Dynamic MRI Using SmooThness Regularization on Manifolds (SToRM)

Self-navigated subspace reconstruction for real-time MR imaging of the vocal tract

PURPOSE

Real-time MRI offers a continuous and dynamic view of the object being imaged. Researchers have applied real-time MRI to speech production, which allows for the visualization of the vocal tract during speech.

METHODS

This study proposed applying self-navigated subspace reconstruction for real-time vocal tract imaging. We performed experiments on a clinical 3 T MRI using standard RF coils and rapid acquisition. Additionally, 1000 frames were compressed during reconstruction to a few principal components, and iterative low-rank approximation was performed on compressed k-space, in conjunction with the orthogonal basis estimation for the subspace.

RESULTS

The simulation study involving a 32-time acceleration showed that the proposed method produced a reasonably small root mean square error (RMSE) of 0.159, compared to 0.278 for sliding window reconstruction, 0.2527 for SToRM and 0.294 for low-rank reconstruction. The study also presented in vivo images of a typical sagittal image with a temporal resolution of 7 ms/frame or 21 ms/frame for the three-slice scan.

CONCLUSION

Our study presented a subspace reconstruction technique that does not require a navigator echo, which can be used for real-time MRI, particularly in speech imaging applications.

Technical Note: Swing golden angle - A navigator-interleaved golden angle trajectory with eddy current suppression - Application in free-running cardiac MRI

BACKGROUND

Golden angle (GA) radial trajectory is advantageous for dynamic magnetic resonance imaging (MRI). Recently, several advanced algorithms have been developed based on navigator-interleaved GA trajectory to realize free-running cardiac MRI. However, navigator-interleaved GA trajectory suffers from the eddy-current effect, which reduces the image quality.

PURPOSE

This work aims to integrate the navigator-interleaved GA trajectory with clinical cardiac MRI acquisition, with the minimum eddy-current artifacts. The ultimate goal is to realize a high-quality free-running cardiac imaging technique.

METHODS

In this paper, we propose a new "swing golden angle" (swingGA) radial profile order. SwingGA samples the k-space by rotating back and forth at the generalized golden ratio interval, with smoothly interleaved navigator readouts. The sampling efficiency and angle increment distributions were investigated by numerical simulations. Static phantom imaging experiments were conducted to evaluate the eddy current effect, compared with cartesian, golden angle radial (GA), and tiny golden angle (tGA) trajectories. Furthermore, 12 heart-healthy subjects (aged 21-25 years) were recruited for free-running cardiac imaging with different sampling trajectories. Dynamic images were reconstructed by a low-rank subspace-constrained algorithm. The image quality was evaluated by signal-to-noise-ratio and spectrum analysis in the heart region, and compared with traditional clinical cardiac MRI images.

RESULTS

SwingGA pattern achieves the highest sampling efficiency (mSE > 0.925) and the minimum azimuthal angle increment (mAD < 1.05). SwingGA can effectively suppress eddy currents in static phantom images, with the lowest normalized root mean square error (nRMSE) values among radial trajectories. For the in-vivo cardiac images, swingGA enjoys the highest SNR both in the blood pool and myocardium, and contains the minimum level of high-frequency artifacts. The free-running cardiac images have good consistency with traditional clinical cardiac MRI, and the swingGA sampling pattern achieves the best image quality among all sampling patterns.

CONCLUSIONS

The proposed swingGA sampling pattern can effectively improve the sampling efficiency and reduce the eddy currents for the navigator-interleaved GA sequence. SwingGA is a promising sampling pattern for free-running cardiac MRI.

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.

Motion-compensated image reconstruction for improved kidney function assessment using dynamic contrast-enhanced MRI

Accurately measuring renal function is crucial for pediatric patients with kidney conditions. Traditional methods have limitations, but dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) provides a safe and efficient approach for detailed anatomical evaluation and renal function assessment. However, motion artifacts during DCE-MRI can degrade image quality and introduce misalignments, leading to unreliable results. This study introduces a motion-compensated reconstruction technique for DCE-MRI data acquired using golden-angle radial sampling. Our proposed method achieves three key objectives: (1) identifying and removing corrupted data (outliers) using a Gaussian process model fitting with a k -space center navigator, (2) efficiently clustering the data into motion phases and performing interphase registration, and (3) utilizing a novel formulation of motion-compensated radial reconstruction. We applied the proposed motion correction (MoCo) method to DCE-MRI data affected by varying degrees of motion, including both respiratory and bulk motion. We compared the outcomes with those obtained from the conventional radial reconstruction. Our evaluation encompassed assessing the quality of images, concentration curves, and tracer kinetic model fitting, and estimating renal function. The proposed MoCo reconstruction improved the temporal signal-to-noise ratio for all subjects, with a 21.8% increase on average, while total variation values of the aorta, right, and left kidney concentration were improved for each subject, with 32.5%, 41.3%, and 42.9% increases on average, respectively. Furthermore, evaluation of tracer kinetic model fitting indicated that the median standard deviation of the estimated filtration rate (σ F T ), mean normalized root-mean-squared error (nRMSE), and chi-square goodness-of-fit of tracer kinetic model fit were decreased from 0.10 to 0.04, 0.27 to 0.24, and, 0.43 to 0.27, respectively. The proposed MoCo technique enabled more reliable renal function assessment and improved image quality for detailed anatomical evaluation in the case of bulk and respiratory motion during the acquisition of DCE-MRI.

