Acceleration of MR parameter mapping using annihilating filter-based low rank hankel matrix (ALOHA)

POSE: POSition Encoding for accelerated quantitative MRI

Quantitative MRI utilizes multiple acquisitions with varying sequence parameters to sufficiently characterize a biophysical model of interest, resulting in undesirable scan times. Here we propose, validate and demonstrate a new general strategy for accelerating MRI using subvoxel shifting as a source of encoding called POSition Encoding (POSE). The POSE framework applies unique subvoxel shifts along the acquisition parameter dimension, thereby creating an extra source of encoding. Combining with a biophysical signal model of interest, accelerated and enhanced resolution maps of biophysical parameters are obtained. This has been validated and demonstrated through numerical Bloch equation simulations, phantom experiments and in vivo experiments using the variable flip angle signal model in 3D acquisitions as an application example. Monte Carlo simulations were performed using in vivo data to investigate our method's noise performance. POSE quantification results from numerical Bloch equation simulations of both a numerical phantom and realistic digital brain phantom concur well with the reference method, validating our method both theoretically and for realistic situations. NIST phantom experiment results show excellent overall agreement with the reference method, confirming our method's applicability for a wide range of T1 values. In vivo results not only exhibit good agreement with the reference method, but also show g-factors that significantly outperforms conventional parallel imaging methods with identical acceleration. Furthermore, our results show that POSE can be combined with parallel imaging to further accelerate while maintaining superior noise performance over parallel imaging that uses lower acceleration factors.

High Spatial-Resolution and Acquisition-Efficiency Cardiac MR T1 Mapping Based on Radial bSSFP and a Low-Rank Tensor Constraint

BACKGROUND

Cardiac T1 mapping is valuable for evaluating myocardial fibrosis, yet its resolution and acquisition efficiency are limited, potentially obscuring visualization of small pathologies.

PURPOSE

To develop a technique for high-resolution cardiac T1 mapping with a less-than-100-millisecond acquisition window based on radial MOdified Look-Locker Inversion recovery (MOLLI) and a calibrationless space-contrast-coil locally low-rank tensor (SCC-LLRT) constrained reconstruction.

STUDY TYPE

Prospective.

SUBJECTS/PHANTOM

Sixteen healthy subjects (age 25 ± 3 years, 44% females) and 12 patients with suspected cardiomyopathy (age 57 ± 15 years, 42% females), NiCl2-agar phantom.

FIELD STRENGTH/SEQUENCE

3-T, standard MOLLI, radial MOLLI, inversion-recovery spin-echo, late gadolinium enhancement.

ASSESSMENT

SCC-LLRT was compared to a conventional locally low-rank (LLR) method through simulations using Normalized Root-Mean-Square Error (NRMSE) and Structural Similarity Index Measure (SSIM). Radial MOLLI was compared to standard MOLLI across phantom, healthy subjects, and patients. Three independent readers subjectively evaluated the quality of T1 maps using a 5-point scale (5 = best).

STATISTICAL TESTS

Paired t-test, Wilcoxon signed-rank test, intraclass correlation coefficient analysis, linear regression, Bland-Altman analysis. P < 0.05 was considered statistically significant.

RESULTS

In simulations, SCC-LLRT demonstrated a significant improvement in NRMSE and SSIM compared to LLR. In phantom, both radial MOLLI and standard MOLLI provided consistent T1 estimates across different heart rates. In healthy subjects, radial MOLLI exhibited a significantly lower mean T1 (1115 ± 39 msec vs. 1155 ± 36 msec), similar T1 SD (74 ± 14 msec vs. 67 ± 23 msec, P = 0.20), and similar T1 reproducibility (28 ± 18 msec vs. 22 ± 15 msec, P = 0.34) compared to standard MOLLI. In patients, the proposed method significantly improved the sharpness of myocardial boundaries (4.50 ± 0.65 vs. 3.25 ± 0.43), the conspicuity of papillary muscles and fine structures (4.33 ± 0.74 vs. 3.33 ± 0.47), and artifacts (4.75 ± 0.43 vs. 3.83 ± 0.55). The reconstruction time for a single slice was 5.2 hours.

DATA CONCLUSION

The proposed method enables high-resolution cardiac T1 mapping with a short acquisition window and improved image quality.

EVIDENCE LEVEL

1 TECHNICAL EFFICACY: Stage 1.

Predictive uncertainty in deep learning-based MR image reconstruction using deep ensembles: Evaluation on the fastMRI data set

PURPOSE

To estimate pixel-wise predictive uncertainty for deep learning-based MR image reconstruction and to examine the impact of domain shifts and architecture robustness.

METHODS

Uncertainty prediction could provide a measure for robustness of deep learning (DL)-based MR image reconstruction from undersampled data. DL methods bear the risk of inducing reconstruction errors like in-painting of unrealistic structures or missing pathologies. These errors may be obscured by visual realism of DL reconstruction and thus remain undiscovered. Furthermore, most methods are task-agnostic and not well calibrated to domain shifts. We propose a strategy that estimates aleatoric (data) and epistemic (model) uncertainty, which entails training a deep ensemble (epistemic) with nonnegative log-likelihood (aleatoric) loss in addition to the conventional applied losses terms. The proposed procedure can be paired with any DL reconstruction, enabling investigations of their predictive uncertainties on a pixel level. Five different architectures were investigated on the fastMRI database. The impact on the examined uncertainty of in-distributional and out-of-distributional data with changes to undersampling pattern, imaging contrast, imaging orientation, anatomy, and pathology were explored.

RESULTS

Predictive uncertainty could be captured and showed good correlation to normalized mean squared error. Uncertainty was primarily focused along the aliased anatomies and on hyperintense and hypointense regions. The proposed uncertainty measure was able to detect disease prevalence shifts. Distinct predictive uncertainty patterns were observed for changing network architectures.

