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.Affiliations [3 and 6] has been split into two different affiliations. Please check if action taken is appropriate and amend if necessary.looks good.

Prospectively accelerated dynamic speech magnetic resonance imaging at 3 T using a self-navigated spiral-based manifold regularized scheme.

This work develops and evaluates a self-navigated variable density spiral (VDS)-based manifold regularization scheme to prospectively improve dynamic speech magnetic resonance imaging (MRI) at 3 T. Short readout duration spirals (1.3-ms long) were used to minimize sensitivity to off-resonance. A custom 16-channel speech coil was used for improved parallel imaging of vocal tract structures. The manifold model leveraged similarities between frames sharing similar vocal tract postures without explicit motion binning. The self-navigating capability of VDS was leveraged to learn the Laplacian structure of the manifold. Reconstruction was posed as a sensitivity-encoding-based nonlocal soft-weighted temporal regularization scheme. Our approach was compared with view-sharing, low-rank, temporal finite difference, extra dimension-based sparsity reconstruction constraints. Undersampling experiments were conducted on five volunteers performing repetitive and arbitrary speaking tasks at different speaking rates. Quantitative evaluation in terms of mean square error over moving edges was performed in a retrospective undersampling experiment on one volunteer. For prospective undersampling, blinded image quality evaluation in the categories of alias artifacts, spatial blurring, and temporal blurring was performed by three experts in voice research. Region of interest analysis at articulator boundaries was performed in both experiments to assess articulatory motion. Improved performance with manifold reconstruction constraints was observed over existing constraints. With prospective undersampling, a spatial resolution of 2.4 × 2.4 mm2/pixel and a temporal resolution of 17.4 ms/frame for single-slice imaging, and 52.2 ms/frame for concurrent three-slice imaging, were achieved. We demonstrated implicit motion binning by analyzing the mechanics of the Laplacian matrix. Manifold regularization demonstrated superior image quality scores in reducing spatial and temporal blurring compared with all other reconstruction constraints. While it exhibited faint (nonsignificant) alias artifacts that were similar to temporal finite difference, it provided statistically significant improvements compared with the other constraints. In conclusion, the self-navigated manifold regularized scheme enabled robust high spatiotemporal resolution dynamic speech MRI at 3 T.

Optimizing Deep Learning for Cardiac MRI Segmentation: The Impact of Automated Slice Range Classification.

RATIONALE AND OBJECTIVES: Cardiac magnetic resonance imaging is crucial for diagnosing cardiovascular diseases, but lengthy postprocessing and manual segmentation can lead to observer bias. Deep learning (DL) has been proposed for automated cardiac segmentation; however, its effectiveness is limited by the slice range selection from base to apex. MATERIALS AND METHODS: In this study, we integrated an automated slice range classification step to identify basal to apical short-axis slices before DL-based segmentation. We employed publicly available Multi-Disease, Multi-View & Multi-Center Right Ventricular Segmentation in Cardiac MRI data set with short-axis cine data from 160 training, 40 validation, and 160 testing cases. Three classification and seven segmentation DL models were studied. The top-performing segmentation model was assessed with and without the classification model. Model validation to compare automated and manual segmentation was performed using Dice score and Hausdorff distance and clinical indices (correlation score and Bland-Altman plots). RESULTS: The combined classification (CBAM-integrated 2D-CNN) and segmentation model (2D-UNet with dilated convolution block) demonstrated superior performance, achieving Dice scores of 0.952 for left ventricle (LV), 0.933 for right ventricle (RV), and 0.875 for myocardium, compared to the stand-alone segmentation model (0.949 for LV, 0.925 for RV, and 0.867 for myocardium). Combined classification and segmentation model showed high correlation (0.92-0.99) with manual segmentation for biventricular volumes, ejection fraction, and myocardial mass. The mean absolute difference (2.8-8.3 mL) for clinical parameters between automated and manual segmentation was within the interobserver variability range, indicating comparable performance to manual annotation. CONCLUSION: Integrating an initial automated slice range classification step into the segmentation process improves the performance of DL-based cardiac chamber segmentation.

ComBat Harmonization of Myocardial Radiomic Features Sensitive to Cardiac MRI Acquisition Parameters.

