Deep Generalization of Structured Low-Rank Algorithms (Deep-SLR)

One for multiple: Physics-informed synthetic data boosts generalizable deep learning for fast MRI reconstruction

Magnetic resonance imaging (MRI) is a widely used radiological modality renowned for its radiation-free, comprehensive insights into the human body, facilitating medical diagnoses. However, the drawback of prolonged scan times hinders its accessibility. The k-space undersampling offers a solution, yet the resultant artifacts necessitate meticulous removal during image reconstruction. Although deep learning (DL) has proven effective for fast MRI image reconstruction, its broader applicability across various imaging scenarios has been constrained. Challenges include the high cost and privacy restrictions associated with acquiring large-scale, diverse training data, coupled with the inherent difficulty of addressing mismatches between training and target data in existing DL methodologies. Here, we present a novel Physics-Informed Synthetic data learning Framework for fast MRI, called PISF. PISF marks a breakthrough by enabling generalizable DL for multi-scenario MRI reconstruction through a single trained model. Our approach separates the reconstruction of a 2D image into many 1D basic problems, commencing with 1D data synthesis to facilitate generalization. We demonstrate that training DL models on synthetic data, coupled with enhanced learning techniques, yields in vivo MRI reconstructions comparable to or surpassing those of models trained on matched realistic datasets, reducing the reliance on real-world MRI data by up to 96 %. With a single trained model, our PISF supports the high-quality reconstruction under 4 sampling patterns, 5 anatomies, 6 contrasts, 5 vendors, and 7 centers, exhibiting remarkable generalizability. Its adaptability to 2 neuro and 2 cardiovascular patient populations has been validated through evaluations by 10 experienced medical professionals. In summary, PISF presents a feasible and cost-effective way to significantly boost the widespread adoption of DL in various fast MRI applications.

Spatial-frequency aware zero-centric residual unfolding network for MRI reconstruction

Magnetic Resonance Imaging is a cornerstone of medical diagnostics, providing high-quality soft tissue contrast through non-invasive methods. However, MRI technology faces critical limitations in imaging speed and resolution. Prolonged scan times not only increase patient discomfort but also contribute to motion artifacts, further compromising image quality. Compressed Sensing (CS) theory has enabled the acquisition of partial k-space data, which can then be effectively reconstructed to recover the original image using advanced reconstruction algorithms. Recently, deep learning has been widely applied to MRI reconstruction, aiming to reduce the artifacts in the image domain caused by undersampling in k-space and enhance image quality. As deep learning continues to evolve, the undersampling factors in k-space have gradually increased in recent years. However, these layers are limited in compensating for reconstruction errors in the unsampled areas, impeding further performance improvements. To address this, we propose a learnable spatial-frequency difference-aware module that complements the learnable data consistency layer, mapping k-space domain differences to the spatial image domain for perceptual compensation. Additionally, inspired by wavelet decomposition, we introduce explicit priors by decomposing images into mean and residual components, enforcing a refined zero-mean constraint on the residuals while maintaining computational efficiency. Comparative experiments on the FastMRI and Calgary-Campinas datasets demonstrate that our method achieves superior reconstruction performance against seven state-of-the-art techniques. Ablation studies further confirm the efficacy of our model's architecture, establishing a new pathway for enhanced MRI reconstruction.

SPIRiT-Diffusion: Self-Consistency Driven Diffusion Model for Accelerated MRI

Diffusion models have emerged as a leading methodology for image generation and have proven successful in the realm of magnetic resonance imaging (MRI) reconstruction. However, existing reconstruction methods based on diffusion models are primarily formulated in the image domain, making the reconstruction quality susceptible to inaccuracies in coil sensitivity maps (CSMs). k-space interpolation methods can effectively address this issue but conventional diffusion models are not readily applicable in k-space interpolation. To overcome this challenge, we introduce a novel approach called SPIRiT-Diffusion, which is a diffusion model for k-space interpolation inspired by the iterative self-consistent SPIRiT method. Specifically, we utilize the iterative solver of the self-consistent term (i.e., k-space physical prior) in SPIRiT to formulate a novel stochastic differential equation (SDE) governing the diffusion process. Subsequently, k-space data can be interpolated by executing the diffusion process. This innovative approach highlights the optimization model's role in designing the SDE in diffusion models, enabling the diffusion process to align closely with the physics inherent in the optimization model-a concept referred to as model-driven diffusion. We evaluated the proposed SPIRiT-Diffusion method using a 3D joint intracranial and carotid vessel wall imaging dataset. The results convincingly demonstrate its superiority over image-domain reconstruction methods, achieving high reconstruction quality even at a substantial acceleration rate of 10. Our code are available at https://github.com/zhyjSIAT/SPIRiT-Diffusion.