CONCLUSION

The proposed approach enables aleatoric and epistemic uncertainty prediction for DL-based MR reconstruction with an interpretable examination on a pixel level.

Constrained alternating minimization for parameter mapping (CAMP)

OBJECTIVE

To improve image quality in highly accelerated parameter mapping by incorporating a linear constraint that relates consecutive images.

APPROACH

In multi-echo T1 or T2 mapping, scan time is often shortened by acquiring undersampled but complementary measures of k-space at each TE or TI. However, residual undersampling artifacts from the individual images can then degrade the quality of the final parameter maps. In this work, a new reconstruction method, dubbed Constrained Alternating Minimization for Parameter mapping (CAMP), is introduced. This method simultaneously extracts T2 or T1* maps in addition to an image for each TE or TI from accelerated datasets, leveraging the constraints of the decay to improve the reconstructed image quality. The model enforces exponential decay through a linear constraint, resulting in a biconvex objective function that lends itself to alternating minimization. The method was tested in four in vivo volunteer experiments and validated in phantom studies and healthy subjects, using T2 and T1 mapping, with accelerations of up to 12.

MAIN RESULTS

CAMP is demonstrated for accelerated radial and Cartesian acquisitions in T2 and T1 mapping. The method is even applied to generate an entire T2 weighted image series from a single TSE dataset, despite the blockwise k-space sampling at each echo time. Experimental undersampled phantom and in vivo results processed with CAMP exhibit reduced artifacts without introducing bias.

SIGNIFICANCE

For a wide array of applications, CAMP linearizes the model cost function without sacrificing model accuracy so that the well-conditioned and highly efficient reconstruction algorithm improves the image quality of accelerated parameter maps.

DPP: deep phase prior for parallel imaging with wave encoding

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

A model-based MR parameter mapping network robust to substantial variations in acquisition settings

Deep learning methods show great potential for the efficient and precise estimation of quantitative parameter maps from multiple magnetic resonance (MR) images. Current deep learning-based MR parameter mapping (MPM) methods are mostly trained and tested using data with specific acquisition settings. However, scan protocols usually vary with centers, scanners, and studies in practice. Thus, deep learning methods applicable to MPM with varying acquisition settings are highly required but still rarely investigated. In this work, we develop a model-based deep network termed MMPM-Net for robust MPM with varying acquisition settings. A deep learning-based denoiser is introduced to construct the regularization term in the nonlinear inversion problem of MPM. The alternating direction method of multipliers is used to solve the optimization problem and then unrolled to construct MMPM-Net. The variation in acquisition parameters can be addressed by the data fidelity component in MMPM-Net. Extensive experiments are performed on R2 mapping and R1 mapping datasets with substantial variations in acquisition settings, and the results demonstrate that the proposed MMPM-Net method outperforms other state-of-the-art MR parameter mapping methods both qualitatively and quantitatively.

Low-rank tensor assisted K-space generative model for parallel imaging reconstruction

Although recent deep learning methods, especially generative models, have shown good performance in magnetic resonance imaging, there is still much room for improvement. Considering that the sample number and internal dimension in score-based generative model have key influence on estimating the gradients of data distribution, we present a new idea for parallel imaging reconstruction, named low-rank tensor assisted k-space generative model (LR-KGM). It means that we transform low-rank information into high-dimensional prior information for learning. More specifically, the multi-channel data is constructed into a large Hankel matrix to reduce the number of training samples, which is subsequently collapsed into a tensor for the stage of prior learning. In the testing phase, the low-rank rotation strategy is utilized to impose low-rank constraints on the output tensors of the generative network. Furthermore, we alternate the reconstruction between traditional generative iterations and low-rank high-dimensional tensor iterations. Experimental comparisons with the state-of-the-arts demonstrated that the proposed LR-KGM method achieved better performance.

WKGM: weighted k-space generative model for parallel imaging reconstruction

Deep learning based parallel imaging (PI) has made great progress in recent years to accelerate MRI. Nevertheless, it still has some limitations: for example, the robustness and flexibility of existing methods are greatly deficient. In this work, we propose a method to explore the k-space domain learning via robust generative modeling for flexible calibrationless PI reconstruction, coined the weighted k-space generative model (WKGM). Specifically, WKGM is a generalized k-space domain model, where the k-space weighting technology and high-dimensional space augmentation design are efficiently incorporated for score-based generative model training, resulting in good and robust reconstructions. In addition, WKGM is flexible and thus can be synergistically combined with various traditional k-space PI models, which can make full use of the correlation between multi-coil data and realize calibrationless PI. Even though our model was trained on only 500 images, experimental results with varying sampling patterns and acceleration factors demonstrate that WKGM can attain state-of-the-art reconstruction results with the well learned k-space generative prior.

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.

K-UNN: k-space interpolation with untrained neural network

Recently, untrained neural networks (UNNs) have shown satisfactory performances for MR image reconstruction on random sampling trajectories without using additional full-sampled training data. However, the existing UNN-based approaches lack the modeling of physical priors, resulting in poor performance in some common scenarios (e.g., partial Fourier (PF), regular sampling, etc.) and the lack of theoretical guarantees for reconstruction accuracy. To bridge this gap, we propose a safeguarded k-space interpolation method for MRI using a specially designed UNN with a tripled architecture driven by three physical priors of the MR images (or k-space data), including transform sparsity, coil sensitivity smoothness, and phase smoothness. We also prove that the proposed method guarantees tight bounds for interpolated k-space data accuracy. Finally, ablation experiments show that the proposed method can characterize the physical priors of MR images well. Additionally, experiments show that the proposed method consistently outperforms traditional parallel imaging methods and existing UNNs, and is even competitive against supervised-trained deep learning methods in PF and regular undersampling reconstruction.