Purpose: To investigate the effect of ComBat harmonization methods on the robustness of cardiac MRI-derived radiomic features to variations in imaging parameters. Materials and Methods: This Health Insurance Portability and Accountability Act-compliant retrospective study used a publicly available data set of 11 healthy controls (mean age, 33 years ± 16 [SD]; six men) and five patients (mean age, 52 years ± 16; four men). A single midventricular short-axis section was acquired with 3-T MRI using cine balanced steady-state free precision, T1-weighted, T2-weighted, T1 mapping, and T2 mapping imaging sequences. Each sequence was acquired using baseline parameters and after variations in flip angle, spatial resolution, section thickness, and parallel imaging. Image registration was performed for all sequences at a per-individual level. Manual myocardial contouring was performed, and 1652 radiomic features per sequence were extracted using baseline and variations in imaging parameters. Radiomic feature stability to change in imaging parameters was assessed using Cohen d sensitivity. The stability of radiomic features was assessed both without and after ComBat harmonization of radiomic features. Three ComBat methods were studied: parametric, nonparametric, and Gaussian mixture model (GMM). Results: For all sequences combined, 51.4% of features were robust to changes in imaging parameters when no ComBat method was applied. ComBat harmonization substantially increased the number of stable features to 95.1% (95% CI: 94.9, 95.3) when parametric ComBat was used and 90.9% (95% CI: 90.6, 91.2) when nonparametric ComBat was used. GMM combat resulted in only 52.6% stable features. Conclusion: ComBat harmonization improved the stability of radiomic features to changes in imaging parameters across all cardiac MRI sequences.Keywords: Cardiac MRI, Radiomics, ComBat, Harmonization Supplemental material is available for this article. © RSNA, 2023.

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.

Memory-efficient model-based deep learning with convergence and robustness guarantees.

Computational imaging has been revolutionized by compressed sensing algorithms, which offer guaranteed uniqueness, convergence, and stability properties. Model-based deep learning methods that combine imaging physics with learned regularization priors have emerged as more powerful alternatives for image recovery. The main focus of this paper is to introduce a memory efficient model-based algorithm with similar theoretical guarantees as CS methods. The proposed iterative algorithm alternates between a gradient descent involving the score function and a conjugate gradient algorithm to encourage data consistency. The score function is modeled as a monotone convolutional neural network. Our analysis shows that the monotone constraint is necessary and sufficient to enforce the uniqueness of the fixed point in arbitrary inverse problems. In addition, it also guarantees the convergence to a fixed point, which is robust to input perturbations. We introduce two implementations of the proposed MOL framework, which differ in the way the monotone property is imposed. The first approach enforces a strict monotone constraint, while the second one relies on an approximation. The guarantees are not valid for the second approach in the strict sense. However, our empirical studies show that the convergence and robustness of both approaches are comparable, while the less constrained approximate implementation offers better performance. The proposed deep equilibrium formulation is significantly more memory efficient than unrolled methods, which allows us to apply it to 3D or 2D+time problems that current unrolled algorithms cannot handle.

Joint Cardiac T1 Mapping and Cardiac Cine Using Manifold Modeling.

The main focus of this work is to introduce a single free-breathing and ungated imaging protocol to jointly estimate cardiac function and myocardial T1 maps. We reconstruct a time series of images corresponding to k-space data from a free-breathing and ungated inversion recovery gradient echo sequence using a manifold algorithm. We model each image in the time series as a non-linear function of three variables: cardiac and respiratory phases and inversion time. The non-linear function is realized using a convolutional neural networks (CNN) generator, while the CNN parameters, as well as the phase information, are estimated from the measured k-t space data. We use a dense conditional auto-encoder to estimate the cardiac and respiratory phases from the central multi-channel k-space samples acquired at each frame. The latent vectors of the auto-encoder are constrained to be bandlimited functions with appropriate frequency bands, which enables the disentanglement of the latent vectors into cardiac and respiratory phases, even when the data are acquired with intermittent inversion pulses. Once the phases are estimated, we pose the image recovery as the learning of the parameters of the CNN generator from the measured k-t space data. The learned CNN generator is used to generate synthetic data on demand by feeding it with appropriate latent vectors. The proposed approach capitalizes on the synergies between cine MRI and T1 mapping to reduce the scan time and improve patient comfort. The framework also enables the generation of synthetic breath-held cine movies with different inversion contrasts, which improves the visualization of the myocardium. In addition, the approach also enables the estimation of the T1 maps with specific phases, which is challenging with breath-held approaches.

