Scan-specific artifact reduction in k-space (SPARK) neural networks synergize with physics-based reconstruction to accelerate MRI

JUST-Net: Jointly unrolled cross-domain optimization based spatio-temporal reconstruction network for accelerated 3D myelin water imaging

PURPOSE

We introduced a novel reconstruction network, jointly unrolled cross-domain optimization-based spatio-temporal reconstruction network (JUST-Net), aimed at accelerating 3D multi-echo gradient-echo (mGRE) data acquisition and improving the quality of resulting myelin water imaging (MWI) maps.

METHOD

An unrolled cross-domain spatio-temporal reconstruction network was designed. The main idea is to combine frequency and spatio-temporal image feature representations and to sequentially implement convolution layers in both domains. The k-space subnetwork utilizes shared information from adjacent frames, whereas the image subnetwork applies separate convolutions in both spatial and temporal dimensions. The proposed reconstruction network was evaluated for both retrospectively and prospectively accelerated acquisition. Furthermore, it was assessed in simulation studies and real-world cases with k-space corruptions to evaluate its potential for motion artifact reduction.

RESULTS

The proposed JUST-Net enabled highly reproducible and accelerated 3D mGRE acquisition for whole-brain MWI, reducing the acquisition time from fully sampled 15:23 to 2:22 min within a 3-min reconstruction time. The normalized root mean squared error of the reconstructed mGRE images increased by less than 4.0%, and the correlation coefficients for MWI showed a value of over 0.68 when compared to the fully sampled reference. Additionally, the proposed method demonstrated a mitigating effect on both simulated and clinical motion-corrupted cases.

CONCLUSION

The proposed JUST-Net has demonstrated the capability to achieve high acceleration factors for 3D mGRE-based MWI, which is expected to facilitate widespread clinical applications of MWI.

DPP: deep phase prior for parallel imaging with wave encoding

Objective.In Magnetic Resonance (MR) parallel imaging with virtual channel-expanded Wave encoding, limitations are imposed on the ability to comprehensively and accurately characterize the background phase. These limitations are primarily attributed to the calibration process relying solely on center low-frequency Auto-Calibration Signals (ACS) data for calibration.Approach.To tackle the challenge of accurately estimating the background phase in wave encoding, a novel deep neural network model guided by deep phase priors is proposed with integrated virtual conjugate coil (VCC) extension. Concretely, within the proposed framework, the background phase is implicitly characterized by employing a carefully designed decoder convolutional neural network, leveraging the inherent characteristics of phase smoothness and compact support in the transformed domain. Furthermore, the proposed model with wave encoding benefits from additional priors, which incorporate transmission sparsity of the latent image and coil sensitivity smoothness.Main results.Ablation experiments were conducted to ascertain the proposed method's capability to implicitly represent CSM and the background phase. Subsequently, the superiority of the proposed method is demonstrated through confidence comparisons with competing methods, employing 4-fold and 5-fold acceleration experiments. In achieving 4-fold and 5-fold acceleration, the optimal quantitative metrics (PSNR/SSIM/NMSE) are 44.1359 dB/0.9863/0.0008 (4-fold) and 41.2074/0.9846/0.0017 (5-fold), respectively. Furthermore, the generalizability of the proposed method is further validated by conducting acceleration experiments with T1, T2, T2*, and various undersampling patterns. In addition, the DPP delivered much better performance than the conventional methods by exploring accelerated phase-sensitive SWI imaging. In SWI accelerated imaging, it also surpasses the optimal competing method in terms of (PSNR/SSIM/NMSE) with 0.096%/0.009%/0.0017%.Significance.The proposed method enables precise characterization of the background phase in the integrated VCC and wave encoding framework, supported via theoretical analysis and empirical findings. Our code is available at:https://github.com/sober235/DPP.