Cardiac MR image reconstruction using cascaded hybrid dual domain deep learning framework

Recovering diagnostic-quality cardiac MR images from highly under-sampled data is a current research focus, particularly in addressing cardiac and respiratory motion. Techniques such as Compressed Sensing (CS) and Parallel Imaging (pMRI) have been proposed to accelerate MRI data acquisition and improve image quality. However, these methods have limitations in high spatial-resolution applications, often resulting in blurring or residual artifacts. Recently, deep learning-based techniques have gained attention for their accuracy and efficiency in image reconstruction. Deep learning-based MR image reconstruction methods are divided into two categories: (a) single domain methods (image domain learning and k-space domain learning) and (b) cross/dual domain methods. Single domain methods, which typically use U-Net in either the image or k-space domain, fail to fully exploit the correlation between these domains. This paper introduces a dual-domain deep learning approach that incorporates multi-coil data consistency (MCDC) layers for reconstructing cardiac MR images from 1-D Variable Density (VD) random under-sampled data. The proposed hybrid dual-domain deep learning models integrate data from both the domains to improve image quality, reduce artifacts, and enhance overall robustness and accuracy of the reconstruction process. Experimental results demonstrate that the proposed methods outperform than conventional deep learning and CS techniques, as evidenced by higher Structural Similarity Index (SSIM), lower Root Mean Square Error (RMSE), and higher Peak Signal-to-Noise Ratio (PSNR).

Fast and Reliable Score-Based Generative Model for Parallel MRI

The score-based generative model (SGM) can generate high-quality samples, which have been successfully adopted for magnetic resonance imaging (MRI) reconstruction. However, the recent SGMs may take thousands of steps to generate a high-quality image. Besides, SGMs neglect to exploit the redundancy in space. To overcome the above two drawbacks, in this article, we propose a fast and reliable SGM (FRSGM). First, we propose deep ensemble denoisers (DEDs) consisting of SGM and the deep denoiser, which are used to solve the proximal problem of the implicit regularization term. Second, we propose a spatially adaptive self-consistency (SASC) term as the regularization term of the -space data. We use the alternating direction method of multipliers (ADMM) algorithm to solve the minimization model of compressed sensing (CS)-MRI incorporating the image prior term and the SASC term, which is significantly faster than the related works based on SGM. Meanwhile, we can prove that the iterating sequence of the proposed algorithm has a unique fixed point. In addition, the DED and the SASC term can significantly improve the generalization ability of the algorithm. The features mentioned above make our algorithm reliable, including the fixed-point convergence guarantee, the exploitation of the space, and the powerful generalization ability.

Physics-Informed DeepMRI: k-Space Interpolation Meets Heat Diffusion

Recently, diffusion models have shown considerable promise for MRI reconstruction. However, extensive experimentation has revealed that these models are prone to generating artifacts due to the inherent randomness involved in generating images from pure noise. To achieve more controlled image reconstruction, we reexamine the concept of interpolatable physical priors in k-space data, focusing specifically on the interpolation of high-frequency (HF) k-space data from low-frequency (LF) k-space data. Broadly, this insight drives a shift in the generation paradigm from random noise to a more deterministic approach grounded in the existing LF k-space data. Building on this, we first establish a relationship between the interpolation of HF k-space data from LF k-space data and the reverse heat diffusion process, providing a fundamental framework for designing diffusion models that generate missing HF data. To further improve reconstruction accuracy, we integrate a traditional physics-informed k-space interpolation model into our diffusion framework as a data fidelity term. Experimental validation using publicly available datasets demonstrates that our approach significantly surpasses traditional k-space interpolation methods, deep learning-based k-space interpolation techniques, and conventional diffusion models, particularly in HF regions. Finally, we assess the generalization performance of our model across various out-of-distribution datasets. Our code are available at https://github.com/ZhuoxuCui/Heat-Diffusion.

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.

