Adapting model-based deep learning to multiple acquisition conditions: Ada-MoDL

PURPOSE

The aim of this work is to introduce a single model-based deep network that can provide high-quality reconstructions from undersampled parallel MRI data acquired with multiple sequences, acquisition settings, and field strengths.

METHODS

A single unrolled architecture, which offers good reconstructions for multiple acquisition settings, is introduced. The proposed scheme adapts the model to each setting by scaling the convolutional neural network (CNN) features and the regularization parameter with appropriate weights. The scaling weights and regularization parameter are derived using a multilayer perceptron model from conditional vectors, which represents the specific acquisition setting. The perceptron parameters and the CNN weights are jointly trained using data from multiple acquisition settings, including differences in field strengths, acceleration, and contrasts. The conditional network is validated using datasets acquired with different acquisition settings.

RESULTS

The comparison of the adaptive framework, which trains a single model using the data from all the settings, shows that it can offer consistently improved performance for each acquisition condition. The comparison of the proposed scheme with networks that are trained independently for each acquisition setting shows that it requires less training data per acquisition setting to offer good performance.

CONCLUSION

The Ada-MoDL framework enables the use of a single model-based unrolled network for multiple acquisition settings. In addition to eliminating the need to train and store multiple networks for different acquisition settings, this approach reduces the training data needed for each acquisition setting.

Emerging Trends in Fast MRI Using Deep-Learning Reconstruction on Undersampled k-Space Data: A Systematic Review

Magnetic Resonance Imaging (MRI) is an essential medical imaging modality that provides excellent soft-tissue contrast and high-resolution images of the human body, allowing us to understand detailed information on morphology, structural integrity, and physiologic processes. However, MRI exams usually require lengthy acquisition times. Methods such as parallel MRI and Compressive Sensing (CS) have significantly reduced the MRI acquisition time by acquiring less data through undersampling k-space. The state-of-the-art of fast MRI has recently been redefined by integrating Deep Learning (DL) models with these undersampled approaches. This Systematic Literature Review (SLR) comprehensively analyzes deep MRI reconstruction models, emphasizing the key elements of recently proposed methods and highlighting their strengths and weaknesses. This SLR involves searching and selecting relevant studies from various databases, including Web of Science and Scopus, followed by a rigorous screening and data extraction process using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. It focuses on various techniques, such as residual learning, image representation using encoders and decoders, data-consistency layers, unrolled networks, learned activations, attention modules, plug-and-play priors, diffusion models, and Bayesian methods. This SLR also discusses the use of loss functions and training with adversarial networks to enhance deep MRI reconstruction methods. Moreover, we explore various MRI reconstruction applications, including non-Cartesian reconstruction, super-resolution, dynamic MRI, joint learning of reconstruction with coil sensitivity and sampling, quantitative mapping, and MR fingerprinting. This paper also addresses research questions, provides insights for future directions, and emphasizes robust generalization and artifact handling. Therefore, this SLR serves as a valuable resource for advancing fast MRI, guiding research and development efforts of MRI reconstruction for better image quality and faster data acquisition.

A flexible 16-channel custom coil array for accelerated imaging of upper and infraglottic airway at 3 T

PURPOSE

To develop a custom coil and evaluate its utility for accelerated upper and infraglottic airway MRI at 3 T.

METHODS

A 16-channel flexible and anatomy-conforming coil was developed to provide localized sensitivity over upper and infraglottic airway regions of interest. Parallel-imaging capabilities were compared against existing head and head-neck coils. SENSE geometry factor losses were quantified for retrospectively accelerating 3D MRI. Blinded image-quality ratings from two experts were performed. Spiral GRAPPA reconstructions were evaluated for a speaking task at a time resolution of 40 ms. Contrast-to-noise ratios between air and tissue at key landmarks along the vocal tract were compared. SENSE imaging with the custom coil in the lateral recumbent posture was evaluated. Multislice imaging was performed to image swallowing at 17 ms/frame via constrained reconstruction.

RESULTS

The custom coil showed improved SENSE imaging up to 3-fold acceleration when accelerated along either the anterior-posterior or the superior-inferior direction and a net 4-fold acceleration when accelerated along both directions. Spiral GRAPPA reconstructions with the custom coil showed higher contrast-to-noise ratio when compared with existing coils. In the lateral posture, robust SENSE imaging was achieved at up to 2-fold and 3-fold acceleration levels in the superior-inferior and anterior-posterior directions, respectively. Key events of swallowing in the multislice dynamic images were identified by an otolaryngologist.