Self-Supervised Deep Unrolled Reconstruction Using Regularization by Denoising

Deep learning methods have been successfully used in various computer vision tasks. Inspired by that success, deep learning has been explored in magnetic resonance imaging (MRI) reconstruction. In particular, integrating deep learning and model-based optimization methods has shown considerable advantages. However, a large amount of labeled training data is typically needed for high reconstruction quality, which is challenging for some MRI applications. In this paper, we propose a novel reconstruction method, named DURED-Net, that enables interpretable self-supervised learning for MR image reconstruction by combining a self-supervised denoising network and a plug-and-play method. We aim to boost the reconstruction performance of Noise2Noise in MR reconstruction by adding an explicit prior that utilizes imaging physics. Specifically, the leverage of a denoising network for MRI reconstruction is achieved using Regularization by Denoising (RED). Experiment results demonstrate that the proposed method requires a reduced amount of training data to achieve high reconstruction quality among the state-of-the-art approaches utilizing Noise2Noise.

The CALIPR framework for highly accelerated myelin water imaging with improved precision and sensitivity

Quantitative magnetic resonance imaging (MRI) techniques are powerful tools for the study of human tissue, but, in practice, their utility has been limited by lengthy acquisition times. Here, we introduce the Constrained, Adaptive, Low-dimensional, Intrinsically Precise Reconstruction (CALIPR) framework in the context of myelin water imaging (MWI); a quantitative MRI technique generally regarded as the most rigorous approach for noninvasive, in vivo measurement of myelin content. The CALIPR framework exploits data redundancy to recover high-quality images from a small fraction of an imaging dataset, which allowed MWI to be acquired with a previously unattainable sequence (fully sampled acquisition 2 hours:57 min:20 s) in 7 min:26 s (4.2% of the dataset, acceleration factor 23.9). CALIPR quantitative metrics had excellent precision (myelin water fraction mean coefficient of variation 3.2% for the brain and 3.0% for the spinal cord) and markedly increased sensitivity to demyelinating disease pathology compared to a current, widely used technique. The CALIPR framework facilitates drastically improved MWI and could be similarly transformative for other quantitative MRI applications.

Respiratory motion management using a single rapid MRI scan for a 0.35 T MRI-Linac system

BACKGROUND

MRI has a rapidly growing role in radiation therapy (RT) for treatment planning, real-time image guidance, and beam gating (e.g., MRI-Linac). Free-breathing 4D-MRI is desirable in respiratory motion management for therapy. Moreover, high-quality 3D-MRIs without motion artifacts are needed to delineate lesions. Existing MRI methods require multiple scans with lengthy acquisition times or are limited by low spatial resolution, contrast, and signal-to-noise ratio.

PURPOSE

We developed a novel method to obtain motion-resolved 4D-MRIs and motion-integrated 3D-MRI reconstruction using a single rapid (35-45 s scan on a 0.35 T MRI-Linac.

METHODS

Golden-angle radial stack-of-stars MRI scans were acquired from a respiratory motion phantom and 12 healthy volunteers (n = 12) on a 0.35 T MRI-Linac. A self-navigated method was employed to detect respiratory motion using 2000 (acquisition time = 5-7 min) and the first 200 spokes (acquisition time = 35-45 s). Multi-coil non-uniform fast Fourier transform (MCNUFFT), compressed sensing (CS), and deep-learning Phase2Phase (P2P) methods were employed to reconstruct motion-resolved 4D-MRI using 2000 spokes (MCNUFFT2000) and 200 spokes (CS200 and P2P200). Deformable motion vector fields (MVFs) were computed from the 4D-MRIs and used to reconstruct motion-corrected 3D-MRIs with the MOtion Transformation Integrated forward-Fourier (MOTIF) method. Image quality was evaluated quantitatively using the structural similarity index measure (SSIM) and the root mean square error (RMSE), and qualitatively in a blinded radiological review.

RESULTS

Evaluation using the respiratory motion phantom experiment showed that the proposed method reversed the effects of motion blurring and restored edge sharpness. In the human study, P2P200 had smaller inaccuracy in MVFs estimation than CS200. P2P200 had significantly greater SSIMs (p < 0.0001) and smaller RMSEs (p < 0.001) than CS200 in motion-resolved 4D-MRI and motion-corrected 3D-MRI. The radiological review found that MOTIF 3D-MRIs using MCNUFFT2000 exhibited the highest image quality (scoring > 8 out of 10), followed by P2P200 (scoring > 5 out of 10), and then motion-uncorrected (scoring < 3 out of 10) in sharpness, contrast, and artifact-freeness.

CONCLUSIONS

We have successfully demonstrated a method for respiratory motion management for MRI-guided RT. The method integrated self-navigated respiratory motion detection, deep-learning P2P 4D-MRI reconstruction, and a motion integrated reconstruction (MOTIF) for 3D-MRI using a single rapid MRI scan (35-45 s) on a 0.35 T MRI-Linac system.

Evaluation of kernel low-rank compressed sensing in preclinical diffusion magnetic resonance imaging

Compressed sensing (CS) is widely used to accelerate clinical diffusion MRI acquisitions, but it is not widely used in preclinical settings yet. In this study, we optimized and compared several CS reconstruction methods for diffusion imaging. Different undersampling patterns and two reconstruction approaches were evaluated: conventional CS, based on Berkeley Advanced Reconstruction Toolbox (BART-CS) toolbox, and a new kernel low-rank (KLR)-CS, based on kernel principal component analysis and low-resolution-phase (LRP) maps. 3D CS acquisitions were performed at 9.4T using a 4-element cryocoil on mice (wild type and a MAP6 knockout). Comparison metrics were error and structural similarity index measure (SSIM) on fractional anisotropy (FA) and mean diffusivity (MD), as well as reconstructions of the anterior commissure and fornix. Acceleration factors (AF) up to 6 were considered. In the case of retrospective undersampling, the proposed KLR-CS outperformed BART-CS up to AF = 6 for FA and MD maps and tractography. For instance, for AF = 4, the maximum errors were, respectively, 8.0% for BART-CS and 4.9% for KLR-CS, considering both FA and MD in the corpus callosum. Regarding undersampled acquisitions, these maximum errors became, respectively, 10.5% for BART-CS and 7.0% for KLR-CS. This difference between simulations and acquisitions arose mainly from repetition noise, but also from differences in resonance frequency drift, signal-to-noise ratio, and in reconstruction noise. Despite this increased error, fully sampled and AF = 2 yielded comparable results for FA, MD and tractography, and AF = 4 showed minor faults. Altogether, KLR-CS based on LRP maps seems a robust approach to accelerate preclinical diffusion MRI and thereby limit the effect of the frequency drift.