Dual-domain faster Fourier convolution based network for MR image reconstruction

Deep learning methods for fast MRI have shown promise in reconstructing high-quality images from undersampled multi-coil k-space data, leading to reduced scan duration. However, existing methods encounter challenges related to limited receptive fields in dual-domain (k-space and image domains) reconstruction networks, rigid data consistency operations, and suboptimal refinement structures, which collectively restrict overall reconstruction performance. This study introduces a comprehensive framework that addresses these challenges and enhances MR image reconstruction quality. Firstly, we propose Faster Inverse Fourier Convolution (FasterIFC), a frequency domain convolutional operator that significantly expands the receptive field of k-space domain reconstruction networks. Expanding the information extraction range to the entire frequency spectrum according to the spectral convolution theorem in Fourier theory enables the network to easily utilize richer redundant long-range information from adjacent, symmetrical, and diagonal locations of multi-coil k-space data. Secondly, we introduce a novel softer Data Consistency (softerDC) layer, which achieves an enhanced balance between data consistency and smoothness. This layer facilitates the implementation of diverse data consistency strategies across distinct frequency positions, addressing the inflexibility observed in current methods. Finally, we present the Dual-Domain Faster Fourier Convolution Based Network (D2F2), which features a centrosymmetric dual-domain parallel structure based on FasterIFC. This architecture optimally leverages dual-domain data characteristics while substantially expanding the receptive field in both domains. Coupled with the softerDC layer, D2F2 demonstrates superior performance on the NYU fastMRI dataset at multiple acceleration factors, surpassing state-of-the-art methods in both quantitative and qualitative evaluations.

Deep learning for accelerated and robust MRI reconstruction

Deep learning (DL) has recently emerged as a pivotal technology for enhancing magnetic resonance imaging (MRI), a critical tool in diagnostic radiology. This review paper provides a comprehensive overview of recent advances in DL for MRI reconstruction, and focuses on various DL approaches and architectures designed to improve image quality, accelerate scans, and address data-related challenges. It explores end-to-end neural networks, pre-trained and generative models, and self-supervised methods, and highlights their contributions to overcoming traditional MRI limitations. It also discusses the role of DL in optimizing acquisition protocols, enhancing robustness against distribution shifts, and tackling biases. Drawing on the extensive literature and practical insights, it outlines current successes, limitations, and future directions for leveraging DL in MRI reconstruction, while emphasizing the potential of DL to significantly impact clinical imaging practices.

Integrating data distribution prior via Langevin dynamics for end-to-end MR reconstruction

PURPOSE

To develop a novel deep learning-based method inheriting the advantages of data distribution prior and end-to-end training for accelerating MRI.

METHODS

Langevin dynamics is used to formulate image reconstruction with data distribution before facilitate image reconstruction. The data distribution prior is learned implicitly through the end-to-end adversarial training to mitigate the hyper-parameter selection and shorten the testing time compared to traditional probabilistic reconstruction. By seamlessly integrating the deep equilibrium model, the iteration of Langevin dynamics culminates in convergence to a fix-point, ensuring the stability of the learned distribution.

RESULTS

The feasibility of the proposed method is evaluated on the brain and knee datasets. Retrospective results with uniform and random masks show that the proposed method demonstrates superior performance both quantitatively and qualitatively than the state-of-the-art.

CONCLUSION

The proposed method incorporating Langevin dynamics with end-to-end adversarial training facilitates efficient and robust reconstruction for MRI. Empirical evaluations conducted on brain and knee datasets compellingly demonstrate the superior performance of the proposed method in terms of artifact removing and detail preserving.

Scan-Specific Self-Supervised Bayesian Deep Non-Linear Inversion for Undersampled MRI Reconstruction

Magnetic resonance imaging is subject to slow acquisition times due to the inherent limitations in data sampling. Recently, supervised deep learning has emerged as a promising technique for reconstructing sub-sampled MRI. However, supervised deep learning requires a large dataset of fully-sampled data. Although unsupervised or self-supervised deep learning methods have emerged to address the limitations of supervised deep learning approaches, they still require a database of images. In contrast, scan-specific deep learning methods learn and reconstruct using only the sub-sampled data from a single scan. Here, we introduce Scan-Specific Self-Supervised Bayesian Deep Non-Linear Inversion (DNLINV) that does not require an auto calibration scan region. DNLINV utilizes a Deep Image Prior-type generative modeling approach and relies on approximate Bayesian inference to regularize the deep convolutional neural network. We demonstrate our approach on several anatomies, contrasts, and sampling patterns and show improved performance over existing approaches in scan-specific calibrationless parallel imaging and compressed sensing.

