Denoising sparse images from GRAPPA using the nullspace method

Residual RAKI: A hybrid linear and non-linear approach for scan-specific k-space deep learning

Parallel imaging is the most clinically used acceleration technique for magnetic resonance imaging (MRI) in part due to its easy inclusion into routine acquisitions. In k-space based parallel imaging reconstruction, sub-sampled k-space data are interpolated using linear convolutions. At high acceleration rates these methods have inherent noise amplification and reduced image quality. On the other hand, non-linear deep learning methods provide improved image quality at high acceleration, but the availability of training databases for different scans, as well as their interpretability hinder their adaptation. In this work, we present an extension of Robust Artificial-neural-networks for k-space Interpolation (RAKI), called residual-RAKI (rRAKI), which achieves scan-specific machine learning reconstruction using a hybrid linear and non-linear methodology. In rRAKI, non-linear CNNs are trained jointly with a linear convolution implemented via a skip connection. In effect, the linear part provides a baseline reconstruction, while the non-linear CNN that runs in parallel provides further reduction of artifacts and noise arising from the linear part. The explicit split between the linear and non-linear aspects of the reconstruction also help improve interpretability compared to purely non-linear methods. Experiments were conducted on the publicly available fastMRI datasets, as well as high-resolution anatomical imaging, comparing GRAPPA and its variants, compressed sensing, RAKI, Scan Specific Artifact Reduction in K-space (SPARK) and the proposed rRAKI. Additionally, highly-accelerated simultaneous multi-slice (SMS) functional MRI reconstructions were also performed, where the proposed rRAKI was compred to Read-out SENSE-GRAPPA and RAKI. Our results show that the proposed rRAKI method substantially improves the image quality compared to conventional parallel imaging, and offers sharper images compared to SPARK and ℓ₁-SPIRiT. Furthermore, rRAKI shows improved preservation of time-varying dynamics compared to both parallel imaging and RAKI in highly-accelerated SMS fMRI.

Improving GRAPPA reconstruction using joint nonlinear kernel mapped and phase conjugated virtual coils

To improve the reconstruction condition and alleviate the noise amplification of GRAPPA reconstruction by aggregating the phase conjugated and nonlinear kernel mapped coils with the original physical coil. Nonlinear GRAPPA (NL-GRAPPA) is a kernel-based non-iterative approach which can reduce noise-induced error in GRAPPA reconstruction. And virtual conjugate coil (VCC) embeds the conjugate symmetric property of k-space into GRAPPA data synthesis to improve reconstruction condition. This work proposed NL-VCC-GRAPPA to jointly utilize the nonlinear mapped virtual coil and phase conjugated virtual coil to further reduce noise amplification in parallel imaging. In vivo static and dynamic 2D imaging accelerated by uniform undersampling schemes were performed to evaluate the proposed method in terms of visual image quality, root-mean-square-error (RMSE), and geometry factor (g-factor). The effects of acceleration factors, calibration data size and kernel shape on the proposed model were also separately analyzed and discussed. The proposed method illustrated improved visual image quality evidenced by reduced retrospective RMSE and prospective g-factor comparing with conventional GRAPPA and the recently proposed iterative SENSE-LORAKS reconstructions. Although a larger amount of calibration data and smaller kernel size were required to stabilize the calibration of fourfold extended kernel for the proposed method, it was non-iterative and relatively insensitive to parameter adjustment in the applications. The proposed NL-VCC-extension to conventional GRAPPA brings visible improvements for imaging scenarios accelerated by the widely available uniform undersampling schemes in a practically efficient manner without iteration.

KerNL: Kernel-Based Nonlinear Approach to Parallel MRI Reconstruction

The conventional calibration-based parallel imaging method assumes a linear relationship between the acquired multi-channel k-space data and the unacquired missing data, where the linear coefficients are estimated using some auto-calibration data. In this paper, we first analyze the model errors in the conventional calibration-based methods and demonstrate the nonlinear relationship. Then, a much more general nonlinear framework is proposed for auto-calibrated parallel imaging. In this framework, kernel tricks are employed to represent the general nonlinear relationship between acquired and unacquired k-space data without increasing the computational complexity. Identification of the nonlinear relationship is still performed by solving linear equations. Experimental results demonstrate that the proposed method can achieve reconstruction quality superior to GRAPPA and NL-GRAPPA at high net reduction factors.