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

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSION

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

Calibrationless reconstruction of uniformly‐undersampled multi‐channel MR data with deep learning estimated ESPIRiT maps

PURPOSE

To develop a truly calibrationless reconstruction method that derives An Eigenvalue Approach to Autocalibrating Parallel MRI (ESPIRiT) maps from uniformly-undersampled multi-channel MR data by deep learning.

METHODS

ESPIRiT, one commonly used parallel imaging reconstruction technique, forms the images from undersampled MR k-space data using ESPIRiT maps that effectively represents coil sensitivity information. Accurate ESPIRiT map estimation requires quality coil sensitivity calibration or autocalibration data. We present a U-Net based deep learning model to estimate the multi-channel ESPIRiT maps directly from uniformly-undersampled multi-channel multi-slice MR data. The model is trained using fully-sampled multi-slice axial brain datasets from the same MR receiving coil system. To utilize subject-coil geometric parameters available for each dataset, the training imposes a hybrid loss on ESPIRiT maps at the original locations as well as their corresponding locations within the standard reference multi-slice axial stack. The performance of the approach was evaluated using publicly available T1-weighed brain and cardiac data.

RESULTS

The proposed model robustly predicted multi-channel ESPIRiT maps from uniformly-undersampled k-space data. They were highly comparable to the reference ESPIRiT maps directly computed from 24 consecutive central k-space lines. Further, they led to excellent ESPIRiT reconstruction performance even at high acceleration, exhibiting a similar level of errors and artifacts to that by using reference ESPIRiT maps.

CONCLUSION

A new deep learning approach is developed to estimate ESPIRiT maps directly from uniformly-undersampled MR data. It presents a general strategy for calibrationless parallel imaging reconstruction through learning from the coil and protocol-specific data.

Improving robustness of 3D multi-shot EPI by structured low-rank reconstruction of segmented CAIPI sampling for fMRI at 7T

Three-dimensional (3D) encoding methods are increasingly being explored as alternatives to two-dimensional (2D) multi-slice acquisitions in fMRI, particularly in cases where high isotropic resolution is needed. 3D multi-shot EPI acquisition, as the workhorse of 3D fMRI imaging, is susceptible to physiological fluctuations which can induce inter-shot phase variations, and thus reducing the achievable tSNR, negating some of the benefit of 3D encoding. This issue can be particularly problematic at ultra-high fields like 7T, which have more severe off-resonance effects. In this work, we aim to improve the temporal stability of 3D multi-shot EPI at 7T by improving its robustness to inter-shot phase variations. We presented a 3D segmented CAIPI sampling trajectory ("seg-CAIPI") and an improved reconstruction method based on Hankel structured low-rank matrix recovery. Simulation and in-vivo results demonstrate that the combination of the seg-CAIPI sampling scheme and the proposed structured low-rank reconstruction is a promising way to effectively reduce the unwanted temporal variance induced by inter-shot physiological fluctuations, and thus improve the robustness of 3D multi-shot EPI for fMRI.

Data-driven optimization of sampling patterns for MR brain T1ρ mapping

PURPOSE

The goal of this study was to apply a fast data-driven optimization algorithm, called bias-accelerated subset selection, for MR brain T1ρ mapping to generate optimized sampling patterns (SPs) for compressed sensing reconstruction of brain 3D-T1ρ MRI.

METHODS

Five healthy volunteers were recruited, and fully sampled Cartesian 3D-T1ρ MRIs were obtained. Variable density (VD) and Poisson disc (PD) undersampling was used as the input to SP optimization process. The reconstruction used 3 compressed sensing methods: spatiotemporal finite differences, low-rank plus sparse with spatial finite differences, and low rank. The performance of images and T1ρ maps using PD-SP and VD-SP and their optimized sampling patterns (PD-OSP and VD-OSP) were compared to the fully sampled reference using normalized root mean square error (NRMSE).

RESULTS

The VD-OSP with spatiotemporal finite differences reconstruction (NRMSE = 0.078) and the PD-OSP with spatiotemporal finite differences reconstruction (NRMSE = 0.079) at the highest acceleration factors (AF = 30) showed the largest improvement compared to the respective nonoptimized SPs (VD NRMSE = 0.087 and PD NRMSE = 0.149). Prospective undersampling was tested at AF = 4, with VD-OSP NRMSE = 0.057 versus PD-OSP NRMSE = 0.060, with optimized sampling performing better that input PD or VD sampling. For brain T1ρ mapping, the VD-OSP with low rank reconstruction for AFs <10 and VD-OSP with spatiotemporal finite differences for AFs >10 perform better.

CONCLUSIONS

The study demonstrated that the appropriate use of data-driven optimized sampling and suitable compressed sensing reconstruction technique can be employed to potentially accelerate 3D T1ρ mapping for brain imaging applications.

A unified model for reconstruction and R2* mapping of accelerated 7T data using the quantitative recurrent inference machine

Quantitative MRI (qMRI) acquired at the ultra-high field of 7 Tesla has been used in visualizing and analyzing subcortical structures. qMRI relies on the acquisition of multiple images with different scan settings, leading to extended scanning times. Data redundancy and prior information from the relaxometry model can be exploited by deep learning to accelerate the imaging process. We propose the quantitative Recurrent Inference Machine (qRIM), with a unified forward model for joint reconstruction and R₂^*-mapping from sparse data, embedded in a Recurrent Inference Machine (RIM), an iterative inverse problem-solving network. To study the dependency of the proposed extension of the unified forward model to network architecture, we implemented and compared a quantitative End-to-End Variational Network (qE2EVN). Experiments were performed with high-resolution multi-echo gradient echo data of the brain at 7T of a cohort study covering the entire adult life span. The error in reconstructed R₂^* from undersampled data relative to reference data significantly decreased for the unified model compared to sequential image reconstruction and parameter fitting using the RIM. With increasing acceleration factor, an increasing reduction in the reconstruction error was observed, pointing to a larger benefit for sparser data. Qualitatively, this was following an observed reduction of image blurriness in R₂^*-maps. In contrast, when using the U-Net as network architecture, a negative bias in R₂^* in selected regions of interest was observed. Compressed Sensing rendered accurate, but less precise estimates of R₂^*. The qE2EVN showed slightly inferior reconstruction quality compared to the qRIM but better quality than the U-Net and Compressed Sensing. Subcortical maturation over age measured by a linearly increasing interquartile range of R₂^* in the striatum was preserved up to an acceleration factor of 9. With the integrated prior of the unified forward model, the proposed qRIM can exploit the redundancy among repeated measurements and shared information between tasks, facilitating relaxometry in accelerated MRI.