DFUSNN: zero-shot dual-domain fusion unsupervised neural network for parallel MRI reconstruction

Objective. Recently, deep learning models have been used to reconstruct parallel magnetic resonance (MR) images from undersampled k-space data. However, most existing approaches depend on large databases of fully sampled MR data for training, which can be challenging or sometimes infeasible to acquire in certain scenarios. The goal is to develop an effective alternative for improved reconstruction quality that does not rely on external training datasets.Approach. We introduce a novel zero-shot dual-domain fusion unsupervised neural network (DFUSNN) for parallel MR imaging reconstruction without any external training datasets. We employ the Noise2Noise (N2N) network for the reconstruction in the k-space domain, integrate phase and coil sensitivity smoothness priors into the k-space N2N network, and use an early stopping criterion to prevent overfitting. Additionally, we propose a dual-domain fusion method based on Bayesian optimization to enhance reconstruction quality efficiently.Results. Simulation experiments conducted on three datasets with different undersampling patterns showed that the DFUSNN outperforms all other competing unsupervised methods and the one-shot Hankel-k-space generative model (HKGM). The DFUSNN also achieves comparable results to the supervised Deep-SLR method.Significance. The novel DFUSNN model offers a viable solution for reconstructing high-quality MR images without the need for external training datasets, thereby overcoming a major hurdle in scenarios where acquiring fully sampled MR data is difficult.

Image Reconstruction for Accelerated MR Scan With Faster Fourier Convolutional Neural Networks

High quality image reconstruction from undersampled k -space data is key to accelerating MR scanning. Current deep learning methods are limited by the small receptive fields in reconstruction networks, which restrict the exploitation of long-range information, and impede the mitigation of full-image artifacts, particularly in 3D reconstruction tasks. Additionally, the substantial computational demands of 3D reconstruction considerably hinder advancements in related fields. To tackle these challenges, we propose the following: 1) A novel convolution operator named Faster Fourier Convolution (FasterFC), aims at providing an adaptable broad receptive field for spatial domain reconstruction networks with fast computational speed. 2) A split-slice strategy that substantially reduces the computational load of 3D reconstruction, enabling high-resolution, multi-coil, 3D MR image reconstruction while fully utilizing inter-layer and intra-layer information. 3) A single-to-group algorithm that efficiently utilizes scan-specific and data-driven priors to enhance k -space interpolation effects. 4) A multi-stage, multi-coil, 3D fast MRI method, called the faster Fourier convolution based single-to-group network (FAS-Net), comprising a single-to-group k -space interpolation algorithm and a FasterFC-based image domain reconstruction module, significantly minimizes the computational demands of 3D reconstruction through split-slice strategy. Experimental evaluations conducted on the NYU fastMRI and Stanford MRI Data datasets reveal that the FasterFC significantly enhances the quality of both 2D and 3D reconstruction results. Moreover, FAS-Net, characterized as a method that can achieve high-resolution (320, 320, 256), multi-coil, (8 coils), 3D fast MRI, exhibits superior reconstruction performance compared to other state-of-the-art 2D and 3D methods.

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.

Annihilation-Net: Learned annihilation relation for dynamic MR imaging

BACKGROUND

Deep learning methods driven by the low-rank regularization have achieved attractive performance in dynamic magnetic resonance (MR) imaging. The effectiveness of existing methods lies mainly in their ability to capture interframe relationships using network modules, which are lack interpretability.

PURPOSE

This study aims to design an interpretable methodology for modeling interframe relationships using convolutiona networks, namely Annihilation-Net and use it for accelerating dynamic MRI.

METHODS

Based on the equivalence between Hankel matrix product and convolution, we utilize convolutional networks to learn the null space transform for characterizing low-rankness. We employ low-rankness to represent interframe correlations in dynamic MR imaging, while combining with sparse constraints in the compressed sensing framework. The corresponding optimization problem is solved in an iterative form with the semi-quadratic splitting method (HQS). The iterative steps are unrolled into a network, dubbed Annihilation-Net. All the regularization parameters and null space transforms are set as learnable in the Annihilation-Net.

RESULTS

Experiments on the cardiac cine dataset show that the proposed model outperforms other competing methods both quantitatively and qualitatively. The training set and test set have 800 and 118 images, respectively.

CONCLUSIONS

The proposed Annihilation-Net improves the reconstruction quality of accelerated dynamic MRI with better interpretability.