Knowledge-driven deep learning for fast MR imaging: Undersampled MR image reconstruction from supervised to un-supervised learning

Deep learning (DL) has emerged as a leading approach in accelerating MRI. It employs deep neural networks to extract knowledge from available datasets and then applies the trained networks to reconstruct accurate images from limited measurements. Unlike natural image restoration problems, MRI involves physics-based imaging processes, unique data properties, and diverse imaging tasks. This domain knowledge needs to be integrated with data-driven approaches. Our review will introduce the significant challenges faced by such knowledge-driven DL approaches in the context of fast MRI along with several notable solutions, which include learning neural networks and addressing different imaging application scenarios. The traits and trends of these techniques have also been given which have shifted from supervised learning to semi-supervised learning, and finally, to unsupervised learning methods. In addition, MR vendors' choices of DL reconstruction have been provided along with some discussions on open questions and future directions, which are critical for the reliable imaging systems.

IMJENSE: Scan-Specific Implicit Representation for Joint Coil Sensitivity and Image Estimation in Parallel MRI

Parallel imaging is a commonly used technique to accelerate magnetic resonance imaging (MRI) data acquisition. Mathematically, parallel MRI reconstruction can be formulated as an inverse problem relating the sparsely sampled k-space measurements to the desired MRI image. Despite the success of many existing reconstruction algorithms, it remains a challenge to reliably reconstruct a high-quality image from highly reduced k-space measurements. Recently, implicit neural representation has emerged as a powerful paradigm to exploit the internal information and the physics of partially acquired data to generate the desired object. In this study, we introduced IMJENSE, a scan-specific implicit neural representation-based method for improving parallel MRI reconstruction. Specifically, the underlying MRI image and coil sensitivities were modeled as continuous functions of spatial coordinates, parameterized by neural networks and polynomials, respectively. The weights in the networks and coefficients in the polynomials were simultaneously learned directly from sparsely acquired k-space measurements, without fully sampled ground truth data for training. Benefiting from the powerful continuous representation and joint estimation of the MRI image and coil sensitivities, IMJENSE outperforms conventional image or k-space domain reconstruction algorithms. With extremely limited calibration data, IMJENSE is more stable than supervised calibrationless and calibration-based deep-learning methods. Results show that IMJENSE robustly reconstructs the images acquired at 5× and 6× accelerations with only 4 or 8 calibration lines in 2D Cartesian acquisitions, corresponding to 22.0% and 19.5% undersampling rates. The high-quality results and scanning specificity make the proposed method hold the potential for further accelerating the data acquisition of parallel MRI.

A Systematic Review and Identification of the Challenges of Deep Learning Techniques for Undersampled Magnetic Resonance Image Reconstruction

Deep learning (DL) in magnetic resonance imaging (MRI) shows excellent performance in image reconstruction from undersampled k-space data. Artifact-free and high-quality MRI reconstruction is essential for ensuring accurate diagnosis, supporting clinical decision-making, enhancing patient safety, facilitating efficient workflows, and contributing to the validity of research studies and clinical trials. Recently, deep learning has demonstrated several advantages over conventional MRI reconstruction methods. Conventional methods rely on manual feature engineering to capture complex patterns and are usually computationally demanding due to their iterative nature. Conversely, DL methods use neural networks with hundreds of thousands of parameters and automatically learn relevant features and representations directly from the data. Nevertheless, there are some limitations to DL-based techniques concerning MRI reconstruction tasks, such as the need for large, labeled datasets, the possibility of overfitting, and the complexity of model training. Researchers are striving to develop DL models that are more efficient, adaptable, and capable of providing valuable information for medical practitioners. We provide a comprehensive overview of the current developments and clinical uses by focusing on state-of-the-art DL architectures and tools used in MRI reconstruction. This study has three objectives. Our main objective is to describe how various DL designs have changed over time and talk about cutting-edge tactics, including their advantages and disadvantages. Hence, data pre- and post-processing approaches are assessed using publicly available MRI datasets and source codes. Secondly, this work aims to provide an extensive overview of the ongoing research on transformers and deep convolutional neural networks for rapid MRI reconstruction. Thirdly, we discuss several network training strategies, like supervised, unsupervised, transfer learning, and federated learning for rapid and efficient MRI reconstruction. Consequently, this article provides significant resources for future improvement of MRI data pre-processing and fast image reconstruction.