Deep Matrix Factorization Based on Convolutional Neural Networks for Image Inpainting

In this work, we formulate the image in-painting as a matrix completion problem. Traditional matrix completion methods are generally based on linear models, assuming that the matrix is low rank. When the original matrix is large scale and the observed elements are few, they will easily lead to over-fitting and their performance will also decrease significantly. Recently, researchers have tried to apply deep learning and nonlinear techniques to solve matrix completion. However, most of the existing deep learning-based methods restore each column or row of the matrix independently, which loses the global structure information of the matrix and therefore does not achieve the expected results in the image in-painting. In this paper, we propose a deep matrix factorization completion network (DMFCNet) for image in-painting by combining deep learning and a traditional matrix completion model. The main idea of DMFCNet is to map iterative updates of variables from a traditional matrix completion model into a fixed depth neural network. The potential relationships between observed matrix data are learned in a trainable end-to-end manner, which leads to a high-performance and easy-to-deploy nonlinear solution. Experimental results show that DMFCNet can provide higher matrix completion accuracy than the state-of-the-art matrix completion methods in a shorter running time.

Acceleration Strategies for MR-STAT: Achieving High-Resolution Reconstructions on a Desktop PC Within 3 Minutes

MR-STAT is an emerging quantitative magnetic resonance imaging technique which aims at obtaining multi-parametric tissue parameter maps from single short scans. It describes the relationship between the spatial-domain tissue parameters and the time-domain measured signal by using a comprehensive, volumetric forward model. The MR-STAT reconstruction solves a large-scale nonlinear problem, thus is very computationally challenging. In previous work, MR-STAT reconstruction using Cartesian readout data was accelerated by approximating the Hessian matrix with sparse, banded blocks, and can be done on high performance CPU clusters with tens of minutes. In the current work, we propose an accelerated Cartesian MR-STAT algorithm incorporating two different strategies: firstly, a neural network is trained as a fast surrogate to learn the magnetization signal not only in the full time-domain but also in the compressed low-rank domain; secondly, based on the surrogate model, the Cartesian MR-STAT problem is re-formulated and split into smaller sub-problems by the alternating direction method of multipliers. The proposed method substantially reduces the computational requirements for runtime and memory. Simulated and in-vivo balanced MR-STAT experiments show similar reconstruction results using the proposed algorithm compared to the previous sparse Hessian method, and the reconstruction times are at least 40 times shorter. Incorporating sensitivity encoding and regularization terms is straightforward, and allows for better image quality with a negligible increase in reconstruction time. The proposed algorithm could reconstruct both balanced and gradient-spoiled in-vivo data within 3 minutes on a desktop PC, and could thereby facilitate the translation of MR-STAT in clinical settings.

Generalized self-calibrating simultaneous multi-slice MR image reconstruction from 3D Fourier encoding perspective

This work introduces a novel, k-space based one-step solution for simultaneous multi-slice MR image reconstruction from 3D Fourier encoding perspective. With undersampled SMS imaging, image reconstruction suffers from both inter-slice leakages and in-plane aliasing artifacts. Aliasing separation becomes further challenging in the presence of discrepancies between calibration and imaging. To address them, in this work a measured SMS 3D k-space with additional calibrating signals is decomposed into SMS imaging and self-calibrating data sets. Extended controlled aliasing is performed by upsampling the measured data in the k_z-direction. A slice-specific null space operator is then learned using extended self-calibration exploiting target slices and additional in-plane-shifted images. Inter-slice leakages and in-plane aliasing artifacts are jointly resolved in a single step by solving a constrained optimization problem in which null space reconstruction consistency is balanced with a Hankel-structured low rank prior while data fidelity in 3D Fourier space is enforced. Retrospective and prospective studies are performed to validate the effectiveness of the proposed method in various regions including knee and L-spine.

Accelerated MRI Reconstruction With Separable and Enhanced Low-Rank Hankel Regularization

Magnetic resonance imaging serves as an essential tool for clinical diagnosis, however, suffers from a long acquisition time. Sparse sampling effectively saves this time but images need to be faithfully reconstructed from undersampled data. Among the existing reconstruction methods, the structured low-rank methods have advantages in robustness to the sampling patterns and lower error. However, the structured low-rank methods use the 2D or higher dimension k-space data to build a huge block Hankel matrix, leading to considerable time and memory consumption. To reduce the size of the Hankel matrix, we proposed to separably construct multiple small Hankel matrices from rows and columns of the k-space and then constrain the low-rankness on these small matrices. This separable model can significantly reduce the computational time but ignores the correlation existed in inter- and intra-row or column, resulting in increased reconstruction error. To improve the reconstructed image without obviously increasing the computation, we further introduced the self-consistency of k-space and virtual coil prior. Besides, the proposed separable model can be extended into other imaging scenarios which hold exponential characteristics in the parameter dimension. The in vivo experimental results demonstrated that the proposed method permits the lowest reconstruction error with a fast reconstruction. The proposed approach requires only 4% of the state-of-the-art STDLR-SPIRiT runtime for parallel imaging reconstruction, and achieves the fastest computational speed in parameter imaging reconstruction.