CONCLUSION

The coil provided improved parallel imaging of upper and infraglottic airway in both supine and lateral recumbent postures. It enabled efficient accelerated dynamic imaging of speaking and swallowing.

A review and experimental evaluation of deep learning methods for MRI reconstruction

Following the success of deep learning in a wide range of applications, neural network-based machine-learning techniques have received significant interest for accelerating magnetic resonance imaging (MRI) acquisition and reconstruction strategies. A number of ideas inspired by deep learning techniques for computer vision and image processing have been successfully applied to nonlinear image reconstruction in the spirit of compressed sensing for accelerated MRI. Given the rapidly growing nature of the field, it is imperative to consolidate and summarize the large number of deep learning methods that have been reported in the literature, to obtain a better understanding of the field in general. This article provides an overview of the recent developments in neural-network based approaches that have been proposed specifically for improving parallel imaging. A general background and introduction to parallel MRI is also given from a classical view of k-space based reconstruction methods. Image domain based techniques that introduce improved regularizers are covered along with k-space based methods which focus on better interpolation strategies using neural networks. While the field is rapidly evolving with plenty of papers published each year, in this review, we attempt to cover broad categories of methods that have shown good performance on publicly available data sets. Limitations and open problems are also discussed and recent efforts for producing open data sets and benchmarks for the community are examined.

ENSURE: ENSEMBLE STEIN'S UNBIASED RISK ESTIMATOR FOR UNSUPERVISED LEARNING

Deep learning algorithms are emerging as powerful alternatives to compressed sensing methods, offering improved image quality and computational efficiency. Unfortunately, fully sampled training images may not be available or are difficult to acquire in several applications, including high-resolution and dynamic imaging. Previous studies in image reconstruction have utilized Stein's Unbiased Risk Estimator (SURE) as a mean square error (MSE) estimate for the image denoising step in an unrolled network. Unfortunately, the end-to-end training of a network using SURE remains challenging since the projected SURE loss is a poor approximation to the MSE, especially in the heavily undersampled setting. We propose an ENsemble SURE (ENSURE) approach to train a deep network only from undersampled measurements. In particular, we show that training a network using an ensemble of images, each acquired with a different sampling pattern, can closely approximate the MSE. Our preliminary experimental results show that the proposed ENSURE approach gives comparable reconstruction quality to supervised learning and a recent unsupervised learning method.

Calibration-Less Multi-Coil Compressed Sensing Magnetic Resonance Image Reconstruction Based on OSCAR Regularization

Over the last decade, the combination of compressed sensing (CS) with acquisition over multiple receiver coils in magnetic resonance imaging (MRI) has allowed the emergence of faster scans while maintaining a good signal-to-noise ratio (SNR). Self-calibrating techniques, such as ESPiRIT, have become the standard approach to estimating the coil sensitivity maps prior to the reconstruction stage. In this work, we proceed differently and introduce a new calibration-less multi-coil CS reconstruction method. Calibration-less techniques no longer require the prior extraction of sensitivity maps to perform multi-coil image reconstruction but usually alternate estimation sensitivity map estimation and image reconstruction. Here, to get rid of the nonconvexity of the latter approach we reconstruct as many MR images as the number of coils. To compensate for the ill-posedness of this inverse problem, we leverage structured sparsity of the multi-coil images in a wavelet transform domain while adapting to variations in SNR across coils owing to the OSCAR (octagonal shrinkage and clustering algorithm for regression) regularization. Coil-specific complex-valued MR images are thus obtained by minimizing a convex but nonsmooth objective function using the proximal primal-dual Condat-Vù algorithm. Comparison and validation on retrospective Cartesian and non-Cartesian studies based on the Brain fastMRI data set demonstrate that the proposed reconstruction method outperforms the state-of-the-art (ℓ1-ESPIRiT, calibration-less AC-LORAKS and CaLM methods) significantly on magnitude images for the T1 and FLAIR contrasts. Additionally, further validation operated on 8 to 20-fold prospectively accelerated high-resolution ex vivo human brain MRI data collected at 7 Tesla confirms the retrospective results. Overall, OSCAR-based regularization preserves phase information more accurately (both visually and quantitatively) compared to other approaches, an asset that can only be assessed on real prospective experiments.

Full utilization of conjugate symmetry: combining virtual conjugate coil reconstruction with partial Fourier imaging for g-factor reduction in accelerated MRI

PURPOSE

In this study we propose a method to combine the parallel virtual conjugate coil (VCC) reconstruction with partial Fourier (PF) acquisition to improve reconstruction conditioning and reduce noise amplification in accelerated MRI where PF is used.