Joint spectral quantification of MR spectroscopic imaging using linear tangent space alignment-based manifold learning

PURPOSE

To develop a manifold learning-based method that leverages the intrinsic low-dimensional structure of MR Spectroscopic Imaging (MRSI) signals for joint spectral quantification.

METHODS

A linear tangent space alignment (LTSA) model was proposed to represent MRSI signals. In the proposed model, the signals of each metabolite were represented using a subspace model and the local coordinates of the subspaces were aligned to the global coordinates of the underlying low-dimensional manifold via linear transform. With the basis functions of the subspaces predetermined via quantum mechanics simulations, the global coordinates and the matrices for the local-to-global coordinate alignment were estimated by fitting the proposed LTSA model to noisy MRSI data with a spatial smoothness constraint on the global coordinates and a sparsity constraint on the matrices.

RESULTS

The performance of the proposed method was validated using numerical simulation data and in vivo proton-MRSI experimental data acquired on healthy volunteers at 3T. The results of the proposed method were compared with the QUEST method and the subspace-based method. In all the compared cases, the proposed method achieved superior performance over the QUEST and the subspace-based methods both qualitatively in terms of noise and artifacts in the estimated metabolite concentration maps, and quantitatively in terms of spectral quantification accuracy measured by normalized root mean square errors.

CONCLUSION

Joint spectral quantification using linear tangent space alignment-based manifold learning improves the accuracy of MRSI spectral quantification.

Deep Learning-Based Reconstruction for Cardiac MRI: A Review

Cardiac magnetic resonance (CMR) is an essential clinical tool for the assessment of cardiovascular disease. Deep learning (DL) has recently revolutionized the field through image reconstruction techniques that allow unprecedented data undersampling rates. These fast acquisitions have the potential to considerably impact the diagnosis and treatment of cardiovascular disease. Herein, we provide a comprehensive review of DL-based reconstruction methods for CMR. We place special emphasis on state-of-the-art unrolled networks, which are heavily based on a conventional image reconstruction framework. We review the main DL-based methods and connect them to the relevant conventional reconstruction theory. Next, we review several methods developed to tackle specific challenges that arise from the characteristics of CMR data. Then, we focus on DL-based methods developed for specific CMR applications, including flow imaging, late gadolinium enhancement, and quantitative tissue characterization. Finally, we discuss the pitfalls and future outlook of DL-based reconstructions in CMR, focusing on the robustness, interpretability, clinical deployment, and potential for new methods.

Manifold Learning via Linear Tangent Space Alignment (LTSA) for Accelerated Dynamic MRI With Sparse Sampling

The spatial resolution and temporal frame-rate of dynamic magnetic resonance imaging (MRI) can be improved by reconstructing images from sparsely sampled k -space data with mathematical modeling of the underlying spatiotemporal signals. These models include sparsity models, linear subspace models, and non-linear manifold models. This work presents a novel linear tangent space alignment (LTSA) model-based framework that exploits the intrinsic low-dimensional manifold structure of dynamic images for accelerated dynamic MRI. The performance of the proposed method was evaluated and compared to state-of-the-art methods using numerical simulation studies as well as 2D and 3D in vivo cardiac imaging experiments. The proposed method achieved the best performance in image reconstruction among all the compared methods. The proposed method could prove useful for accelerating many MRI applications, including dynamic MRI, multi-parametric MRI, and MR spectroscopic imaging.

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.

MR image reconstruction from undersampled data for image-guided radiation therapy using a patient-specific deep manifold image prior

Introduction

Recent advancements in radiotherapy (RT) have allowed for the integration of a Magnetic Resonance (MR) imaging scanner with a medical linear accelerator to use MR images for image guidance to position tumors against the treatment beam. Undersampling in MR acquisition is desired to accelerate the imaging process, but unavoidably deteriorates the reconstructed image quality. In RT, a high-quality MR image of a patient is available for treatment planning. In light of this unique clinical scenario, we proposed to exploit the patient-specific image prior to facilitate high-quality MR image reconstruction.

Methods

Utilizing the planning MR image, we established a deep auto-encoder to form a manifold of image patches of the patient. The trained manifold was then incorporated as a regularization to restore MR images of the same patient from undersampled data. We performed a simulation study using a patient case, a real patient study with three liver cancer patient cases, and a phantom experimental study using data acquired on an in-house small animal MR scanner. We compared the performance of the proposed method with those of the Fourier transform method, a tight-frame based Compressive Sensing method, and a deep learning method with a patient-generic manifold as the image prior.

Results

In the simulation study with 12.5% radial undersampling and 15% increase in noise, our method improved peak-signal-to-noise ratio by 4.46dB and structural similarity index measure by 28% compared to the patient-generic manifold method. In the experimental study, our method outperformed others by producing reconstructions of visually improved image quality.

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.

NC-PDNet: A Density-Compensated Unrolled Network for 2D and 3D Non-Cartesian MRI Reconstruction

Deep Learning has become a very promising avenue for magnetic resonance image (MRI) reconstruction. In this work, we explore the potential of unrolled networks for non-Cartesian acquisition settings. We design the NC-PDNet (Non-Cartesian Primal Dual Netwok), the first density-compensated (DCp) unrolled neural network, and validate the need for its key components via an ablation study. Moreover, we conduct some generalizability experiments to test this network in out-of-distribution settings, for example training on knee data and validating on brain data. The results show that NC-PDNet outperforms baseline (U-Net, Deep image prior) models both visually and quantitatively in all settings. In particular, in the 2D multi-coil acquisition scenario, the NC-PDNet provides up to a 1.2 dB improvement in peak signal-to-noise ratio (PSNR) over baseline networks, while also allowing a gain of at least 1dB in PSNR in generalization settings. We provide the open-source implementation of NC-PDNet, and in particular the Non-uniform Fourier Transform in TensorFlow, tested on 2D multi-coil and 3D single-coil k-space data.