Calibrationless multi-slice Cartesian MRI via orthogonally alternating phase encoding direction and joint low-rank tensor completion

We propose a multi-slice acquisition with orthogonally alternating phase encoding (PE) direction and subsequent joint calibrationless reconstruction for accelerated multiple individual 2D slices or multi-slice 2D Cartesian MRI. Specifically, multi-slice multi-channel data are first acquired with random or uniform PE undersampling while orthogonally alternating PE direction between adjacent slices. They are then jointly reconstructed through a recently developed low-rank multi-slice Hankel tensor completion (MS-HTC) approach. The proposed acquisition and reconstruction strategy was evaluated with human brain MR data. It effectively suppressed aliasing artifacts even at high acceleration factor, outperforming the existing MS-HTC approach, where PE direction is the same between adjacent slices. More importantly, the new strategy worked robustly with uniform undersampling or random undersampling without any consecutive central k-space lines. In summary, our proposed multi-slice MRI strategy exploits both coil sensitivity and image content similarities across adjacent slices. Orthogonally alternating PE direction among slices substantially facilitates the low-rank completion process and improves image reconstruction quality. This new strategy is applicable to uniform and random PE undersampling. It can be easily implemented in practice for Cartesian parallel imaging of multiple individual 2D slices without any coil sensitivity calibration.

EPI phase error correction with deep learning (PEC-DL) at 7 T

PURPOSE

The phase mismatch between odd and even echoes in EPI causes Nyquist ghost artifacts. Existing ghost correction methods often suffer from severe residual artifacts and are ineffective with k-space undersampling data. This study proposed a deep learning-based method (PEC-DL) to correct phase errors for DWI at 7 Tesla.

METHODS

The acquired k-space data were divided into 2 independent undersampled datasets according to their readout polarities. Then the proposed PEC-DL network reconstructed 2 ghost-free images using the undersampled data without calibration and navigator data. The network was trained with fully sampled images and applied to two- and fourfold accelerated data. Healthy volunteers and patients with Moyamoya disease were recruited to validate the efficacy of the PEC-DL method.

RESULTS

The PEC-DL method was capable to mitigate the ghost artifacts in DWI in healthy volunteers as well as patients with Moyamoya disease. The fourfold accelerated results showed much less distortion in the lesions of the Moyamoya patient using high b-value DWI and the corresponding ADC maps. The ghost-to-signal ratios were significantly lower in PEC-DL images compared to conventional linear phase corrections, mini-entropy, and PEC-GRAPPA algorithms.

CONCLUSION

The proposed method can effectively eliminate ghost artifacts for full sampled and up to fourfold accelerated EPI data without calibration and navigator data.

End-to-end deep learning for interior tomography with low-dose x-ray CT

Objective. There are several x-ray computed tomography (CT) scanning strategies used to reduce radiation dose, such as (1) sparse-view CT, (2) low-dose CT and (3) region-of-interest (ROI) CT (called interior tomography). To further reduce the dose, sparse-view and/or low-dose CT settings can be applied together with interior tomography. Interior tomography has various advantages in terms of reducing the number of detectors and decreasing the x-ray radiation dose. However, a large patient or a small field-of-view (FOV) detector can cause truncated projections, and then the reconstructed images suffer from severe cupping artifacts. In addition, although low-dose CT can reduce the radiation exposure dose, analytic reconstruction algorithms produce image noise. Recently, many researchers have utilized image-domain deep learning (DL) approaches to remove each artifact and demonstrated impressive performances, and the theory of deep convolutional framelets supports the reason for the performance improvement. Approach. In this paper, we found that it is difficult to solve coupled artifacts using an image-domain convolutional neural network (CNN) based on deep convolutional framelets. Significance. To address the coupled problem, we decouple it into two sub-problems: (i) image-domain noise reduction inside the truncated projection to solve low-dose CT problem and (ii) extrapolation of the projection outside the truncated projection to solve the ROI CT problem. The decoupled sub-problems are solved directly with a novel proposed end-to-end learning method using dual-domain CNNs. Main results. We demonstrate that the proposed method outperforms the conventional image-domain DL methods, and a projection-domain CNN shows better performance than the image-domain CNNs commonly used by many researchers.

Repeatability and robustness of MP-GRASP T1 mapping

PURPOSE

To demonstrate the repeatability of fast 3D T1 mapping using Magnetization-Prepared Golden-angle RAdial Sparse Parallel (MP-GRASP) MRI and its robustness to variation of imaging parameters including flip angle and spatial resolution in phantoms and the brain.

THEORY AND METHODS

Multiple imaging experiments were performed to (1) assess the robustness of MP-GRASP T1 mapping to B1 inhomogeneity using a single tube phantom filled with uniform MnCl2 liquid; (2) compare the repeatability of T1 mapping between MP-GRASP and inversion recovery-based spin-echo (IR-SE; over 12 scans), using a commercial T1MES phantom; (3) evaluate the longitudinal variation of T1 estimation using MP-GRASP with varying imaging parameters, including spatial resolution, flip angle, TR/TE, and acceleration rate, using the T1MES phantom (106 scans performed over a period of 12 months); and (4) evaluate the variation of T1 estimation using MP-GRASP with varying imaging parameters in the brain (24 scans in a single visit). In addition, the accuracy of MP-GRASP T1 mapping was also validated against IR-SE by performing linear correlation and calculating the Lin's concordance correlation coefficient (CCC).

RESULTS

MP-GRASP demonstrates good robustness to B1 inhomogeneity, with intra-slice variability below 1% in the single tube phantom experiment. The longitudinal variability is good both in the phantom (below 2.5%) and in the brain (below 2%) with varying imaging parameters. The T1 values estimated from MP-GRASP are accurate compared to that from the IR-SE imaging (R2 = 0.997, Lin's CCC = 0.996).