Content-aware compressive magnetic resonance image reconstruction

This paper describes an adaptive approach to regularizing model-based reconstructions in magnetic resonance imaging to account for local structure or image content. In conjunction with common models like wavelet and total variation sparsity, this content-aware regularization avoids oversmoothing or compromising image features while suppressing noise and incoherent aliasing from accelerated imaging. To evaluate this regularization approach, the experiments reconstruct images from single- and multi-channel, Cartesian and non-Cartesian, brain and cardiac data. These reconstructions combine common analysis-form regularizers and autocalibrating parallel imaging (when applicable). In most cases, the results show widespread improvement in structural similarity and peak-signal-to-error ratio relative to the fully sampled images. These results suggest that this content-aware regularization can preserve local image structures such as edges while providing denoising power superior to sparsity-promoting or sparsity-reweighted regularization.

Improving parallel imaging by jointly reconstructing multi-contrast data

PURPOSE

To develop parallel imaging techniques that simultaneously exploit coil sensitivity encoding, image phase prior information, similarities across multiple images, and complementary k-space sampling for highly accelerated data acquisition.

METHODS

We introduce joint virtual coil (JVC)-generalized autocalibrating partially parallel acquisitions (GRAPPA) to jointly reconstruct data acquired with different contrast preparations, and show its application in 2D, 3D, and simultaneous multi-slice (SMS) acquisitions. We extend the joint parallel imaging concept to exploit limited support and smooth phase constraints through Joint (J-) LORAKS formulation. J-LORAKS allows joint parallel imaging from limited autocalibration signal region, as well as permitting partial Fourier sampling and calibrationless reconstruction.

RESULTS

We demonstrate highly accelerated 2D balanced steady-state free precession with phase cycling, SMS multi-echo spin echo, 3D multi-echo magnetization-prepared rapid gradient echo, and multi-echo gradient recalled echo acquisitions in vivo. Compared to conventional GRAPPA, proposed joint acquisition/reconstruction techniques provide more than 2-fold reduction in reconstruction error.

CONCLUSION

JVC-GRAPPA takes advantage of additional spatial encoding from phase information and image similarity, and employs different sampling patterns across acquisitions. J-LORAKS achieves a more parsimonious low-rank representation of local k-space by considering multiple images as additional coils. Both approaches provide dramatic improvement in artifact and noise mitigation over conventional single-contrast parallel imaging reconstruction. Magn Reson Med 80:619-632, 2018. © 2018 International Society for Magnetic Resonance in Medicine.

P-LORAKS: Low-rank modeling of local k-space neighborhoods with parallel imaging data

PURPOSE

To propose and evaluate P-LORAKS a new calibrationless parallel imaging reconstruction framework.

THEORY AND METHODS

LORAKS is a flexible and powerful framework that was recently proposed for constrained MRI reconstruction. LORAKS was based on the observation that certain matrices constructed from fully sampled k-space data should have low rank whenever the image has limited support or smooth phase, and made it possible to accurately reconstruct images from undersampled or noisy data using low-rank regularization. This paper introduces P-LORAKS, which extends LORAKS to the context of parallel imaging. This is achieved by combining the LORAKS matrices from different channels to yield a larger but more parsimonious low-rank matrix model of parallel imaging data. This new model can be used to regularize the reconstruction of undersampled parallel imaging data, and implicitly imposes phase, support, and parallel imaging constraints without needing to calibrate phase, support, or sensitivity profiles.

RESULTS

The capabilities of P-LORAKS are evaluated with retrospectively undersampled data and compared against existing parallel MRI reconstruction methods. Results show that P-LORAKS can improve parallel imaging reconstruction quality, and can enable the use of new k-space trajectories that are not compatible with existing reconstruction methods.

CONCLUSION

The P-LORAKS framewok provides a new and effective way to regularize parallel imaging reconstruction.

Fast GRAPPA reconstruction with random projection

PURPOSE

To address the issue of computational complexity in generalized autocalibrating partially parallel acquisition (GRAPPA) when several calibration data are used.

METHOD

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.

RESULTS

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.

CONCLUSION

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.