Accelerating MR Parameter Mapping Using Nonlinear Compressive Manifold Learning and Regularized Pre-Imaging

In this study, we presented a novel method to reconstruct the MR parametric maps from highly undersampled k-space data. Specifically, we utilized a nonlinear model to sparsely represent the unknown MR parameter-weighted images in high-dimensional feature space. Each image at a specific time point is assumed to belong to a low-dimensional manifold which is learned from training images created based on the parametric model. The final reconstruction is carried out by venturing the sparse representation of the images in the feature space back to the input space, using the pre-imaging technique. Particularly, among an infinite number of solutions that satisfy the data consistency, the one that is closest to the manifold is selected as the desired solution. The underlying optimization problem is solved using kernel trick, sparse coding, and split Bregman iteration algorithm. In addition, both spatial and temporal regularizations were utilized to further improve the reconstruction quality. The proposed method was validated on both phantom and in vivo human brain T2 mapping data. Results showed the proposed method was superior to the conventional linear model-based reconstruction methods, in terms of artifact removal and quantitative estimate accuracy. The proposed method could be potentially beneficial for quantitative MR applications.

Time-Dependent Deep Image Prior for Dynamic MRI

We propose a novel unsupervised deep-learning-based algorithm for dynamic magnetic resonance imaging (MRI) reconstruction. Dynamic MRI requires rapid data acquisition for the study of moving organs such as the heart. We introduce a generalized version of the deep-image-prior approach, which optimizes the weights of a reconstruction network to fit a sequence of sparsely acquired dynamic MRI measurements. Our method needs neither prior training nor additional data. In particular, for cardiac images, it does not require the marking of heartbeats or the reordering of spokes. The key ingredients of our method are threefold: 1) a fixed low-dimensional manifold that encodes the temporal variations of images; 2) a network that maps the manifold into a more expressive latent space; and 3) a convolutional neural network that generates a dynamic series of MRI images from the latent variables and that favors their consistency with the measurements in k -space. Our method outperforms the state-of-the-art methods quantitatively and qualitatively in both retrospective and real fetal cardiac datasets. To the best of our knowledge, this is the first unsupervised deep-learning-based method that can reconstruct the continuous variation of dynamic MRI sequences with high spatial resolution.

Learning Data Consistency and its Application to Dynamic MR Imaging

Magnetic resonance (MR) image reconstruction from undersampled k-space data can be formulated as a minimization problem involving data consistency and image prior. Existing deep learning (DL)-based methods for MR reconstruction employ deep networks to exploit the prior information and integrate the prior knowledge into the reconstruction under the explicit constraint of data consistency, without considering the real distribution of the noise. In this work, we propose a new DL-based approach termed Learned DC that implicitly learns the data consistency with deep networks, corresponding to the actual probability distribution of system noise. The data consistency term and the prior knowledge are both embedded in the weights of the networks, which provides an utterly implicit manner of learning reconstruction model. We evaluated the proposed approach with highly undersampled dynamic data, including the dynamic cardiac cine data with up to 24-fold acceleration and dynamic rectum data with the acceleration factor equal to the number of phases. Experimental results demonstrate the superior performance of the Learned DC both quantitatively and qualitatively than the state-of-the-art.

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.

qModeL: A plug-and-play model-based reconstruction for highly accelerated multi-shot diffusion MRI using learned priors

PURPOSE

To introduce a joint reconstruction method for highly undersampled multi-shot diffusion weighted (msDW) scans.

METHODS

Multi-shot EPI methods enable higher spatial resolution for diffusion MRI, but at the expense of long scan-time. Highly accelerated msDW scans are needed to enable their utilization in advanced microstructure studies, which require high q-space coverage. Previously, joint k-q undersampling methods coupled with compressed sensing were shown to enable very high acceleration factors. However, the reconstruction of this data using sparsity priors is challenging and is not suited for multi-shell data. We propose a new reconstruction that recovers images from the combined k-q data jointly. The proposed qModeL reconstruction brings together the advantages of model-based iterative reconstruction and machine learning, extending the idea of plug-and-play algorithms. Specifically, qModeL works by prelearning the signal manifold corresponding to the diffusion measurement space using deep learning. The prelearned manifold prior is incorporated into a model-based reconstruction to provide a voxel-wise regularization along the q-dimension during the joint recovery. Notably, the learning does not require in vivo training data and is derived exclusively from biophysical modeling. Additionally, a plug-and-play total variation denoising provides regularization along the spatial dimension. The proposed framework is tested on k-q undersampled single-shell and multi-shell msDW acquisition at various acceleration factors.

RESULTS

The qModeL joint reconstruction is shown to recover DWIs from 8-fold accelerated msDW acquisitions with error less than 5% for both single-shell and multi-shell data. Advanced microstructural analysis performed using the undersampled reconstruction also report reasonable accuracy.

CONCLUSION

qModeL enables the joint recovery of highly accelerated multi-shot dMRI utilizing learning-based priors. The bio-physically driven approach enables the use of accelerated multi-shot imaging for multi-shell sampling and advanced microstructure studies.

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.