CONCLUSION

MP-GRASP shows excellent repeatability of T1 estimation over time, and it is also robust to variation of different imaging parameters evaluated in this study.

Blip up-down acquisition for spin- and gradient-echo imaging (BUDA-SAGE) with self-supervised denoising enables efficient T2 , T2 *, para- and dia-magnetic susceptibility mapping

PURPOSE

To rapidly obtain high resolution T₂ , T₂ *, and quantitative susceptibility mapping (QSM) source separation maps with whole-brain coverage and high geometric fidelity.

METHODS

We propose Blip Up-Down Acquisition for Spin And Gradient Echo imaging (BUDA-SAGE), an efficient EPI sequence for quantitative mapping. The acquisition includes multiple T₂ *-, T₂ '-, and T₂ -weighted contrasts. We alternate the phase-encoding polarities across the interleaved shots in this multi-shot navigator-free acquisition. A field map estimated from interim reconstructions was incorporated into the joint multi-shot EPI reconstruction with a structured low rank constraint to eliminate distortion. A self-supervised neural network (NN), MR-Self2Self (MR-S2S), was used to perform denoising to boost SNR. Using Slider encoding allowed us to reach 1 mm isotropic resolution by performing super-resolution reconstruction on volumes acquired with 2 mm slice thickness. Quantitative T₂ (=1/R₂ ) and T₂ * (=1/R₂ *) maps were obtained using Bloch dictionary matching on the reconstructed echoes. QSM was estimated using nonlinear dipole inversion on the gradient echoes. Starting from the estimated R₂ /R₂ * maps, R₂ ' information was derived and used in source separation QSM reconstruction, which provided additional para- and dia-magnetic susceptibility maps.

RESULTS

In vivo results demonstrate the ability of BUDA-SAGE to provide whole-brain, distortion-free, high-resolution, multi-contrast images and quantitative T₂ /T₂ * maps, as well as yielding para- and dia-magnetic susceptibility maps. Estimated quantitative maps showed comparable values to conventional mapping methods in phantom and in vivo measurements.

CONCLUSION

BUDA-SAGE acquisition with self-supervised denoising and Slider encoding enables rapid, distortion-free, whole-brain T₂ /T₂ * mapping at 1 mm isotropic resolution under 90 s.

Rapid MR relaxometry using deep learning: An overview of current techniques and emerging trends

Quantitative mapping of MR tissue parameters such as the spin-lattice relaxation time (T1 ), the spin-spin relaxation time (T2 ), and the spin-lattice relaxation in the rotating frame (T1ρ ), referred to as MR relaxometry in general, has demonstrated improved assessment in a wide range of clinical applications. Compared with conventional contrast-weighted (eg T1 -, T2 -, or T1ρ -weighted) MRI, MR relaxometry provides increased sensitivity to pathologies and delivers important information that can be more specific to tissue composition and microenvironment. The rise of deep learning in the past several years has been revolutionizing many aspects of MRI research, including image reconstruction, image analysis, and disease diagnosis and prognosis. Although deep learning has also shown great potential for MR relaxometry and quantitative MRI in general, this research direction has been much less explored to date. The goal of this paper is to discuss the applications of deep learning for rapid MR relaxometry and to review emerging deep-learning-based techniques that can be applied to improve MR relaxometry in terms of imaging speed, image quality, and quantification robustness. The paper is comprised of an introduction and four more sections. Section 2 describes a summary of the imaging models of quantitative MR relaxometry. In Section 3, we review existing "classical" methods for accelerating MR relaxometry, including state-of-the-art spatiotemporal acceleration techniques, model-based reconstruction methods, and efficient parameter generation approaches. Section 4 then presents how deep learning can be used to improve MR relaxometry and how it is linked to conventional techniques. The final section concludes the review by discussing the promise and existing challenges of deep learning for rapid MR relaxometry and potential solutions to address these challenges.

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.

Simultaneous Multislice Brain MRI T1 Mapping with Improved Low-Rank Modeling

To accelerate data acquisition speed in magnetic resonance imaging (MRI), multiple slices are simultaneously acquired using multiband pulses. Simultaneous multislice (SMS) imaging typically unfolds slice aliasing from the acquired collapsed slices. In this study, we extended the SMS framework to accelerated MR parameter quantification such as T1 mapping. Assuming that the slice-specific null space and signal subspace are invariant along the parameter dimension, we formulated the SMS framework as a constrained optimization problem under a joint reconstruction framework such that the noise and signal subspaces are used for slice separation and recovery, respectively. The proposed method was validated on 3T MR human brain scans. We successfully demonstrated that the proposed method outperforms competing methods in suppressing aliasing artifacts and noise at high SMS accelerations, thus leading to accurate T1 maps.

High-dimensional fast convolutional framework (HICU) for calibrationless MRI

PURPOSE

To present a computational procedure for accelerated, calibrationless magnetic resonance image (Cl-MRI) reconstruction that is fast, memory efficient, and scales to high-dimensional imaging.

THEORY AND METHODS

Cl-MRI methods can enable high acceleration rates and flexible sampling patterns, but their clinical application is limited by computational complexity and large memory footprint. The proposed computational procedure, HIgh-dimensional fast convolutional framework (HICU), provides fast, memory-efficient recovery of unsampled k-space points. For demonstration, HICU is applied to 6 2D T2-weighted brain, 7 2D cardiac cine, 5 3D knee, and 1 multi-shot diffusion weighted imaging (MSDWI) datasets.

RESULTS

The 2D imaging results show that HICU can offer 1-2 orders of magnitude computation speedup compared to other Cl-MRI methods without sacrificing imaging quality. The 2D cine and 3D imaging results show that the computational acceleration techniques included in HICU yield computing time on par with SENSE-based compressed sensing methods with up to 3 dB improvement in signal-to-error ratio and better perceptual quality. The MSDWI results demonstrate the feasibility of HICU for a challenging multi-shot echo-planar imaging application.