Parallel-stream fusion of scan-specific and scan-general priors for learning deep MRI reconstruction in low-data regimes

Magnetic resonance imaging (MRI) is an essential diagnostic tool that suffers from prolonged scan times. Reconstruction methods can alleviate this limitation by recovering clinically usable images from accelerated acquisitions. In particular, learning-based methods promise performance leaps by employing deep neural networks as data-driven priors. A powerful approach uses scan-specific (SS) priors that leverage information regarding the underlying physical signal model for reconstruction. SS priors are learned on each individual test scan without the need for a training dataset, albeit they suffer from computationally burdening inference with nonlinear networks. An alternative approach uses scan-general (SG) priors that instead leverage information regarding the latent features of MRI images for reconstruction. SG priors are frozen at test time for efficiency, albeit they require learning from a large training dataset. Here, we introduce a novel parallel-stream fusion model (PSFNet) that synergistically fuses SS and SG priors for performant MRI reconstruction in low-data regimes, while maintaining competitive inference times to SG methods. PSFNet implements its SG prior based on a nonlinear network, yet it forms its SS prior based on a linear network to maintain efficiency. A pervasive framework for combining multiple priors in MRI reconstruction is algorithmic unrolling that uses serially alternated projections, causing error propagation under low-data regimes. To alleviate error propagation, PSFNet combines its SS and SG priors via a novel parallel-stream architecture with learnable fusion parameters. Demonstrations are performed on multi-coil brain MRI for varying amounts of training data. PSFNet outperforms SG methods in low-data regimes, and surpasses SS methods with few tens of training samples. On average across tasks, PSFNet achieves 3.1 dB higher PSNR, 2.8% higher SSIM, and 0.3 × lower RMSE than baselines. Furthermore, in both supervised and unsupervised setups, PSFNet requires an order of magnitude lower samples compared to SG methods, and enables an order of magnitude faster inference compared to SS methods. Thus, the proposed model improves deep MRI reconstruction with elevated learning and computational efficiency.

One-Shot Generative Prior in Hankel-k-Space for Parallel Imaging Reconstruction

Magnetic resonance imaging serves as an essential tool for clinical diagnosis. However, it suffers from a long acquisition time. The utilization of deep learning, especially the deep generative models, offers aggressive acceleration and better reconstruction in magnetic resonance imaging. Nevertheless, learning the data distribution as prior knowledge and reconstructing the image from limited data remains challenging. In this work, we propose a novel Hankel-k-space generative model (HKGM), which can generate samples from a training set of as little as one k-space. At the prior learning stage, we first construct a large Hankel matrix from k-space data, then extract multiple structured k-space patches from the Hankel matrix to capture the internal distribution among different patches. Extracting patches from a Hankel matrix enables the generative model to be learned from the redundant and low-rank data space. At the iterative reconstruction stage, the desired solution obeys the learned prior knowledge. The intermediate reconstruction solution is updated by taking it as the input of the generative model. The updated result is then alternatively operated by imposing low-rank penalty on its Hankel matrix and data consistency constraint on the measurement data. Experimental results confirmed that the internal statistics of patches within single k-space data carry enough information for learning a powerful generative model and providing state-of-the-art reconstruction.

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.

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.

A Hybrid Residual Attention Convolutional Neural Network for Compressed Sensing Magnetic Resonance Image Reconstruction

We propose a dual-domain deep learning technique for accelerating compressed sensing magnetic resonance image reconstruction. An advanced convolutional neural network with residual connectivity and an attention mechanism was developed for frequency and image domains. First, the sensor domain subnetwork estimates the unmeasured frequencies of k-space to reduce aliasing artifacts. Second, the image domain subnetwork performs a pixel-wise operation to remove blur and noisy artifacts. The skip connections efficiently concatenate the feature maps to alleviate the vanishing gradient problem. An attention gate in each decoder layer enhances network generalizability and speeds up image reconstruction by eliminating irrelevant activations. The proposed technique reconstructs real-valued clinical images from sparsely sampled k-spaces that are identical to the reference images. The performance of this novel approach was compared with state-of-the-art direct mapping, single-domain, and multi-domain methods. With acceleration factors (AFs) of 4 and 5, our method improved the mean peak signal-to-noise ratio (PSNR) to 8.67 and 9.23, respectively, compared with the single-domain Unet model; similarly, our approach increased the average PSNR to 3.72 and 4.61, respectively, compared with the multi-domain W-net. Remarkably, using an AF of 6, it enhanced the PSNR by 9.87 ± 1.55 and 6.60 ± 0.38 compared with Unet and W-net, respectively.

