imaging reconstruction, and prescan required method, correlation imaging.

CONCLUSIONS

The proposed method can significantly increase signal sparsity and improve the ill-conditioning of the parallel imaging system using reference adaptive regularization. This technique can be easily adapted to other imaging applications where multiple images need to be acquired sequentially and a reference prior is also available.

SENSE with improved tolerance to inaccuracies in coil sensitivity maps

In this work, an extension of the Cartesian sensitivity encoding (SENSE) parallel imaging framework is proposed. In the well-known SENSE solution, the overdetermined reconstruction inversion problem is optimized to get the highest signal-to-noise ratio in the image. In this extension, the probability of artifacts due to incorrect knowledge of the receiver coil sensitivities is also taken into account. This is realized by assuming an uncertainty in measured receiver coil sensitivities to enable weighting of residual artifact level and signal-to-noise ratio in the inversion problem. This inversion problem can still be solved by a least-squares optimization without the need of any complex iterative scheme. Results in abdominal imaging show that artifact levels can be substantially reduced, at the cost of a signal-to-noise ratio penalty. The size of the signal-to-noise ratio penalty depends on the assumed inaccuracy of the coil sensitivities, sensitivity encoding acceleration factor, and coil configuration.

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.

Modeling non-stationarity of kernel weights for k-space reconstruction in partially parallel imaging

PURPOSE

In partially parallel imaging, most k-space-based reconstruction algorithms such as GRAPPA adopt a single finite-size kernel to approximate the true relationship between sampled and nonsampled signals. However, the estimation of this kernel based on k-space signals is imperfect, and the authors are investigating methods dealing with local variation of k-space signals.

METHODS

To model nonstationarity of kernel weights, similar to performing a spatially adaptive regularization, the authors fit a set of linear functions using concepts from geographically weighted regression, a methodology used in geophysical analysis. Instead of a reconstruction with a single set of kernel weights, the authors use multiple sets. A missing signal is reconstructed with its kernel weights set determined by k-space clustering. Simulated and acquired MR data with several different image content and acquisition schemes, including MR tagging, were tested. A perceptual difference model (Case-PDM) was used to quantitatively evaluate the quality of over 1000 test images, and to optimize the parameters of our algorithm.

RESULTS

A MOdeling Non-stationarity of KErnel wEightS ("MONKEES") reconstruction with two sets of kernel weights gave reconstructions with significantly better image quality than the original GRAPPA in all test images. Using more sets produced improved image quality but with diminishing returns. As a rule of thumb, at least two sets of kernel weights, one from low- and the other from high frequency k-space, should be used.

CONCLUSIONS

The authors conclude that the MONKEES can significantly and robustly improve the image quality in parallel MR imaging, particularly, cardiac imaging.

Exploiting sparsity to accelerate noncontrast MR angiography in the context of parallel imaging

Noncontrast techniques for peripheral MR angiography are receiving renewed interest because of safety concerns about the use of gadolinium in patients with renal insufficiency. One class of techniques involves subtraction of dark-blood images acquired during fast systolic flow from bright-blood images obtained during slow diastolic flow. The goal of this work was to determine whether the inherent sparsity of the difference images could be exploited to achieve greater acceleration without loss of image quality in the context of generalized autocalibrating partially parallel acquisition (GRAPPA). It is shown that noise amplification at high acceleration factors can be reduced by performing subtraction on the raw data, before calculation of the GRAPPA weights, rather than on the final magnitude images. Use of the difference data to calculate the GRAPPA weights decreases the geometry factor (g-factor), because the difference data represent a sparse image set. This demonstrates an inherent property of GRAPPA and does not require the use of compressed sensing. Application of this approach to highly accelerated data from healthy volunteers resulted in similar depiction of large arteries to that obtained with low acceleration and standard reconstruction. However, visualization of very small vessels and arterial branches was compromised.

Highly accelerated contrast-enhanced MR angiography: improved reconstruction accuracy and reduced noise amplification with complex subtraction

Contrast-enhanced magnetic resonance angiography is routinely performed using parallel imaging to best capture the first pass of contrast material through the target vasculature, followed by digital subtraction to suppress the appearance of unwanted signal from background tissue. Both processes, however, amplify noise and can produce uninterpretable images when large acceleration factors are used. Using a phantom study of contrast-enhanced magnetic resonance angiography, we show that complex subtraction processing prior to partially parallel reconstruction improves reconstruction accuracy relative to magnitude subtraction processing for reduction factors as large as 12. Time-resolved contrast-enhanced magnetic resonance angiographic data obtained with complex subtraction in volunteers supported the results of the phantom study and when compared with magnitude subtraction processing demonstrated reduced geometry factors as well as improved image quality at large reduction factors.

Cross-sampled GRAPPA for parallel MRI

As one widely-used parallel-imaging method, Generalized Auto-calibrating Partially Parallel Acquisitions (GRAPPA) technique reconstructs the missing k-space data by a linear combination of the acquired data using a set of weights. These weights are usually derived from auto-calibration signal (ACS) lines that are acquired in parallel to the reduced lines. In this paper, a cross sampling method is proposed to acquire the ACS lines orthogonal to the reduced lines. This cross sampling method increases the amount of calibration data along the direction that the k-space is undersampled and thus improves the calibration accuracy, especially when a small number of ACS lines are acquired. Both phantom and in vivo experiments demonstrate that the proposed method, named cross-sampled GRAPPA (CS-GRAPPA), can effectively reduce the aliasing artifacts of GRAPPA when high acceleration is desired.

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.

k-TE generalized autocalibrating partially parallel acquisition (GRAPPA) for accelerated multiple gradient-recalled echo (MGRE) R2* mapping in the abdomen

Multiple gradient-recalled echo (MGRE) methods are commonly used for abdominal R(2)* mapping. Accelerated MGRE acquisitions would offer the potential to shorten requisite breathhold times and/or increase spatial resolution and coverage. In both phantom and normal volunteer studies, view-sharing (VS) methods, generalized autocalibrating partially parallel acquisition (GRAPPA) methods, and newly proposed k-echo time (k-TE) GRAPPA methods were compared for the purpose of accelerating MGRE acquisitions. Utilization of water-selective spatial spectral excitation pulses reduced artifact levels for both VS and k-TE GRAPPA approaches. VS approaches were found to be highly sensitive to off-resonance effects, particularly at increasing acceleration rates. k-TE GRAPPA significantly reduced residual artifact levels compared to GRAPPA approaches while improving the accuracy of accelerated abdominal R(2)* measurements. These initial feasibility studies demonstrate that k-TE GRAPPA is an effective method to reduce scan times during abdominal R(2)*-mapping procedures.