Joint Cross-Attention Network With Deep Modality Prior for Fast MRI Reconstruction

Current deep learning-based reconstruction models for accelerated multi-coil magnetic resonance imaging (MRI) mainly focus on subsampled k-space data of single modality using convolutional neural network (CNN). Although dual-domain information and data consistency constraint are commonly adopted in fast MRI reconstruction, the performance of existing models is still limited mainly by three factors: inaccurate estimation of coil sensitivity, inadequate utilization of structural prior, and inductive bias of CNN. To tackle these challenges, we propose an unrolling-based joint Cross-Attention Network, dubbed as jCAN, using deep guidance of the already acquired intra-subject data. Particularly, to improve the performance of coil sensitivity estimation, we simultaneously optimize the latent MR image and sensitivity map (SM). Besides, we introduce Gating layer and Gaussian layer into SM estimation to alleviate the "defocus" and "over-coupling" effects and further ameliorate the SM estimation. To enhance the representation ability of the proposed model, we deploy Vision Transformer (ViT) and CNN in the image and k-space domains, respectively. Moreover, we exploit pre-acquired intra-subject scan as reference modality to guide the reconstruction of subsampled target modality by resorting to the self- and cross-attention scheme. Experimental results on public knee and in-house brain datasets demonstrate that the proposed jCAN outperforms the state-of-the-art methods by a large margin in terms of SSIM and PSNR for different acceleration factors and sampling masks. Our code is publicly available at https://github.com/sunkg/jCAN.

Accelerated submillimeter wave-encoded magnetic resonance imaging via deep untrained neural network

BACKGROUND

Wave gradient encoding can adequately utilize coil sensitivity profiles to facilitate higher accelerations in parallel magnetic resonance imaging (pMRI). However, there are limitations in mainstream pMRI and a few deep learning (DL) methods for recovering missing data under wave encoding framework: the former is prone to introduce errors from the auto-calibration signals (ACS) signal acquisition and is time-consuming, while the latter requires a large amount of training data.

PURPOSE

To tackle the above issues, an untrained neural network (UNN) model incorporating wave-encoded physical properties and deep generative model, named WDGM, was proposed with additional ACS- and training data-free.

METHODS

Generally, the proposed method can provide powerful missing data interpolation capability using the wave physical encoding framework and designed UNN to characterize the MR image (k-space data) priors. Specifically, the MRI reconstruction combining physical wave encoding and elaborate UNN is modeled as a generalized minimization problem. The designation of UNN is driven by the coil sensitivity maps (CSM) smoothness and k-space linear predictability. And then, the iterative paradigm to recover the full k-space signal is determined by the projected gradient descent, and the complex computation is unrolled to the network with optimized parameters by the optimizer. Simulated wave encoding and in vivo experiments are exploited to demonstrate the feasibility of the proposed method. The best quantitative metrics RMSE/SSIM/PSNR of 0.0413, 0.9514, and 37.4862 gave competitive results in all experiments with at least six-fold acceleration, respectively.

RESULTS

In vivo experiments of human brains and knees showed that the proposed method can achieve comparable reconstruction quality and even has superiority relative to the comparison, especially at a high resolution of 0.67 mm and fewer ACS. In addition, the proposed method has a higher computational efficiency achieving a computation time of 9.6 s/per slice.

CONCLUSIONS

The model proposed in this work addresses two limitations of MRI reconstruction in the wave encoding framework. The first is to eliminate the need for ACS signal acquisition to perform the time-consuming calibration process and to avoid errors such as motion during the acquisition procedure. Furthermore, the proposed method has clinical application friendly without the need to prepare large training datasets, which is difficult in the clinical. All results of the proposed method demonstrate more confidence in both quantitative and qualitative metrics. In addition, the proposed method can achieve higher computational efficiency.

Equilibrated Zeroth-Order Unrolled Deep Network for Parallel MR Imaging

In recent times, model-driven deep learning has evolved an iterative algorithm into a cascade network by replacing the regularizer's first-order information, such as the (sub)gradient or proximal operator, with a network module. This approach offers greater explainability and predictability compared to typical data-driven networks. However, in theory, there is no assurance that a functional regularizer exists whose first-order information matches the substituted network module. This implies that the unrolled network output may not align with the regularization models. Furthermore, there are few established theories that guarantee global convergence and robustness (regularity) of unrolled networks under practical assumptions. To address this gap, we propose a safeguarded methodology for network unrolling. Specifically, for parallel MR imaging, we unroll a zeroth-order algorithm, where the network module serves as a regularizer itself, allowing the network output to be covered by a regularization model. Additionally, inspired by deep equilibrium models, we conduct the unrolled network before backpropagation to converge to a fixed point and then demonstrate that it can tightly approximate the actual MR image. We also prove that the proposed network is robust against noisy interferences if the measurement data contain noise. Finally, numerical experiments indicate that the proposed network consistently outperforms state-of-the-art MRI reconstruction methods, including traditional regularization and unrolled deep learning techniques.