ENSURE: A General Approach for Unsupervised Training of Deep Image Reconstruction Algorithms.

Image reconstruction using deep learning algorithms offers improved reconstruction quality and lower reconstruction time than classical compressed sensing and model-based algorithms. Unfortunately, clean and fully sampled ground-truth data to train the deep networks is often unavailable in several applications, restricting the applicability of the above methods. We introduce a novel metric termed the ENsemble Stein's Unbiased Risk Estimate (ENSURE) framework, which can be used to train deep image reconstruction algorithms without fully sampled and noise-free images. The proposed framework is the generalization of the classical SURE and GSURE formulation to the setting where the images are sampled by different measurement operators, chosen randomly from a set. We evaluate the expectation of the GSURE loss functions over the sampling patterns to obtain the ENSURE loss function. We show that this loss is an unbiased estimate for the true mean-square error, which offers a better alternative to GSURE, which only offers an unbiased estimate for the projected error. Our experiments show that the networks trained with this loss function can offer reconstructions comparable to the supervised setting. While we demonstrate this framework in the context of MR image recovery, the ENSURE framework is generally applicable to arbitrary inverse problems.

Motion Compensated Unsupervised Deep Learning for 5D MRI.

We propose an unsupervised deep learning algorithm for the motion-compensated reconstruction of 5D cardiac MRI data from 3D radial acquisitions. Ungated free-breathing 5D MRI simplifies the scan planning, improves patient comfort, and offers several clinical benefits over breath-held 2D exams, including isotropic spatial resolution and the ability to reslice the data to arbitrary views. However, the current reconstruction algorithms for 5D MRI take very long computational time, and their outcome is greatly dependent on the uniformity of the binning of the acquired data into different physiological phases. The proposed algorithm is a more data-efficient alternative to current motion-resolved reconstructions. This motion-compensated approach models the data in each cardiac/respiratory bin as Fourier samples of the deformed version of a 3D image template. The deformation maps are modeled by a convolutional neural network driven by the physiological phase information. The deformation maps and the template are then jointly estimated from the measured data. The cardiac and respiratory phases are estimated from 1D navigators using an auto-encoder. The proposed algorithm is validated on 5D bSSFP datasets acquired from two subjects.

DEEP FACTOR MODEL: A NOVEL APPROACH FOR MOTION COMPENSATED MULTI-DIMENSIONAL MRI.

Recent quantitative parameter mapping methods including MR fingerprinting (MRF) collect a time series of images that capture the evolution of magnetization. The focus of this work is to introduce a novel approach termed as Deep Factor Model(DFM), which offers an efficient representation of the multi-contrast image time series. The higher efficiency of the representation enables the acquisition of the images in a highly undersampled fashion, which translates to reduced scan time in 3D high-resolution multi-contrast applications. The approach integrates motion estimation and compensation, making the approach robust to subject motion during the scan.

ACCELERATED PARALLEL MRI USING MEMORY EFFICIENT AND ROBUST MONOTONE OPERATOR LEARNING (MOL).

Model-based deep learning methods that combine imaging physics with learned regularization priors have been emerging as powerful tools for parallel MRI acceleration. The main focus of this paper is to determine the utility of the monotone operator learning (MOL) framework in the parallel MRI setting. The MOL algorithm alternates between a gradient descent step using a monotone convolutional neural network (CNN) and a conjugate gradient algorithm to encourage data consistency. The benefits of this approach include similar guarantees as compressive sensing algorithms including uniqueness, convergence, and stability, while being significantly more memory efficient than unrolled methods. We validate the proposed scheme by comparing it with different unrolled algorithms in the context of accelerated parallel MRI for static and dynamic settings.

