Discrepancy-based adaptive regularization for GRAPPA reconstruction

Simultaneous multislice EPI prospective motion correction by real-time receiver phase correction and coil sensitivity map interpolation

PURPOSE

To improve the image reconstruction for prospective motion correction (PMC) of simultaneous multislice (SMS) EPI of the brain, an update of receiver phase and resampling of coil sensitivities are proposed and evaluated.

METHODS

A camera-based system was used to track head motion (3 translations and 3 rotations) and dynamically update the scan position and orientation. We derived the change in receiver phase associated with a shifted field of view (FOV) and applied it in real-time to each k-space line of the EPI readout trains. Second, for the SMS reconstruction, we adapted resampled coil sensitivity profiles reflecting the movement of slices. Single-shot gradient-echo SMS-EPI scans were performed in phantoms and human subjects for validation.

RESULTS

Brain SMS-EPI scans in the presence of motion with PMC and no phase correction for scan plane shift showed noticeable artifacts. These artifacts were visually and quantitatively attenuated when corrections were enabled. Correcting misaligned coil sensitivity maps improved the temporal SNR (tSNR) of time series by 24% (p = 0.0007) for scans with large movements (up to ˜35 mm and 30°). Correcting the receiver phase improved the tSNR of a scan with minimal head movement by 50% from 50 to 75 for a United Kingdom biobank protocol.

CONCLUSION

Reconstruction-induced motion artifacts in single-shot SMS-EPI scans acquired with PMC can be removed by dynamically adjusting the receiver phase of each line across EPI readout trains and updating coil sensitivity profiles during reconstruction. The method may be a valuable tool for SMS-EPI scans in the presence of subject motion.

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.

Estimation error bound for GRAPPA diffusion-weighted MRI

In recent years, diffusion weight magnetic resonance imaging (DW-MRI) has become one of the most important MRI imaging modalities. The importance of the DW-MRI grew thanks to the combination of parallel magnetic resonance imaging (pMRI) techniques with the echo-planar imaging (EPI), which minimize scan time and lead to reduced distortion, allowing the DW-MRI to become a routine clinical exam. Additionally, this has brought various new parameters that influence image quality and biomarkers used in DW-MRI. This work aims to investigate the effects of these parameters on the estimation quality, by using the Cramér-Rao bound tool, which gives analytical expressions of the lower limit on the estimation error variance of different DW-MRI variables when using the pMRI technique. In particular, these bounds will be used to study and optimize the impact of different factors of generalized autocalibrating partially parallel acquisition (GRAPPA) technique and system parameters on the estimation quality of the desired clinical metrics. Moreover, the obtained results of this study can be exploited and adapted in all human body DW-MRI clinical routines, further improving disease diagnosis, and tractography studies.

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.

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.

ESPIRiT--an eigenvalue approach to autocalibrating parallel MRI: where SENSE meets GRAPPA

PURPOSE

Parallel imaging allows the reconstruction of images from undersampled multicoil data. The two main approaches are: SENSE, which explicitly uses coil sensitivities, and GRAPPA, which makes use of learned correlations in k-space. The purpose of this work is to clarify their relationship and to develop and evaluate an improved algorithm.

THEORY AND METHODS

A theoretical analysis shows: (1) The correlations in k-space are encoded in the null space of a calibration matrix. (2) Both approaches restrict the solution to a subspace spanned by the sensitivities. (3) The sensitivities appear as the main eigenvector of a reconstruction operator computed from the null space. The basic assumptions and the quality of the sensitivity maps are evaluated in experimental examples. The appearance of additional eigenvectors motivates an extended SENSE reconstruction with multiple maps, which is compared to existing methods.

RESULTS

The existence of a null space and the high quality of the extracted sensitivities are confirmed. The extended reconstruction combines all advantages of SENSE with robustness to certain errors similar to GRAPPA.

CONCLUSION

In this article the gap between both approaches is finally bridged. A new autocalibration technique combines the benefits of both.

Three-dimensional echo planar imaging with controlled aliasing: A sequence for high temporal resolution functional MRI

PURPOSE

In this work, we combine three-dimensional echo planar imaging (3D-EPI) with controlled aliasing to substantially increase temporal resolution in whole-brain functional MRI (fMRI) while minimizing geometry-factor (g-factor) losses.

THEORY AND METHODS

The study was performed on a 7 Tesla scanner equipped with a 32-channel receive coil. The proposed 3D-EPI-CAIPI sequence was evaluated for: (i) image quality, compared with a conventionally undersampled parallel imaging acquisition; (ii) temporal resolution, the ability to sample and remove physiological signal fluctuations from the fMRI signal of interest and (iii) the ability to distinguish small changes in hemodynamic responses in an event-related fMRI experiment.