METHODS

Accelerated measurements are reconstructed in k-space by GRAPPA, with a VCC reconstruction kernel trained and applied in the central, symmetrically sampled part of k-space, while standard reconstruction is performed on the asymmetrically sampled periphery. The two reconstructed regions are merged to form a full reconstructed dataset, followed by PF reconstruction. The method is tested in vivo using T1-weighted spin-echo and T2*-weighted gradient-echo echo planar imaging (EPI) sequences, using both in-plane and simultaneous multislice (SMS) acceleration, at 1.5T and 3T field strengths. Noise amplification is estimated with theoretical calculations and pseudo-multiple-replica computations, for different PF factors, using zero-filling, homodyne, and projection onto convex sets (POCS) PF reconstruction.

RESULTS

Depending on the PF algorithm and the inherent benefit of VCC reconstruction without PF, approximately 35% to 80%, 15% to 60%, and 5% to 30% of that intrinsic SNR gain can be retained for PF factors 7/8, 6/8, and 5/8, respectively, by including the VCC signals in the reconstruction. Compared with VCC-reconstructed acquisitions of higher acceleration, without PF, but having the same net acceleration, the combined method can provide a higher SNR if the inherent benefit of VCC is low or moderate.

CONCLUSION

The proposed technique enables the partial application of VCC reconstruction to measurements with PF using either in-plane or SMS acceleration, and therefore can reduce the noise amplification of such acquisitions.

Virtual slice concept for improved simultaneous multi-slice MRI employing an extended leakage constraint

PURPOSE

To develop a novel, simultaneous multi-slice (SMS) reconstruction that extends an inter-slice leakage constraint to intra-slice aliasing with a virtual slice concept for artifact reduction.

METHODS

Inter-slice leakage constraint has been used for SMS reconstruction that mitigates leakage artifacts from the adjacent slices. In this work, the leakage constraint is extended to more general framework that includes SMS and parallel MRI as special cases by viewing intra-slice aliasing artifacts from undersampling as virtual slices while imposing data fidelity to ensure the measurement consistency. In this way, the reconstruction makes it feasible to directly estimate the individual slices from the undersampled SMS acquisition as a one-step method. The performance of the extended method is evaluated with data acquired using 2D GRE and EPI sequences.

RESULTS

Compared to a two-step method that performs slice unaliasing followed by inplane unaliasing, the proposed one-step method reduces aliasing artifacts by employing the extended leakage constraint while lowering the noise amplification by improving the conditioning for the inverse problem.

CONCLUSIONS

The proposed one-step method takes advantage of virtual slices as additional encoding power for improved image quality. We successfully demonstrated that the proposed one-step method minimizes a trade-off between aliasing artifacts and amplified noises over the two-step method.

LORAKS makes better SENSE: Phase-constrained partial fourier SENSE reconstruction without phase calibration

PURPOSE

Parallel imaging and partial Fourier acquisition are two classical approaches for accelerated MRI. Methods that combine these approaches often rely on prior knowledge of the image phase, but the need to obtain this prior information can place practical restrictions on the data acquisition strategy. In this work, we propose and evaluate SENSE-LORAKS, which enables combined parallel imaging and partial Fourier reconstruction without requiring prior phase information.

THEORY AND METHODS

The proposed formulation is based on combining the classical SENSE model for parallel imaging data with the more recent LORAKS framework for MR image reconstruction using low-rank matrix modeling. Previous LORAKS-based methods have successfully enabled calibrationless partial Fourier parallel MRI reconstruction, but have been most successful with nonuniform sampling strategies that may be hard to implement for certain applications. By combining LORAKS with SENSE, we enable highly accelerated partial Fourier MRI reconstruction for a broader range of sampling trajectories, including widely used calibrationless uniformly undersampled trajectories.

RESULTS

Our empirical results with retrospectively undersampled datasets indicate that when SENSE-LORAKS reconstruction is combined with an appropriate k-space sampling trajectory, it can provide substantially better image quality at high-acceleration rates relative to existing state-of-the-art reconstruction approaches.