Variational Manifold Learning From Incomplete Data: Application to Multislice Dynamic MRI.

Current deep learning-based manifold learning algorithms such as the variational autoencoder (VAE) require fully sampled data to learn the probability density of real-world datasets. However, fully sampled data is often unavailable in a variety of problems, including the recovery of dynamic and high-resolution magnetic resonance imaging (MRI). We introduce a novel variational approach to learn a manifold from undersampled data. The VAE uses a decoder fed by latent vectors, drawn from a conditional density estimated from the fully sampled images using an encoder. Since fully sampled images are not available in our setting, we approximate the conditional density of the latent vectors by a parametric model whose parameters are estimated from the undersampled measurements using back-propagation. We use the framework for the joint alignment and recovery of multi-slice free breathing and ungated cardiac MRI data from highly undersampled measurements. Experimental results demonstrate the utility of the proposed scheme in dynamic imaging alignment and reconstructions.

Dynamic imaging using motion-compensated smoothness regularization on manifolds (MoCo-SToRM).

Objective. We introduce an unsupervised motion-compensated reconstruction scheme for high-resolution free-breathing pulmonary magnetic resonance imaging.Approach. We model the image frames in the time series as the deformed version of the 3D template image volume. We assume the deformation maps to be points on a smooth manifold in high-dimensional space. Specifically, we model the deformation map at each time instant as the output of a CNN-based generator that has the same weight for all time-frames, driven by a low-dimensional latent vector. The time series of latent vectors account for the dynamics in the dataset, including respiratory motion and bulk motion. The template image volume, the parameters of the generator, and the latent vectors are learned directly from the k-t space data in an unsupervised fashion.Main results. Our experimental results show improved reconstructions compared to state-of-the-art methods, especially in the context of bulk motion during the scans.Significance. The proposed unsupervised motion-compensated scheme jointly estimates the latent vectors that capture the motion dynamics, the corresponding deformation maps, and the reconstructed motion-compensated images from the raw k-t space data of each subject. Unlike current motion-resolved strategies, the proposed scheme is more robust to bulk motion events during the scan.

Dynamic Imaging Using Deep Bi-Linear Unsupervised Representation (DEBLUR).

Bilinear models such as low-rank and dictionary methods, which decompose dynamic data to spatial and temporal factor matrices are powerful and memory-efficient tools for the recovery of dynamic MRI data. Current bilinear methods rely on sparsity and energy compaction priors on the factor matrices to regularize the recovery. Motivated by deep image prior, we introduce a novel bilinear model, whose factor matrices are generated using convolutional neural networks (CNNs). The CNN parameters, and equivalently the factors, are learned from the undersampled data of the specific subject. Unlike current unrolled deep learning methods that require the storage of all the time frames in the dataset, the proposed approach only requires the storage of the factors or compressed representation; this approach allows the direct use of this scheme to large-scale dynamic applications, including free breathing cardiac MRI considered in this work. To reduce the run time and to improve performance, we initialize the CNN parameters using existing factor methods. We use sparsity regularization of the network parameters to minimize the overfitting of the network to measurement noise. Our experiments on free-breathing and ungated cardiac cine data acquired using a navigated golden-angle gradient-echo radial sequence show the ability of our method to provide reduced spatial blurring as compared to classical bilinear methods as well as a recent unsupervised deep-learning approach.

Multi-band- and in-plane-accelerated diffusion MRI enabled by model-based deep learning in q-space and its extension to learning in the spherical harmonic domain.