RESULTS

Whole-brain fMRI data with a voxel size of 2 × 2 × 2 mm(3) and temporal resolution of 371 ms could be acquired with acceptable image quality. Ten-fold parallel imaging accelerated 3D-EPI-CAIPI data were shown to lower the maximum g-factor losses up to 62% with respect to a 10-fold accelerated 3D-EPI dataset. FMRI with 400 ms temporal resolution allowed the detection of time-to-peak variations in functional responses due to multisensory facilitation in temporal, occipital and frontal cortices.

CONCLUSION

3D-EPI-CAIPI allows increased temporal resolution that enables better characterization of physiological noise, thus improving sensitivity to signal changes of interest. Furthermore, subtle changes in hemodynamic response dynamics can be studied in shorter scan times by avoiding the need for jittering. Magn Reson Med 75:2350-2361, 2016. © 2015 Wiley Periodicals, Inc.

Signal-to-noise ratio and MR tissue parameters in human brain imaging at 3, 7, and 9.4 tesla using current receive coil arrays

PURPOSE

Relaxation times, transmit homogeneity, signal-to-noise ratio (SNR) and parallel imaging g-factor were determined in the human brain at 3T, 7T, and 9.4T, using standard, tight-fitting coil arrays.

METHODS

The same human subjects were scanned at all three field strengths, using identical sequence parameters and similar 31- or 32-channel receive coil arrays. The SNR of three-dimensional (3D) gradient echo images was determined using a multiple replica approach and corrected with measured flip angle and T2 (*) distributions and the T1 of white matter to obtain the intrinsic SNR. The g-factor maps were derived from 3D gradient echo images with several GRAPPA accelerations.

RESULTS

As expected, T1 values increased, T2 (*) decreased and the B1 -homogeneity deteriorated with increasing field. The SNR showed a distinctly supralinear increase with field strength by a factor of 3.10 ± 0.20 from 3T to 7T, and 1.76 ± 0.13 from 7T to 9.4T over the entire cerebrum. The g-factors did not show the expected decrease, indicating a dominating role of coil design.

CONCLUSION

In standard experimental conditions, SNR increased supralinearly with field strength (SNR ∼ B0 (1.65) ). To take full advantage of this gain, the deteriorating B1 -homogeneity and the decreasing T2 (*) have to be overcome.

Paradoxical effect of the signal-to-noise ratio of GRAPPA calibration lines: A quantitative study

PURPOSE

Intuitively, GRAPPA auto-calibration signal (ACS) lines with higher signal-to-noise ratio (SNR) may be expected to boost the accuracy of kernel estimation and increase the SNR of GRAPPA reconstructed images. Paradoxically, Sodickson and his colleagues pointed out that using ACS lines with high SNR may actually lead to lower SNR in the GRAPPA reconstructed images. A quantitative study of how the noise in the ACS lines affects the SNR of the GRAPPA reconstructed images is presented.

METHODS

In a phantom, the singular values of the GRAPPA encoding matrix and the root-mean-square error of GRAPPA reconstruction were evaluated using multiple sets of ACS lines with variant SNR. In volunteers, ACS lines with high and low SNR were estimated, and the SNR of corresponding TGRAPPA reconstructed images was evaluated.

RESULTS

We show that the condition number of the GRAPPA kernel estimation equations is proportional to the SNR of the ACS lines. In dynamic image series reconstructed with TGRAPPA, high SNR ACS lines result in reduced SNR if appropriate regularization is not applied.

CONCLUSION

Noise has a similar effect to Tikhonov regularization. Without appropriate regularization, a GRAPPA kernel estimated from ACS lines with higher SNR amplifies random noise in the GRAPPA reconstruction. Magn Reson Med 74:231-239, 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.

A new perceptual difference model for diagnostically relevant quantitative image quality evaluation: a preliminary study

PURPOSE

Most objective image quality metrics average over a wide range of image degradations. However, human clinicians demonstrate bias toward different types of artifacts. Here, we aim to create a perceptual difference model based on Case-PDM that mimics the preference of human observers toward different artifacts.

METHOD

We measured artifact disturbance to observers and calibrated the novel perceptual difference model (PDM). To tune the new model, which we call Artifact-PDM, degradations were synthetically added to three healthy brain MR data sets. Four types of artifacts (noise, blur, aliasing or "oil painting" which shows up as flattened, over-smoothened regions) of standard compressed sensing (CS) reconstruction, within a reasonable range of artifact severity, as measured by both PDM and visual inspection, were considered. After the model parameters were tuned by each synthetic image, we used a functional measurement theory pair-comparison experiment to measure the disturbance of each artifact to human observers and determine the weights of each artifact's PDM score. To validate Artifact-PDM, human ratings obtained from a Double Stimulus Continuous Quality Scale experiment were compared to the model for noise, blur, aliasing, oil painting and overall qualities using a large set of CS-reconstructed MR images of varying quality. Finally, we used this new approach to compare CS to GRAPPA, a parallel MRI reconstruction algorithm.