Free-Breathing and Ungated Dynamic MRI Using Navigator-Less Spiral SToRM

We introduce a kernel low-rank algorithm to recover free-breathing and ungated dynamic MRI from spiral acquisitions without explicit k-space navigators. It is often challenging for low-rank methods to recover free-breathing and ungated images from undersampled measurements; extensive cardiac and respiratory motion often results in the Casorati matrix not being sufficiently low-rank. Therefore, we exploit the non-linear structure of the dynamic data, which gives the low-rank kernel matrix. Unlike prior work that rely on navigators to estimate the manifold structure, we propose a kernel low-rank matrix completion method to directly fill in the missing k-space data from variable density spiral acquisitions. We validate the proposed scheme using simulated data and in-vivo data. Our results show that the proposed scheme provides improved reconstructions compared to the classical methods such as low-rank and XD-GRASP. The comparison with breath-held cine data shows that the quantitative metrics agree, whereas the image quality is marginally lower.

Bulk motion-compensated DCE-MRI for functional imaging of kidneys in newborns

BACKGROUND

Evaluation of kidney function in newborns with hydronephrosis is important for clinical decisions. Dynamic contrast-enhanced (DCE) MRI can provide the necessary anatomical and functional information. Golden angle dynamic radial acquisition and compressed sensing reconstruction provides sufficient spatiotemporal resolution to achieve accurate parameter estimation for functional imaging of kidneys. However, bulk motion during imaging (rigid or nonrigid movement of the subject resulting in signal dropout) remains an unresolved challenge.

PURPOSE

To evaluate a motion-compensated (MoCo) DCE-MRI technique for robust evaluation of kidney function in newborns. Our method includes: 1) motion detection, 2) motion-robust image reconstruction, 3) joint realignment of the volumes, and 4) tracer-kinetic (TK) model fitting to evaluate kidney function parameters.

STUDY TYPE

Retrospective.

SUBJECTS

Eleven newborn patients (ages <6 months, 6 female).

FIELD STRENGTH/SEQUENCE

3T; dynamic "stack-of-stars" 3D fast low-angle shot (FLASH) sequence using a multichannel body-matrix coil.

ASSESSMENT

We evaluated the proposed technique in terms of the signal-to-noise ratio (SNR) of the reconstructed images, the presence of discontinuities in the contrast agent concentration time curves due to motion with a total variation (TV) metric and the goodness of fit of the TK model, and the standard variation of its parameters.

STATISTICAL TESTS

We used a paired t-test to compare the MoCo and no-MoCo results.

RESULTS

The proposed MoCo method successfully detected motion and improved the SNR by 3.3 (P = 0.012) and decreased TV by 0.374 (P = 0.017) across all subjects. Moreover, it decreased nRMSE of the TK model fit for the subjects with less than five isolated bulk motion events in 6 minutes (mean 1.53, P = 0.043), but not for the subjects with more frequent events or no motion (P = 0.745 and P = 0.683).

DATA CONCLUSION

Our results indicate that the proposed MoCo technique improves the image quality and accuracy of the TK model fit for subjects who present isolated bulk motion events.

LEVEL OF EVIDENCE

3 Technical Efficacy Stage: 1 J. Magn. Reson. Imaging 2020;52:207-216.

Multi-scale Unrolled Deep Learning Framework for Accelerated Magnetic Resonance Imaging

Accelerating data acquisition in magnetic resonance imaging (MRI) has been of perennial interest due to its prohibitively slow data acquisition process. Recent trends in accelerating MRI employ data-centric deep learning frameworks due to its fast inference time and 'one-parameter-fit-all' principle unlike in traditional model-based acceleration techniques. Unrolled deep learning framework that combines the deep priors and model knowledge are robust compared to naive deep learning based framework. In this paper, we propose a novel multi-scale unrolled deep learning framework which learns deep image priors through multi-scale CNN and is combined with unrolled framework to enforce data-consistency and model knowledge. Essentially, this framework combines the best of both learning paradigms:model-based and data-centric learning paradigms. Proposed method is verified using several experiments on numerous data sets.

Bi-Linear Modeling of Data Manifolds for Dynamic-MRI Recovery

This paper puts forth a novel bi-linear modeling framework for data recovery via manifold-learning and sparse-approximation arguments and considers its application to dynamic magnetic-resonance imaging (dMRI). Each temporal-domain MR image is viewed as a point that lies onto or close to a smooth manifold, and landmark points are identified to describe the point cloud concisely. To facilitate computations, a dimensionality reduction module generates low-dimensional/compressed renditions of the landmark points. Recovery of high-fidelity MRI data is realized by solving a non-convex minimization task for the linear decompression operator and affine combinations of landmark points which locally approximate the latent manifold geometry. An algorithm with guaranteed convergence to stationary solutions of the non-convex minimization task is also provided. The aforementioned framework exploits the underlying spatio-temporal patterns and geometry of the acquired data without any prior training on external data or information. Extensive numerical results on simulated as well as real cardiac-cine MRI data illustrate noteworthy improvements of the advocated machine-learning framework over state-of-the-art reconstruction techniques.

From Compressed-Sensing to Artificial Intelligence-Based Cardiac MRI Reconstruction

Cardiac magnetic resonance (CMR) imaging is an important tool for the non-invasive assessment of cardiovascular disease. However, CMR suffers from long acquisition times due to the need of obtaining images with high temporal and spatial resolution, different contrasts, and/or whole-heart coverage. In addition, both cardiac and respiratory-induced motion of the heart during the acquisition need to be accounted for, further increasing the scan time. Several undersampling reconstruction techniques have been proposed during the last decades to speed up CMR acquisition. These techniques rely on acquiring less data than needed and estimating the non-acquired data exploiting some sort of prior information. Parallel imaging and compressed sensing undersampling reconstruction techniques have revolutionized the field, enabling 2- to 3-fold scan time accelerations to become standard in clinical practice. Recent scientific advances in CMR reconstruction hinge on the thriving field of artificial intelligence. Machine learning reconstruction approaches have been recently proposed to learn the non-linear optimization process employed in CMR reconstruction. Unlike analytical methods for which the reconstruction problem is explicitly defined into the optimization process, machine learning techniques make use of large data sets to learn the key reconstruction parameters and priors. In particular, deep learning techniques promise to use deep neural networks (DNN) to learn the reconstruction process from existing datasets in advance, providing a fast and efficient reconstruction that can be applied to all newly acquired data. However, before machine learning and DNN can realize their full potentials and enter widespread clinical routine for CMR image reconstruction, there are several technical hurdles that need to be addressed. In this article, we provide an overview of the recent developments in the area of artificial intelligence for CMR image reconstruction. The underlying assumptions of established techniques such as compressed sensing and low-rank reconstruction are briefly summarized, while a greater focus is given to recent advances in dictionary learning and deep learning based CMR reconstruction. In particular, approaches that exploit neural networks as implicit or explicit priors are discussed for 2D dynamic cardiac imaging and 3D whole-heart CMR imaging. Current limitations, challenges, and potential future directions of these techniques are also discussed.