CONCLUSION

The SENSE-LORAKS framework provides promising new opportunities for highly accelerated MRI. Magn Reson Med 77:1021-1035, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

A subspace-based coil combination method for phased-array magnetic resonance imaging

PURPOSE

Coil-by-coil reconstruction methods are followed by coil combination to obtain a single image representing a spin density map. Typical coil combination methods, such as square-root sum-of-squares and adaptive coil combining, yield images that exhibit spatially varying modulation of image intensity. Existing practice is to first combine coils according to a signal-to-noise criterion, then postprocess to correct intensity inhomogeneity. If inhomogeneity is severe, however, intensity correction methods can yield poor results. The purpose of this article is to present an alternative optimality criterion for coil combination; the resulting procedure yields reduced intensity inhomogeneity while preserving contrast.

THEORY AND METHODS

A minimum mean squared error criterion is adopted for combining coils via a subspace decomposition. Techniques are compared using both simulated and in vivo data.

RESULTS

Experimental results for simulated and in vivo data demonstrate lower bias, higher signal-to-noise ratio (about 7×) and contrast-to-noise ratio (about 2×), compared to existing coil combination techniques.

CONCLUSION

The proposed coil combination method is noniterative and does not require estimation of coil sensitivity maps or image mask; the method is particularly suited to cases where intensity inhomogeneity is too severe for existing approaches.

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.

Comparison of phase-constrained parallel MRI approaches: Analogies and differences

PURPOSE

Phase-constrained parallel MRI approaches have the potential for significantly improving the image quality of accelerated MRI scans. The purpose of this study was to investigate the properties of two different phase-constrained parallel MRI formulations, namely the standard phase-constrained approach and the virtual conjugate coil (VCC) concept utilizing conjugate k-space symmetry.

METHODS

Both formulations were combined with image-domain algorithms (SENSE) and a mathematical analysis was performed. Furthermore, the VCC concept was combined with k-space algorithms (GRAPPA and ESPIRiT) for image reconstruction. In vivo experiments were conducted to illustrate analogies and differences between the individual methods. Furthermore, a simple method of improving the signal-to-noise ratio by modifying the sampling scheme was implemented.

RESULTS

For SENSE, the VCC concept was mathematically equivalent to the standard phase-constrained formulation and therefore yielded identical results. In conjunction with k-space algorithms, the VCC concept provided more robust results when only a limited amount of calibration data were available. Additionally, VCC-GRAPPA reconstructed images provided spatial phase information with full resolution.

CONCLUSIONS

Although both phase-constrained parallel MRI formulations are very similar conceptually, there exist important differences between image-domain and k-space domain reconstructions regarding the calibration robustness and the availability of high-resolution phase information.

Improve GRAPPA with cross-sampled ACS lines and nonlinear kernel model

Among the methods of parallel magnetic resonance imaging (PMRI), Generalized Auto-calibrating Partially Parallel Acquisitions (GRAPPA) technique reconstructs the missing k-space data by a set of weights, which are derived from auto-calibration signal (ACS) lines acquired in parallel to the reduced lines. In this paper, a novel hybrid method is proposed to reconstruct by cross sampling the ACS lines orthogonal to the reduced lines and estimating weights with a second-order nonlinear model. The proposed method can mix the benefits of cross sampling and the nonlinear kernel model. The in vivo experiments demonstrate this method, named as cross-sampled nonlinear (CSNL) GRAPPA, can effectively reduce the aliasing artifacts and noises when high acceleration is desired.

Parallel imaging performance investigation of an 8-channel common-mode differential-mode (CMDM) planar array for 7T MRI

An 8-channel planar phased array was proposed based on the common-mode differential-mode (CMDM) structure for ultrahigh field MRI. The parallel imaging performance of the 8-channel CMDM planar array was numerically investigated based on electromagnetic simulations and Cartesian sensitivity encoding (SENSE) reconstruction. The signal-to-noise ratio (SNR) of multichannel images combined using root-sum-of-squares (rSoS) and covariance weighted root-sum-of-squares (Cov-rSoS) at various reduction factors were compared between 8-channel CMDM array and 4-channel CM and DM array. The results of the study indicated the 8-channel CMDM array excelled the 4-channel CM and DM in SNR. The g-factor maps and artifact power were calculated to evaluate parallel imaging performance of the proposed 8-channel CMDM array. The artifact power of 8-channel CMDM array was reduced dramatically compared with the 4-channel CM and DM arrays demonstrating the parallel imaging feasibility of the CMDM array.

Regularization method for phase-constrained parallel MRI

PURPOSE

To implement a regularization method for the phase-constrained generalized partially parallel acquisitions (GRAPPA) algorithm to reduce image artifacts caused by data inconsistencies.