Wave-CAIPI for highly accelerated 3D imaging

PURPOSE

To introduce the wave-CAIPI (controlled aliasing in parallel imaging) acquisition and reconstruction technique for highly accelerated 3D imaging with negligible g-factor and artifact penalties.

METHODS

The wave-CAIPI 3D acquisition involves playing sinusoidal gy and gz gradients during the readout of each kx encoding line while modifying the 3D phase encoding strategy to incur interslice shifts as in 2D-CAIPI acquisitions. The resulting acquisition spreads the aliasing evenly in all spatial directions, thereby taking full advantage of 3D coil sensitivity distribution. By expressing the voxel spreading effect as a convolution in image space, an efficient reconstruction scheme that does not require data gridding is proposed. Rapid acquisition and high-quality image reconstruction with wave-CAIPI is demonstrated for high-resolution magnitude and phase imaging and quantitative susceptibility mapping.

RESULTS

Wave-CAIPI enables full-brain gradient echo acquisition at 1 mm isotropic voxel size and R = 3 × 3 acceleration with maximum g-factors of 1.08 at 3T and 1.05 at 7T. Relative to the other advanced Cartesian encoding strategies (2D-CAIPI and bunched phase encoding) wave-CAIPI yields up to two-fold reduction in maximum g-factor for nine-fold acceleration at both field strengths.

CONCLUSION

Wave-CAIPI allows highly accelerated 3D acquisitions with low artifact and negligible g-factor penalties, and may facilitate clinical application of high-resolution volumetric imaging.

Fast reconstruction for multichannel compressed sensing using a hierarchically semiseparable solver

PURPOSE

The adoption of multichannel compressed sensing (CS) for clinical magnetic resonance imaging (MRI) hinges on the ability to accurately reconstruct images from an undersampled dataset in a reasonable time frame. When CS is combined with SENSE parallel imaging, reconstruction can be computationally intensive. As an alternative to iterative methods that repetitively evaluate a forward CS+SENSE model, we introduce a technique for the fast computation of a compact inverse model solution.

METHODS

A recently proposed hierarchically semiseparable (HSS) solver is used to compactly represent the inverse of the CS+SENSE encoding matrix to a high level of accuracy. To investigate the computational efficiency of the proposed HSS-Inverse method, we compare reconstruction time with the current state-of-the-art. In vivo 3T brain data at multiple image contrasts, resolutions, acceleration factors, and number of receive channels were used for this comparison.

RESULTS

The HSS-Inverse method allows for >6× speedup when compared to current state-of-the-art reconstruction methods with the same accuracy. Efficient computational scaling is demonstrated for CS+SENSE with respect to image size. The HSS-Inverse method is also shown to have minimal dependency on the number of parallel imaging channels/acceleration factor.

CONCLUSIONS

The proposed HSS-Inverse method is highly efficient and should enable real-time CS reconstruction on standard MRI vendors' computational hardware.

Non-cartesian MRI reconstruction with automatic regularization Via Monte-Carlo SURE

Magnetic resonance image (MRI) reconstruction from undersampled k-space data requires regularization to reduce noise and aliasing artifacts. Proper application of regularization however requires appropriate selection of associated regularization parameters. In this work, we develop a data-driven regularization parameter adjustment scheme that minimizes an estimate [based on the principle of Stein's unbiased risk estimate (SURE)] of a suitable weighted squared-error measure in k-space. To compute this SURE-type estimate, we propose a Monte-Carlo scheme that extends our previous approach to inverse problems (e.g., MRI reconstruction) involving complex-valued images. Our approach depends only on the output of a given reconstruction algorithm and does not require knowledge of its internal workings, so it is capable of tackling a wide variety of reconstruction algorithms and nonquadratic regularizers including total variation and those based on the l1-norm. Experiments with simulated and real MR data indicate that the proposed approach is capable of providing near mean squared-error optimal regularization parameters for single-coil undersampled non-Cartesian MRI reconstruction.

Monte Carlo SURE-based parameter selection for parallel magnetic resonance imaging reconstruction

PURPOSE

Regularizing parallel magnetic resonance imaging (MRI) reconstruction significantly improves image quality but requires tuning parameter selection. We propose a Monte Carlo method for automatic parameter selection based on Stein's unbiased risk estimate that minimizes the multichannel k-space mean squared error (MSE). We automatically tune parameters for image reconstruction methods that preserve the undersampled acquired data, which cannot be accomplished using existing techniques.