CONCLUSIONS

The presented method, HICU, offers efficient computation and scalability as well as extendibility to a wide variety of MRI applications.

Improving subspace constrained radial fast spin echo MRI using block matching driven non-local low rank regularization

Subspace-constrained reconstruction methods restrict the relaxation signals (of size M) in the scene to a pre-determined subspace (of size K≪M) and allow multi-contrast imaging and parameter mapping from accelerated acquisitions. However, these constraints yield poor image quality at some imaging contrasts, which can impact the parameter mapping performance. Additional regularization such as the use of joint-sparse (JS) or locally-low-rank (LLR) constraints can help improve the recovery of these images but are not sufficient when operating at high acceleration rates. We propose a method, non-local rank 3D (NLR3D), that is built on block matching and transform domain low rank constraints to allow high quality recovery of subspace-coefficient images (SCI) and subsequent multi-contrast imaging and parameter mapping. The performance of NLR3D was evaluated using Monte-Carlo (MC) simulations and compared against the JS and LLR methods. In vivo T 2 mapping results are presented on brain and knee datasets. MC results demonstrate improved bias, variance, and MSE behavior in both the multi-contrast images and parameter maps when compared to the JS and LLR methods. In vivo brain and knee results at moderate and high acceleration rates demonstrate improved recovery of high SNR early TE images as well as parameter maps. No significant difference was found in the T2 values measured in ROIs between the NLR3D reconstructions and the reference images (Wilcoxon signed rank test). The proposed method, NLR3D, enables recovery of high-quality SCI and, consequently, the associated multi-contrast images and parameter maps.

Joint calibrationless reconstruction of highly undersampled multicontrast MR datasets using a low-rank Hankel tensor completion framework

PURPOSE

To jointly reconstruct highly undersampled multicontrast two-dimensional (2D) datasets through a low-rank Hankel tensor completion framework.

METHODS

A multicontrast Hankel tensor completion (MC-HTC) framework is proposed to exploit the shareable information in multicontrast datasets with respect to their highly correlated image structure, common spatial support, and shared coil sensitivity for joint reconstruction. This is achieved by first organizing multicontrast k-space datasets into a single block-wise Hankel tensor. Subsequent low-rank tensor approximation via higher-order singular value decomposition (HOSVD) uses the image structural correlation by considering different contrasts as virtual channels. Meanwhile, the HOSVD imposes common spatial support and shared coil sensitivity by treating data from different contrasts as from additional k-space kernels. The missing k-space data are then recovered by iteratively performing such low-rank approximation and enforcing data consistency. This joint reconstruction framework was evaluated using multicontrast multichannel 2D human brain datasets (T₁ -weighted, T₂ -weighted, fluid-attenuated inversion recovery, and T₁ -weighted-inversion recovery) of identical image geometry with random and uniform undersampling schemes.

RESULTS

The proposed method offered high acceleration, exhibiting significantly less residual errors when compared with both single-contrast SAKE (simultaneous autocalibrating and k-space estimation) and multicontrast J-LORAKS (joint parallel-imaging-low-rank matrix modeling of local k-space neighborhoods) low-rank reconstruction. Furthermore, the MC-HTC framework was applied uniquely to Cartesian uniform undersampling by incorporating a novel complementary k-space sampling strategy where the phase-encoding direction among different contrasts is orthogonally alternated.

CONCLUSION

The proposed MC-HTC approach presents an effective tensor completion framework to jointly reconstruct highly undersampled multicontrast 2D datasets without coil-sensitivity calibration.

Unpaired Training of Deep Learning tMRA for Flexible Spatio-Temporal Resolution

Time-resolved MR angiography (tMRA) has been widely used for dynamic contrast enhanced MRI (DCE-MRI) due to its highly accelerated acquisition. In tMRA, the periphery of the k -space data are sparsely sampled so that neighbouring frames can be merged to construct one temporal frame. However, this view-sharing scheme fundamentally limits the temporal resolution, and it is not possible to change the view-sharing number to achieve different spatio-temporal resolution trade-offs. Although many deep learning approaches have been recently proposed for MR reconstruction from sparse samples, the existing approaches usually require matched fully sampled k -space reference data for supervised training, which is not suitable for tMRA due to the lack of high spatio-temporal resolution ground-truth images. To address this problem, here we propose a novel unpaired training scheme for deep learning using optimal transport driven cycle-consistent generative adversarial network (cycleGAN). In contrast to the conventional cycleGAN with two pairs of generator and discriminator, the new architecture requires just a single pair of generator and discriminator, which makes the training much simpler but still improves the performance. Reconstruction results using in vivo tMRA and simulation data set confirm that the proposed method can immediately generate high quality reconstruction results at various choices of view-sharing numbers, allowing us to exploit better trade-off between spatial and temporal resolution in time-resolved MR angiography.

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

Structured low-rank (SLR) algorithms, which exploit annihilation relations between the Fourier samples of a signal resulting from different properties, is a powerful image reconstruction framework in several applications. This scheme relies on low-rank matrix completion to estimate the annihilation relations from the measurements. The main challenge with this strategy is the high computational complexity of matrix completion. We introduce a deep learning (DL) approach to significantly reduce the computational complexity. Specifically, we use a convolutional neural network (CNN)-based filterbank that is trained to estimate the annihilation relations from imperfect (under-sampled and noisy) k-space measurements of Magnetic Resonance Imaging (MRI). The main reason for the computational efficiency is the pre-learning of the parameters of the non-linear CNN from exemplar data, compared to SLR schemes that learn the linear filterbank parameters from the dataset itself. Experimental comparisons show that the proposed scheme can enable calibration-less parallel MRI; it can offer performance similar to SLR schemes while reducing the runtime by around three orders of magnitude. Unlike pre-calibrated and self-calibrated approaches, the proposed uncalibrated approach is insensitive to motion errors and affords higher acceleration. The proposed scheme also incorporates image domain priors that are complementary, thus significantly improving the performance over that of SLR schemes.