METHODS

Phase-constrained GRAPPA reconstructions are implemented through the use of virtual coils. To that end, synthetic virtual coils are generated by using complex conjugate symmetric signals from the actual coils. Regularization is achieved by applying coefficient-based penalty factors during the GRAPPA calibration procedure. Different penalizing factors are applied for the actual and virtual coils. The method is tested in vivo using T2-weighted turbo spin echo (TSE) images.

RESULTS

T2 signal decay perturbs conjugate k-space symmetry and produces artifacts in phase-constrained parallel MRI reconstructions of T2-weighted TSE images. Using the proposed regularization method, artifacts are suppressed at the cost of noise amplification. However, there is still a significant SNR gain compared with conventional GRAPPA.

CONCLUSION

The proposed regularization method is an efficient approach for artifact suppression and maintains the SNR benefit of phase-constrained parallel MRI over conventional parallel MRI.

Accelerated fractional ventilation imaging with hyperpolarized Gas MRI

PURPOSE

To investigate the utility of accelerated imaging to enhance multibreath fractional ventilation (r) measurement accuracy using hyperpolarized gas MRI. Undersampling shortens the breath-hold time, thereby reducing the O2 -induced signal decay and allows subjects to maintain a more physiologically relevant breathing pattern. Additionally, it may improve r estimation accuracy by reducing radiofrequency destruction of hyperpolarized gas.

METHODS

Image acceleration was achieved using an eight-channel phased array coil. Undersampled image acquisition was simulated in a series of ventilation images and data was reconstructed for various matrix sizes (48-128) using generalized auto-calibrating partially parallel acquisition. Parallel accelerated r imaging was also performed on five mechanically ventilated pigs.

RESULTS

Optimal acceleration factor was fairly invariable (2.0-2.2×) over the range of simulated resolutions. Estimation accuracy progressively improved with higher resolutions (39-51% error reduction). In vivo r values were not significantly different between the two methods: 0.27 ± 0.09, 0.35 ± 0.06, 0.40 ± 0.04 (standard) versus 0.23 ± 0.05, 0.34 ± 0.03, 0.37 ± 0.02 (accelerated); for anterior, medial, and posterior slices, respectively, whereas the corresponding vertical r gradients were significant (P < 0.001): 0.021 ± 0.007 (standard) versus 0.019 ± 0.005 (accelerated) (cm(-1) ).

CONCLUSION

Quadruple phased array coil simulations resulted in an optimal acceleration factor of ∼2× independent of imaging resolution. Results advocate undersampled image acceleration to improve accuracy of fractional ventilation measurement with hyperpolarized gas MRI.

Accelerating MR parameter mapping using sparsity-promoting regularization in parametric dimension

MR parameter mapping requires sampling along additional (parametric) dimension, which often limits its clinical appeal due to a several-fold increase in scan times compared to conventional anatomic imaging. Data undersampling combined with parallel imaging is an attractive way to reduce scan time in such applications. However, inherent SNR penalties of parallel MRI due to noise amplification often limit its utility even at moderate acceleration factors, requiring regularization by prior knowledge. In this work, we propose a novel regularization strategy, which uses smoothness of signal evolution in the parametric dimension within compressed sensing framework (p-CS) to provide accurate and precise estimation of parametric maps from undersampled data. The performance of the method was demonstrated with variable flip angle T1 mapping and compared favorably to two representative reconstruction approaches, image space-based total variation regularization and an analytical model-based reconstruction. The proposed p-CS regularization was found to provide efficient suppression of noise amplification and preservation of parameter mapping accuracy without explicit utilization of analytical signal models. The developed method may facilitate acceleration of quantitative MRI techniques that are not suitable to model-based reconstruction because of complex signal models or when signal deviations from the expected analytical model exist.

Noise amplification in parallel whole-head ultra-low-field magnetic resonance imaging using 306 detectors

In ultra-low-field magnetic resonance imaging, arrays of up to hundreds of highly sensitive superconducting quantum interference devices (SQUIDs) can be used to detect the weak magnetic fields emitted by the precessing magnetization. Here, we investigate the noise amplification in sensitivity-encoded ultra-low-field MRI at various acceleration rates using a SQUID array consisting of 102 magnetometers, 102 gradiometers, or 306 magnetometers and gradiometers, to cover the whole head. Our results suggest that SQUID arrays consisting of 102 magnetometers and 102 gradiometers are similar in g-factor distribution. A SQUID array of 306 sensors (102 magnetometers and 204 gradiometers) only marginally improves the g-factor. Corroborating with previous studies, the g-factor in 2D sensitivity-encoded ultra-low-field MRI with 9 to 16-fold 2D accelerations using the SQUID array studied here may be acceptable.