A domain-agnostic MR reconstruction framework using a randomly weighted neural network

PURPOSE

To design a randomly-weighted neural network that performs domain-agnostic MR image reconstruction from undersampled k-space data without the need for ground truth or extensive in-vivo training datasets. The network performance must be similar to the current state-of-the-art algorithms that require large training datasets.

METHODS

We propose a Weight Agnostic randomly weighted Network method for MRI reconstruction (termed WAN-MRI) which does not require updating the weights of the neural network but rather chooses the most appropriate connections of the network to reconstruct the data from undersampled k-space measurements. The network architecture has three components, i.e. (1) Dimensionality Reduction Layers comprising of 3d convolutions, ReLu, and batch norm; (2) Reshaping Layer is Fully Connected layer; and (3) Upsampling Layers that resembles the ConvDecoder architecture. The proposed methodology is validated on fastMRI knee and brain datasets.

RESULTS

The proposed method provides a significant boost in performance for structural similarity index measure (SSIM) and root mean squared error (RMSE) scores on fastMRI knee and brain datasets at an undersampling factor of R=4 and R=8 while trained on fractal and natural images, and fine-tuned with only 20 samples from the fastMRI training k-space dataset. Qualitatively, we see that classical methods such as GRAPPA and SENSE fail to capture the subtle details that are clinically relevant. We either outperform or show comparable performance with several existing deep learning techniques (that require extensive training) like GrappaNET, VariationNET, J-MoDL, and RAKI.

CONCLUSION

The proposed algorithm (WAN-MRI) is agnostic to reconstructing images of different body organs or MRI modalities and provides excellent scores in terms of SSIM, PSNR, and RMSE metrics and generalizes better to out-of-distribution examples. The methodology does not require ground truth data and can be trained using very few undersampled multi-coil k-space training samples.

Iterative training of robust k-space interpolation networks for improved image reconstruction with limited scan specific training samples

PURPOSE

To evaluate an iterative learning approach for enhanced performance of robust artificial-neural-networks for k-space interpolation (RAKI), when only a limited amount of training data (auto-calibration signals [ACS]) are available for accelerated standard 2D imaging.

METHODS

In a first step, the RAKI model was tailored for the case of limited training data amount. In the iterative learning approach (termed iterative RAKI [iRAKI]), the tailored RAKI model is initially trained using original and augmented ACS obtained from a linear parallel imaging reconstruction. Subsequently, the RAKI convolution filters are refined iteratively using original and augmented ACS extracted from the previous RAKI reconstruction. Evaluation was carried out on 200 retrospectively undersampled in vivo datasets from the fastMRI neuro database with different contrast settings.

RESULTS

For limited training data (18 and 22 ACS lines for R = 4 and R = 5, respectively), iRAKI outperforms standard RAKI by reducing residual artifacts and yields better noise suppression when compared to standard parallel imaging, underlined by quantitative reconstruction quality metrics. Additionally, iRAKI shows better performance than both GRAPPA and standard RAKI in case of pre-scan calibration with varying contrast between training- and undersampled data.

CONCLUSION

RAKI benefits from the iterative learning approach, which preserves the noise suppression feature, but requires less original training data for the accurate reconstruction of standard 2D images thereby improving net acceleration.

De-Aliasing and Accelerated Sparse Magnetic Resonance Image Reconstruction Using Fully Dense CNN with Attention Gates