Deep Magnetic Resonance Image Reconstruction: Inverse Problems Meet Neural Networks

Image reconstruction from undersampled k-space data has been playing an important role in fast MRI. Recently, deep learning has demonstrated tremendous success in various fields and has also shown potential in significantly accelerating MRI reconstruction with fewer measurements. This article provides an overview of the deep learning-based image reconstruction methods for MRI. Two types of deep learning-based approaches are reviewed: those based on unrolled algorithms and those which are not. The main structure of both approaches are explained, respectively. Several signal processing issues for maximizing the potential of deep reconstruction in fast MRI are discussed. The discussion may facilitate further development of the networks and the analysis of performance from a theoretical point of view.

Deep learning within a priori temporal feature spaces for large-scale dynamic MR image reconstruction: Application to 5-D cardiac MR Multitasking

High spatiotemporal resolution dynamic magnetic resonance imaging (MRI) is a powerful clinical tool for imaging moving structures as well as to reveal and quantify other physical and physiological dynamics. The low speed of MRI necessitates acceleration methods such as deep learning reconstruction from under-sampled data. However, the massive size of many dynamic MRI problems prevents deep learning networks from directly exploiting global temporal relationships. In this work, we show that by applying deep neural networks inside a priori calculated temporal feature spaces, we enable deep learning reconstruction with global temporal modeling even for image sequences with >40,000 frames. One proposed variation of our approach using dilated multi-level Densely Connected Network (mDCN) speeds up feature space coordinate calculation by 3000x compared to conventional iterative methods, from 20 minutes to 0.39 seconds. Thus, the combination of low-rank tensor and deep learning models not only makes large-scale dynamic MRI feasible but also practical for routine clinical application.

Free-Breathing & Ungated Cardiac MRI Using Iterative SToRM (i-SToRM)

We introduce a local manifold regularization approach to recover dynamic MRI data from highly undersampled measurements. The proposed scheme relies on the manifold structure of local image patches at the same spatial location in a free-breathing cardiac MRI dataset; this approach is a generalization of the SmooThness Regularization on Manifolds (SToRM) scheme that exploits the global manifold structure of images in the dataset. Since the manifold structure of the patches varies depending on the spatial location and is often considerably simpler than the global one, this approach significantly reduces the data demand, facilitating the recovery from shorter scans. Since the navigator-based estimation of manifold structure pursued in SToRM is not feasible in this setting, a reformulation of SToRM is introduced. Specifically, the regularization term of the cost function involves the sum of robust distances between images sub-patches in the dataset. The optimization algorithm alternates between updating the images and estimating the manifold structure of the image patches. The utility of the proposed scheme is demonstrated in the context of in-vivo prospective free-breathing cardiac CINE MRI imaging with multichannel acquisitions and simulated phantoms. The new framework facilitates a reduction in scan time, as compared to the SToRM strategy.

Reconstruction techniques for cardiac cine MRI

The present survey describes the state-of-the-art techniques for dynamic cardiac magnetic resonance image reconstruction. Additionally, clinical relevance, main challenges, and future trends of this image modality are outlined. Thus, this paper aims to provide a general vision about cine MRI as the standard procedure in functional evaluation of the heart, focusing on technical methodologies.

Real-time three-dimensional MRI for the assessment of dynamic carpal instability

Background

Carpal instability is defined as a condition where wrist motion and/or loading creates mechanical dysfunction, resulting in weakness, pain and decreased function. When conventional methods do not identify the instability patterns, yet clinical signs of instability exist, the diagnosis of dynamic instability is often suggested to describe carpal derangement manifested only during the wrist’s active motion or stress. We addressed the question: can advanced MRI techniques provide quantitative means to evaluate dynamic carpal instability and supplement standard static MRI acquisition? Our objectives were to (i) develop a real-time, three-dimensional MRI method to image the carpal joints during their active, uninterrupted motion; and (ii) demonstrate feasibility of the method for assessing metrics relevant to dynamic carpal instability, thus overcoming limitations of standard MRI.

Methods

Twenty wrists (bilateral wrists of ten healthy participants) were scanned during radial-ulnar deviation and clenched-fist maneuvers. Images resulting from two real-time MRI pulse sequences, four sparse data-acquisition schemes, and three constrained image reconstruction techniques were compared. Image quality was assessed via blinded scoring by three radiologists and quantitative imaging metrics.

Results

Real-time MRI data-acquisition employing sparse radial sampling with a gradient-recalled-echo acquisition and constrained iterative reconstruction appeared to provide a practical tradeoff between imaging speed (temporal resolution up to 135 ms per slice) and image quality. The method effectively reduced streaking artifacts arising from data undersampling and enabled the derivation of quantitative measures pertinent to evaluating dynamic carpal instability.

Conclusion

This study demonstrates that real-time, three-dimensional MRI of the moving wrist is feasible and may be useful for the evaluation of dynamic carpal instability.