PURPOSE: To propose a new method for the recovery of combined in-plane- and multi-band (MB)-accelerated diffusion MRI data. METHODS: Combining MB acceleration with in-plane acceleration is crucial to improve the time efficiency of high (angular and spatial) resolution diffusion scans. However, as the MB factor and in-plane acceleration increase, the reconstruction becomes challenging due to the heavy aliasing. The new reconstruction utilizes an additional q-space prior to constrain the recovery, which is derived from the previously proposed qModeL framework. Specifically, the qModeL prior provides a pre-learned representation of the diffusion signal space to which the measured data belongs. We show that the pre-learned q-space prior along with a model-based iterative reconstruction that accommodate multi-band unaliasing, can efficiently reconstruct the in-plane- and MB-accelerated data. The power of joint reconstruction is maximally utilized by using an incoherent under-sampling pattern in the k-q domain. We tested the proposed method on single- and multi-shell data, with high/low angular resolution, high/low spatial resolution, healthy/abnormal tissues, and 3T/7T field strengths. Furthermore, the learning is extended to the spherical harmonic basis, to provide a rotational invariant learning framework. RESULTS: The qModeL joint reconstruction is shown to simultaneously unalias and jointly recover DWIs with reasonable accuracy in all the cases studied. The reconstruction error from 18-fold accelerated multi-shell datasets was <3%. The microstructural maps derived from the accelerated acquisitions also exhibit reasonable accuracy for both healthy and abnormal tissues. The deep learning (DL)-enabled reconstructions are comparable to those derived using traditional methods. CONCLUSION: qModeL enables the joint recovery of combined in-plane- and MB-accelerated dMRI utilizing DL.

DYNAMIC IMAGING USING DEEP BILINEAR UNSUPERVISED LEARNING (DEBLUR).

Bilinear models such as low-rank and compressed sensing, which decompose the dynamic data to spatial and temporal factors, are powerful and memory efficient tools for the recovery of dynamic MRI data. These methods rely on sparsity and energy compaction priors on the factors to regularize the recovery. Motivated by deep image prior, we introduce a novel bilinear model, whose factors are regularized using convolutional neural networks. To reduce the run time, we initialize the CNN parameters by pre-training them on pre-acquired data with longer acquistion time. Since fully sampled data is not available, pretraining is performed on undersampled data in an unsupervised fashion. We use sparsity regularization of the network parameters to minimize the overfitting of the network to measurement noise. Our experiments on on free-breathing and ungated cardiac CINE data acquired using a navigated golden-angle gradient-echo radial sequence show the ability of our method to provide reduced spatial blurring as compared to low-rank and SToRM reconstructions.

Recovery of surfaces and functions in high dimensions: sampling theory and links to neural networks.

Several imaging algorithms including patch-based image denoising, image time series recovery, and convolutional neural networks can be thought of as methods that exploit the manifold structure of signals. While the empirical performance of these algorithms is impressive, the understanding of recovery of the signals and functions that live on manifold is less understood. In this paper, we focus on the recovery of signals that live on a union of surfaces. In particular, we consider signals living on a union of smooth band-limited surfaces in high dimensions. We show that an exponential mapping transforms the data to a union of low-dimensional subspaces. Using this relation, we introduce a sampling theoretical framework for the recovery of smooth surfaces from few samples and the learning of functions living on smooth surfaces. The low-rank property of the features is used to determine the number of measurements needed to recover the surface. Moreover, the low-rank property of the features also provides an efficient approach, which resembles a neural network, for the local representation of multidimensional functions on the surface. The direct representation of such a function in high dimensions often suffers from the curse of dimensionality; the large number of parameters would translate to the need for extensive training data. The low-rank property of the features can significantly reduce the number of parameters, which makes the computational structure attractive for learning and inference from limited labeled training data.

DEEP GENERATIVE STORM MODEL FOR DYNAMIC IMAGING.

We introduce a novel generative smoothness regularization on manifolds (SToRM) model for the recovery of dynamic image data from highly undersampled measurements. The proposed generative framework represents the image time series as a smooth non-linear function of low-dimensional latent vectors that capture the cardiac and respiratory phases. The non-linear function is represented using a deep convolutional neural network (CNN). Unlike the popular CNN approaches that require extensive fully-sampled training data that is not available in this setting, the parameters of the CNN generator as well as the latent vectors are jointly estimated from the undersampled measurements using stochastic gradient descent. We penalize the norm of the gradient of the generator to encourage the learning of a smooth surface/manifold, while temporal gradients of the latent vectors are penalized to encourage the time series to be smooth. The main benefits of the proposed scheme are (a) the quite significant reduction in memory demand compared to the analysis based SToRM model, and (b) the spatial regularization brought in by the CNN model. We also introduce efficient progressive approaches to minimize the computational complexity of the algorithm.

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.

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.