When sparsely sampled data are used to accelerate magnetic resonance imaging (MRI), conventional reconstruction approaches produce significant artifacts that obscure the content of the image. To remove aliasing artifacts, we propose an advanced convolutional neural network (CNN) called fully dense attention CNN (FDA-CNN). We updated the Unet model with the fully dense connectivity and attention mechanism for MRI reconstruction. The main benefit of FDA-CNN is that an attention gate in each decoder layer increases the learning process by focusing on the relevant image features and provides a better generalization of the network by reducing irrelevant activations. Moreover, densely interconnected convolutional layers reuse the feature maps and prevent the vanishing gradient problem. Additionally, we also implement a new, proficient under-sampling pattern in the phase direction that takes low and high frequencies from the k-space both randomly and non-randomly. The performance of FDA-CNN was evaluated quantitatively and qualitatively with three different sub-sampling masks and datasets. Compared with five current deep learning-based and two compressed sensing MRI reconstruction techniques, the proposed method performed better as it reconstructed smoother and brighter images. Furthermore, FDA-CNN improved the mean PSNR by 2 dB, SSIM by 0.35, and VIFP by 0.37 compared with Unet for the acceleration factor of 5.

Wave-Encoded Model-Based Deep Learning for Highly Accelerated Imaging with Joint Reconstruction

A recently introduced model-based deep learning (MoDL) technique successfully incorporates convolutional neural network (CNN)-based regularizers into physics-based parallel imaging reconstruction using a small number of network parameters. Wave-controlled aliasing in parallel imaging (CAIPI) is an emerging parallel imaging method that accelerates imaging acquisition by employing sinusoidal gradients in the phase- and slice/partition-encoding directions during the readout to take better advantage of 3D coil sensitivity profiles. We propose wave-encoded MoDL (wave-MoDL) combining the wave-encoding strategy with unrolled network constraints for highly accelerated 3D imaging while enforcing data consistency. We extend wave-MoDL to reconstruct multicontrast data with CAIPI sampling patterns to leverage similarity between multiple images to improve the reconstruction quality. We further exploit this to enable rapid quantitative imaging using an interleaved look-locker acquisition sequence with T₂ preparation pulse (3D-QALAS). Wave-MoDL enables a 40 s MPRAGE acquisition at 1 mm resolution at 16-fold acceleration. For quantitative imaging, wave-MoDL permits a 1:50 min acquisition for T₁, T₂, and proton density mapping at 1 mm resolution at 12-fold acceleration, from which contrast-weighted images can be synthesized as well. In conclusion, wave-MoDL allows rapid MR acquisition and high-fidelity image reconstruction and may facilitate clinical and neuroscientific applications by incorporating unrolled neural networks into wave-CAIPI reconstruction.

Assessment of data consistency through cascades of independently recurrent inference machines for fast and robust accelerated MRI reconstruction

Objective. Machine Learning methods can learn how to reconstruct magnetic resonance images (MRI) and thereby accelerate acquisition, which is of paramount importance to the clinical workflow. Physics-informed networks incorporate the forward model of accelerated MRI reconstruction in the learning process. With increasing network complexity, robustness is not ensured when reconstructing data unseen during training. We aim to embed data consistency (DC) in deep networks while balancing the degree of network complexity. While doing so, we will assess whether either explicit or implicit enforcement of DC in varying network architectures is preferred to optimize performance. Approach. We propose a scheme called Cascades of Independently Recurrent Inference Machines (CIRIM) to assess DC through unrolled optimization. Herein we assess DC both implicitly by gradient descent and explicitly by a designed term. Extensive comparison of the CIRIM to compressed sensing as well as other Machine Learning methods is performed: the End-to-End Variational Network (E2EVN), CascadeNet, KIKINet, LPDNet, RIM, IRIM, and UNet. Models were trained and evaluated on T1-weighted and FLAIR contrast brain data, and T2-weighted knee data. Both 1D and 2D undersampling patterns were evaluated. Robustness was tested by reconstructing 7.5× prospectively undersampled 3D FLAIR MRI data of multiple sclerosis (MS) patients with white matter lesions. Main results. The CIRIM performed best when implicitly enforcing DC, while the E2EVN required an explicit DC formulation. Through its cascades, the CIRIM was able to score higher on structural similarity and PSNR compared to other methods, in particular under heterogeneous imaging conditions. In reconstructing MS patient data, prospectively acquired with a sampling pattern unseen during model training, the CIRIM maintained lesion contrast while efficiently denoising the images. Significance. The CIRIM showed highly promising generalization capabilities maintaining a very fair trade-off between reconstructed image quality and fast reconstruction times, which is crucial in the clinical workflow.

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.

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.