Manifold recovery using kernel low-rank regularization: application to dynamic imaging

We introduce a novel kernel low-rank algorithm to recover free-breathing and ungated dynamic MRI data from highly undersampled measurements. The image frames in the free breathing and ungated dataset are assumed to be points on a bandlimited manifold. We show that the non-linear features of these images satisfy annihilation conditions, which implies that the kernel matrix derived from the dataset is low-rank. We penalize the nuclear norm of the feature matrix to recover the images from highly undersampled measurements. The regularized optimization problem is solved using an iterative reweighted least squares (IRLS) algorithm, which alternates between the update of the Laplacian matrix of the manifold and the recovery of the signals from the noisy measurements. To improve computational efficiency, we use a two step algorithm using navigator measurements. Specifically, the Laplacian matrix is estimated from the navigators using the IRLS scheme, followed by the recovery of the images using a quadratic optimization. We show the relation of this two step algorithm with our recent SToRM approach, thus reconciling SToRM and manifold regularization methods with algorithms that rely on explicit lifting of data to a high dimensional space. The IRLS based estimation of the Laplacian matrix is a systematic and noise-robust alternative to current heuristic strategies based on exponential maps. We also approximate the Laplacian matrix using a few eigen vectors, which results in a fast and memory efficient algorithm. The proposed scheme is demonstrated on several patients with different breathing patterns and cardiac rates.

Dynamic MRI using model-based deep learning and SToRM priors: MoDL-SToRM

PURPOSE

To introduce a novel framework to combine deep-learned priors along with complementary image regularization penalties to reconstruct free breathing & ungated cardiac MRI data from highly undersampled multi-channel measurements.

METHODS

Image recovery is formulated as an optimization problem, where the cost function is the sum of data consistency term, convolutional neural network (CNN) denoising prior, and SmooThness regularization on manifolds (SToRM) prior that exploits the manifold structure of images in the dataset. An iterative algorithm, which alternates between denoizing of the image data using CNN and SToRM, and conjugate gradients (CG) step that minimizes the data consistency cost is introduced. Unrolling the iterative algorithm yields a deep network, which is trained using exemplar data.

RESULTS

The experimental results demonstrate that the proposed framework can offer fast recovery of free breathing and ungated cardiac MRI data from less than 8.2s of acquisition time per slice. The reconstructions are comparable in image quality to SToRM reconstructions from 42s of acquisition time, offering a fivefold reduction in scan time.

CONCLUSIONS

The results show the benefit in combining deep learned CNN priors with complementary image regularization penalties. Specifically, this work demonstrates the benefit in combining the CNN prior that exploits local and population generalizable redundancies together with SToRM, which capitalizes on patient-specific information including cardiac and respiratory patterns. The synergistic combination is facilitated by the proposed framework.

MoDL: Model-Based Deep Learning Architecture for Inverse Problems

We introduce a model-based image reconstruction framework with a convolution neural network (CNN)-based regularization prior. The proposed formulation provides a systematic approach for deriving deep architectures for inverse problems with the arbitrary structure. Since the forward model is explicitly accounted for, a smaller network with fewer parameters is sufficient to capture the image information compared to direct inversion approaches. Thus, reducing the demand for training data and training time. Since we rely on end-to-end training with weight sharing across iterations, the CNN weights are customized to the forward model, thus offering improved performance over approaches that rely on pre-trained denoisers. Our experiments show that the decoupling of the number of iterations from the network complexity offered by this approach provides benefits, including lower demand for training data, reduced risk of overfitting, and implementations with significantly reduced memory footprint. We propose to enforce data-consistency by using numerical optimization blocks, such as conjugate gradients algorithm within the network. This approach offers faster convergence per iteration, compared to methods that rely on proximal gradients steps to enforce data consistency. Our experiments show that the faster convergence translates to improved performance, primarily when the available GPU memory restricts the number of iterations.

Content-aware compressive magnetic resonance image reconstruction

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

MODEL-BASED FREE-BREATHING CARDIAC MRI RECONSTRUCTION USING DEEP LEARNED & STORM PRIORS: MODL-STORM

We introduce a model-based reconstruction framework with deep learned (DL) and smoothness regularization on manifolds (STORM) priors to recover free breathing and ungated (FBU) cardiac MRI from highly undersampled measurements. The DL priors enable us to exploit the local correlations, while the STORM prior enables us to make use of the extensive non-local similarities that are subject dependent. We introduce a novel model-based formulation that allows the seamless integration of deep learning methods with available prior information, which current deep learning algorithms are not capable of. The experimental results demonstrate the preliminary potential of this work in accelerating FBU cardiac MRI.

RECOVERY OF POINT CLOUDS ON SURFACES: APPLICATION TO IMAGE RECONSTRUCTION

We introduce a framework for the recovery of points on a smooth surface in high-dimensional space, with application to dynamic imaging. We assume the surface to be the zero-level set of a bandlimited function. We show that the exponential maps of the points on the surface satisfy annihilation relations, implying that they lie in a finite dimensional subspace. We rely on nuclear norm minimization of the maps to recover the points from noisy and undersampled measurements. Since this direct approach suffers from the curse of dimensionality, we introduce an iterative reweighted algorithm that uses the "kernel trick". The resulting algorithm has similarities to iterative algorithms used in graph signal processing (GSP); this framework can be seen as a continuous domain alternative to discrete GSP theory. The use of the algorithm in recovering free breathing and ungated cardiac data shows the potential of this framework in practical applications.

RECOVERY OF NOISY POINTS ON BANDLIMITED SURFACES: KERNEL METHODS RE-EXPLAINED

We introduce a continuous domain framework for the recovery of points on a surface in high dimensional space, represented as the zero-level set of a bandlimited function. We show that the exponential maps of the points on the surface satisfy annihilation relations, implying that they lie in a finite dimensional subspace. The subspace properties are used to derive sampling conditions, which will guarantee the perfect recovery of the surface from finite number of points. We rely on nuclear norm minimization to exploit the low-rank structure of the maps to recover the points from noisy measurements. Since the direct estimation of the surface is computationally prohibitive in very high dimensions, we propose an iterative reweighted algorithm using the "kernel trick". The iterative algorithm reveals deep links to Laplacian based algorithms widely used in graph signal processing; the theory and the sampling conditions can serve as a basis for discrete-continuous domain processing of signals on a graph.