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.

One-Dimensional Deep Low-Rank and Sparse Network for Accelerated MRI

Deep learning has shown astonishing performance in accelerated magnetic resonance imaging (MRI). Most state-of-the-art deep learning reconstructions adopt the powerful convolutional neural network and perform 2D convolution since many magnetic resonance images or their corresponding k-space are in 2D. In this work, we present a new approach that explores the 1D convolution, making the deep network much easier to be trained and generalized. We further integrate the 1D convolution into the proposed deep network, named as One-dimensional Deep Low-rank and Sparse network (ODLS), which unrolls the iteration procedure of a low-rank and sparse reconstruction model. Extensive results on in vivo knee and brain datasets demonstrate that, the proposed ODLS is very suitable for the case of limited training subjects and provides improved reconstruction performance than state-of-the-art methods both visually and quantitatively. Additionally, ODLS also shows nice robustness to different undersampling scenarios and some mismatches between the training and test data. In summary, our work demonstrates that the 1D deep learning scheme is memory-efficient and robust in fast MRI.

Pyramid Convolutional RNN for MRI Image Reconstruction

Fast and accurate MRI image reconstruction from undersampled data is crucial in clinical practice. Deep learning based reconstruction methods have shown promising advances in recent years. However, recovering fine details from undersampled data is still challenging. In this paper, we introduce a novel deep learning based method, Pyramid Convolutional RNN (PC-RNN), to reconstruct images from multiple scales. Based on the formulation of MRI reconstruction as an inverse problem, we design the PC-RNN model with three convolutional RNN (ConvRNN) modules to iteratively learn the features in multiple scales. Each ConvRNN module reconstructs images at different scales and the reconstructed images are combined by a final CNN module in a pyramid fashion. The multi-scale ConvRNN modules learn a coarse-to-fine image reconstruction. Unlike other common reconstruction methods for parallel imaging, PC-RNN does not employ coil sensitive maps for multi-coil data and directly model the multiple coils as multi-channel inputs. The coil compression technique is applied to standardize data with various coil numbers, leading to more efficient training. We evaluate our model on the fastMRI knee and brain datasets and the results show that the proposed model outperforms other methods and can recover more details. The proposed method is one of the winner solutions in the 2019 fastMRI competition.

Dynamic Imaging Using a Deep Generative SToRM (Gen-SToRM) Model

We introduce a generative smoothness regularization on manifolds (SToRM) model for the recovery of dynamic image data from highly undersampled measurements. The model assumes that the images in the dataset are non-linear mappings of low-dimensional latent vectors. We use the deep convolutional neural network (CNN) to represent the non-linear transformation. The parameters of the generator as well as the low-dimensional latent vectors are jointly estimated only from the undersampled measurements. This approach is different from traditional CNN approaches that require extensive fully sampled training data. We penalize the norm of the gradients of the non-linear mapping to constrain the manifold to be smooth, while temporal gradients of the latent vectors are penalized to obtain a smoothly varying time-series. The proposed scheme brings in the spatial regularization provided by the convolutional network. The main benefit of the proposed scheme is the improvement in image quality and the orders-of-magnitude reduction in memory demand compared to traditional manifold models. To minimize the computational complexity of the algorithm, we introduce an efficient progressive training-in-time approach and an approximate cost function. These approaches speed up the image reconstructions and offers better reconstruction performance.

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.

RECONSTRUCTION AND SEGMENTATION OF PARALLEL MR DATA USING IMAGE DOMAIN DEEP-SLR

The main focus of this work is a novel framework for the joint reconstruction and segmentation of parallel MRI (PMRI) brain data. We introduce an image domain deep network for calibrationless recovery of undersampled PMRI data. The proposed approach is the deep-learning (DL) based generalization of local low-rank based approaches for uncalibrated PMRI recovery including CLEAR [6]. Since the image domain approach exploits additional annihilation relations compared to k-space based approaches, we expect it to offer improved performance. To minimize segmentation errors resulting from undersampling artifacts, we combined the proposed scheme with a segmentation network and trained it in an end-to-end fashion. In addition to reducing segmentation errors, this approach also offers improved reconstruction performance by reducing overfitting; the reconstructed images exhibit reduced blurring and sharper edges than independently trained reconstruction network.