THEORY

We derive a weighted MSE criterion appropriate for data-preserving regularized parallel imaging reconstruction and the corresponding weighted Stein's unbiased risk estimate. We describe a Monte Carlo approximation of the weighted Stein's unbiased risk estimate that uses two evaluations of the reconstruction method per candidate parameter value.

METHODS

We reconstruct images using the denoising sparse images from GRAPPA using the nullspace method (DESIGN) and L1 iterative self-consistent parallel imaging (L1 -SPIRiT). We validate Monte Carlo Stein's unbiased risk estimate against the weighted MSE. We select the regularization parameter using these methods for various noise levels and undersampling factors and compare the results to those using MSE-optimal parameters.

RESULTS

Our method selects nearly MSE-optimal regularization parameters for both DESIGN and L1 -SPIRiT over a range of noise levels and undersampling factors.

CONCLUSION

The proposed method automatically provides nearly MSE-optimal choices of regularization parameters for data-preserving nonlinear parallel MRI reconstruction methods.

Sparsity-promoting calibration for GRAPPA accelerated parallel MRI reconstruction

The amount of calibration data needed to produce images of adequate quality can prevent auto-calibrating parallel imaging reconstruction methods like generalized autocalibrating partially parallel acquisitions (GRAPPA) from achieving a high total acceleration factor. To improve the quality of calibration when the number of auto-calibration signal (ACS) lines is restricted, we propose a sparsity-promoting regularized calibration method that finds a GRAPPA kernel consistent with the ACS fit equations that yields jointly sparse reconstructed coil channel images. Several experiments evaluate the performance of the proposed method relative to unregularized and existing regularized calibration methods for both low-quality and underdetermined fits from the ACS lines. These experiments demonstrate that the proposed method, like other regularization methods, is capable of mitigating noise amplification, and in addition, the proposed method is particularly effective at minimizing coherent aliasing artifacts caused by poor kernel calibration in real data. Using the proposed method, we can increase the total achievable acceleration while reducing degradation of the reconstructed image better than existing regularized calibration methods.

Advanced MR Imaging Technologies in Fetuses

Fetal Magnetic Resonance Imaging (MRI) on clinical scanners has increasingly been realized as a powerful imaging tool and applied for studying the brain abnormalities and the potential of neurodevelopmental disabilities in vivo. The primarily used multi-echo fast imaging sequences reduce the motion artifacts with a tradeoff of image Signal-to-Noise Ratio (SNR) and resolution. In Radio Frequency (RF) hardware for MR signal excitation and reception, there are lack of dedicated RF coils for fetal imaging providing optimized performance in acquisition and safety. There is an urgent demand for novel hardware and fast imaging technology developments to overcome motion artifacts and improve sensitivity and safety. Recent studies have demonstrated that dedicated fetal RF transceiver arrays can improve the SNR, image coverage, and safety. In addition, emerging fast imaging technologies such as parallel imaging and compressed sensing would be advantageous in improving imaging speed and thus reducing motion artifacts in fetal imaging.

Multi-contrast reconstruction with Bayesian compressed sensing

Clinical imaging with structural MRI routinely relies on multiple acquisitions of the same region of interest under several different contrast preparations. This work presents a reconstruction algorithm based on Bayesian compressed sensing to jointly reconstruct a set of images from undersampled k-space data with higher fidelity than when the images are reconstructed either individually or jointly by a previously proposed algorithm, M-FOCUSS. The joint inference problem is formulated in a hierarchical Bayesian setting, wherein solving each of the inverse problems corresponds to finding the parameters (here, image gradient coefficients) associated with each of the images. The variance of image gradients across contrasts for a single volumetric spatial position is a single hyperparameter. All of the images from the same anatomical region, but with different contrast properties, contribute to the estimation of the hyperparameters, and once they are found, the k-space data belonging to each image are used independently to infer the image gradients. Thus, commonality of image spatial structure across contrasts is exploited without the problematic assumption of correlation across contrasts. Examples demonstrate improved reconstruction quality (up to a factor of 4 in root-mean-square error) compared with previous compressed sensing algorithms and show the benefit of joint inversion under a hierarchical Bayesian model.