MLS: Joint Manifold-Learning and Sparsity-Aware Framework for Highly Accelerated Dynamic Magnetic Resonance Imaging

Manifold-based models have been recently exploited for accelerating dynamic magnetic resonance imaging (dMRI). While manifold-based models have shown to be more efficient than conventional low-rank approaches, joint low-rank and sparsity-aware modeling still appears to be very efficient due to the inherent sparsity within dMR images. In this paper, we propose a joint manifold-learning and sparsity-aware framework for dMRI. The proposed method establishes a link between the recently developed manifold models and conventional sparsity-aware models. Dynamic MR images are modeled as points located on or close to a smooth manifold, and a novel data-driven manifold-learning approach, which preserves affine relation among images, is used to learn the low-dimensional embedding of the dynamic images. The temporal basis learnt from such an approach efficiently captures the inherent periodicity of dynamic images and hence sparsity along temporal direction is enforced during reconstruction. The proposed framework is validated by extensive numerical tests on phantom and in-vivo data sets.

CLUSTERING OF DATA WITH MISSING ENTRIES

The analysis of large datasets is often complicated by the presence of missing entries, mainly because most of the current machine learning algorithms are designed to work with full data. The main focus of this work is to introduce a clustering algorithm, that will provide good clustering even in the presence of missing data. The proposed technique solves an ℓ ₀ fusion penalty based optimization problem to recover the clusters. We theoretically analyze the conditions needed for the successful recovery of the clusters. We also propose an algorithm to solve a relaxation of this problem using saturating non-convex fusion penalties. The method is demonstrated on simulated and real datasets, and is observed to perform well in the presence of large fractions of missing entries.

Bi-Linear Modeling of Manifold-Data Geometry for Dynamic-MRI Recovery

This paper establishes a modeling framework for data located onto or close to (unknown) smooth manifolds, embedded in Euclidean spaces, and considers its application to dynamic magnetic resonance imaging (dMRI). The framework comprises several modules: First, a set of landmark points is identified to describe concisely a data cloud formed by highly under-sampled dMRI data, and second, low-dimensional renditions of the landmark points are computed. Searching for the linear operator that decompresses low-dimensional data to high-dimensional ones, and for those combinations of landmark points which approximate the manifold data by affine patches, leads to a bi-linear model of the dMRI data, cognizant of the intrinsic data geometry. Preliminary numerical tests on synthetically generated dMRI phantoms, and comparisons with state-of-the-art reconstruction techniques, underline the rich potential of the proposed method for the recovery of highly under-sampled dMRI data.

A Kernel-Based Low-Rank (KLR) Model for Low-Dimensional Manifold Recovery in Highly Accelerated Dynamic MRI

While many low rank and sparsity-based approaches have been developed for accelerated dynamic magnetic resonance imaging (dMRI), they all use low rankness or sparsity in input space, overlooking the intrinsic nonlinear correlation in most dMRI data. In this paper, we propose a kernel-based framework to allow nonlinear manifold models in reconstruction from sub-Nyquist data. Within this framework, many existing algorithms can be extended to kernel framework with nonlinear models. In particular, we have developed a novel algorithm with a kernel-based low-rank model generalizing the conventional low rank formulation. The algorithm consists of manifold learning using kernel, low rank enforcement in feature space, and preimaging with data consistency. Extensive simulation and experiment results show that the proposed method surpasses the conventional low-rank-modeled approaches for dMRI.

M-MRI: A Manifold-based Framework to Highly Accelerated Dynamic Magnetic Resonance Imaging

High-dimensional signals, including dynamic magnetic resonance (dMR) images, often lie on low dimensional manifold. While many current dynamic magnetic resonance imaging (dMRI) reconstruction methods rely on priors which promote low-rank and sparsity, this paper proposes a novel manifold-based framework, we term M-MRI, for dMRI reconstruction from highly undersampled k-space data. Images in dMRI are modeled as points on or close to a smooth manifold, and the underlying manifold geometry is learned through training data, called "navigator" signals. Moreover, low-dimensional embeddings which preserve the learned manifold geometry and effect concise data representations are computed. Capitalizing on the learned manifold geometry, two regularization loss functions are proposed to reconstruct dMR images from highly undersampled k-space data. The advocated framework is validated using extensive numerical tests on phantom and in-vivo data sets.

High-Resolution Self-Gated Dynamic Abdominal MRI Using Manifold Alignment

We present a novel retrospective self-gating method based on manifold alignment (MA), which enables reconstruction of free breathing, high spatial, and temporal resolution abdominal magnetic resonance imaging sequences. Based on a radial golden-angle acquisition trajectory, our method enables a multidimensional self-gating signal to be extracted from the k -space data for more accurate motion representation. The k -space radial profiles are evenly divided into a number of overlapping groups based on their radial angles. MA is then used to simultaneously learn and align the low dimensional manifolds of all groups, and embed them into a common manifold. In the manifold, k -space profiles that represent similar respiratory positions are close to each other. Image reconstruction is performed by combining radial profiles with evenly distributed angles that are close in the manifold. Our method was evaluated on both 2-D and 3-D synthetic and in vivo data sets. On the synthetic data sets, our method achieved high correlation with the ground truth in terms of image intensity and virtual navigator values. Using the in vivo data, compared with a state-of-the-art approach based on the center of k -space gating, our method was able to make use of much richer profile data for self-gating, resulting in statistically significantly better quantitative measurements in terms of organ sharpness and image gradient entropy.