RESULTS

We found that, for the same Artifact-PDM score, the human observer found incoherent aliasing to be the most disturbing and noise the least. Artifact-PDM results were highly correlated to human observers in both experiments. Optimized CS reconstruction quality compared favorably to GRAPPA's for the same sampling ratio.

CONCLUSIONS

We conclude our novel metric can faithfully represent human observer artifact evaluation and can be useful in evaluating CS and GRAPPA reconstruction algorithms, especially in studying artifact trade-offs.

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.

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.

Variation of noise in multi-run functional MRI using generalized autocalibrating partially parallel acquisition (GRAPPA)

PURPOSE

To investigate the noise variation in multi-run functional MRI (fMRI) scans using generalized autocalibrating partially parallel acquisition (GRAPPA), with a focus on the cause of this variation.

MATERIALS AND METHODS

A phantom was continuously scanned for 10 runs using echo-planar imaging (EPI) combined with GRAPPA to simulate a multi-run fMRI exam. The variation of noise between runs was examined for different GRAPPA acceleration factors. The noise variation was also evaluated in a real fMRI experiment with human subjects at an acceleration factor of two. The cause of noise variation was explored by offline reconstruction using different GRAPPA weights and numerical simulation of GRAPPA reference scans.

RESULTS

It was found that the noise distribution in the image is stable within a run but may vary randomly from run to run. The variation of noise was also observed in fMRI experiments with human subjects. The variation can be significantly reduced if all the images from individual runs are reconstructed using the same reference scan data.

CONCLUSION

Both phantom experiments and human data showed that the noise pattern may change in different fMRI runs. The variation is mainly caused by the random noise in separate reference scans for GRAPPA in each run.

K-space reconstruction with anisotropic kernel support (KARAOKE) for ultrafast partially parallel imaging

PURPOSE

Partially parallel imaging (PPI) greatly accelerates MR imaging by using surface coil arrays and under-sampling k-space. However, the reduction factor (R) in PPI is theoretically constrained by the number of coils (N(C)). A symmetrically shaped kernel is typically used, but this often prevents even the theoretically possible R from being achieved. Here, the authors propose a kernel design method to accelerate PPI faster than R = N(C).

METHODS

K-space data demonstrates an anisotropic pattern that is correlated with the object itself and to the asymmetry of the coil sensitivity profile, which is caused by coil placement and B(1) inhomogeneity. From spatial analysis theory, reconstruction of such pattern is best achieved by a signal-dependent anisotropic shape kernel. As a result, the authors propose the use of asymmetric kernels to improve k-space reconstruction. The authors fit a bivariate Gaussian function to the local signal magnitude of each coil, then threshold this function to extract the kernel elements. A perceptual difference model (Case-PDM) was employed to quantitatively evaluate image quality.

RESULTS

A MR phantom experiment showed that k-space anisotropy increased as a function of magnetic field strength. The authors tested a K-spAce Reconstruction with AnisOtropic KErnel support ("KARAOKE") algorithm with both MR phantom and in vivo data sets, and compared the reconstructions to those produced by GRAPPA, a popular PPI reconstruction method. By exploiting k-space anisotropy, KARAOKE was able to better preserve edges, which is particularly useful for cardiac imaging and motion correction, while GRAPPA failed at a high R near or exceeding N(C). KARAOKE performed comparably to GRAPPA at low Rs.

CONCLUSIONS

As a rule of thumb, KARAOKE reconstruction should always be used for higher quality k-space reconstruction, particularly when PPI data is acquired at high Rs and/or high field strength.

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.

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.

Noise distribution in SENSE- and GRAPPA-reconstructed images: a computer simulation study

This work presents a descriptive study of noise distributions in images reconstructed according to the parallel imaging methods SENSE and GRAPPA. In the computer simulations, two different settings were used for describing an object. The first setting included a synthetic object and eight complex-valued coil sensitivities. In the second setting, a complex-valued in vitro object, composed of four individual coil images, was used. After adding noise and subsampling k-space for each coil image, reconstruction was performed according to SENSE, with and without regularization, and GRAPPA for different reduction factors. A set of images was created for three different reduction factors. Noise distributions were determined for each data set and compared with each other. The results of this study show that the noise distributions in SENSE- and GRAPPA-reconstructed images differ. The noise in images reconstructed according to GRAPPA has a more uniform spatial distribution compared with SENSE-reconstructed images, in which the noise varies regionally according to the geometry factor. The noise distribution in SENSE-reconstructed images using regularization showed a similar but lowered pattern of noise compared with images reconstructed according to SENSE without regularization.