Performance Comparison of Compressed Sensing Algorithms for Accelerating T1ρ Mapping of Human Brain

BACKGROUND

3D-T_1ρ mapping is useful to quantify various neurologic disorders, but data are currently time-consuming to acquire.

PURPOSE

To compare the performance of five compressed sensing (CS) algorithms-spatiotemporal finite differences (STFD), exponential dictionary (EXP), 3D-wavelet transform (WAV), low-rank (LOW) and low-rank plus sparse model with spatial finite differences (L + S SFD)-for 3D-T_1ρ mapping of the human brain with acceleration factors (AFs) of 2, 5, and 10.

STUDY TYPE

Retrospective.

SUBJECTS

Eight healthy volunteers underwent T_1ρ imaging of the whole brain.

FIELD STRENGTH/SEQUENCE

The sequence was fully sampled 3D Cartesian ultrafast gradient echo sequence with a customized T_1ρ preparation module on a clinical 3T scanner.

ASSESSMENT

The fully sampled data was undersampled by factors of 2, 5, and 10 and reconstructed with the five CS algorithms. Image reconstruction quality was evaluated and compared to the SENSE reconstruction of the fully sampled data (reference) and T_1ρ estimation errors were assessed as a function of AF.

STATISTICAL TESTS

Normalized root mean squared errors (nRMSE) and median normalized absolute deviation (MNAD) errors were calculated to compare image reconstruction errors and T_1ρ estimation errors, respectively. Linear regression plots, Bland-Altman plots, and Pearson correlation coefficients (CC) are shown.

RESULTS

For image reconstruction quality, at AF = 2, EXP transforms had the lowest mRMSE (1.56%). At higher AF values, STFD performed better, with the smallest errors (3.16% at AF = 5, 4.32% at AF = 10). For whole-brain quantitative T_1ρ mapping, at AF = 2, EXP performed best (MNAD error = 1.62%). At higher AF values (AF = 5, 10), the STFD technique had the least errors (2.96% at AF = 5, 4.24% at AF = 10) and the smallest variance from the reference T_1ρ estimates.

DATA CONCLUSION

This study demonstrates the use of different CS algorithms that may be useful in reducing the scan time required to perform volumetric T_1ρ mapping of the brain.

LEVEL OF EVIDENCE

2.

TECHNICAL EFFICACY STAGE

1.

Towards accelerated quantitative sodium MRI at 7 T in the skeletal muscle: Comparison of anisotropic acquisition- and compressed sensing techniques

PURPOSE

To compare three anisotropic acquisition schemes and three compressed sensing (CS) approaches for accelerated tissue sodium concentration (TSC) quantification using ²³Na MRI at 7 T.

MATERIALS AND METHODS

Three anisotropic 3D-radial acquisition sequences were evaluated using simulations, phantom- and in vivo TSC measurements: An anisotropic density-adapted 3D-radial sequence (3DPR-C), a 3D acquisition-weighted density-adapted stack-of-stars sampling scheme (SOS) and a SOS approach with golden-ratio rotation (SOS-GR). Eight healthy volunteers were examined at a 7 Tesla MRI system. TSC measurements of the calf were conducted with a nominal spatial resolution of Δx = (3.0 × 3.0 × 15.0) mm³ and a field of view of (156.0 × 156.0 × 240.0) mm³ for multiple undersampling factors (USF). Three CS reconstructions were evaluated: Total variation CS (TV-CS), 3D dictionary-learning compressed sensing (3D-DLCS) and TV-CS with a block matching prior (TV-BL-CS). Results of the simulations and measurements were compared to a simulated ground truth (GT) or a fully sampled reference measurement (FS), respectively. The deviation of the mean TSC evaluated in multiple ROI (mE_GT/FS) and the normalized root-mean-squared error (NRMSE) for simulations were evaluated for CS and NUFFT reconstructions.

RESULTS

In simulations, the SOS-GR yielded the lowest NRMSE and mE_GT (< 4%) with NUFFT for an acquisition time (TA) of less than 2 min. CS further improved the results. In simulations and measurements, the best TSC quantification results were obtained with 3D-DLCS and SOS-GR (lowest NRMSE, mE_GT < 2.6% in simulations, mE_GT < 10.7% for phantom measurements and mE_FS < 6% in vivo) with an USF = 4.1 (TA < 2 min). TV-CS showed no or only slight improvements to NUFFT. The results of TV-BL-CS were similar to 3D-DLCS.

DISCUSSION

The TA for TSC measurements could be reduced to less than 2 min by using adapted sequences such as SOS-GR and CS reconstruction approaches such as 3D-DLCS or TV-BL-CS, while the quantitative accuracy stays comparable to a fully sampled NUFFT reconstruction (approx. 8 min TA). In future, the lower TA could improve clinical applicability of TSC measurements.

Calibrationless parallel imaging reconstruction for multislice MR data using low-rank tensor completion

PURPOSE

To provide joint calibrationless parallel imaging reconstruction of highly accelerated multislice 2D MR k-space data.

METHODS

Adjacent image slices in multislice MR data have similar coil sensitivity maps, spatial support, and image content. Such similarities can be utilized to improve image quality by reconstructing multiple slices jointly with low-rank tensor completion. Specifically, the multichannel k-space data from multiple slices are constructed into a block-wise Hankel tensor and iteratively updated by promoting tensor low-rankness through higher-order SVD. This multislice block-wise Hankel tensor completion was implemented for 2D spiral and Cartesian k-space undersampling where sampling patterns vary between adjacent slices. The approach was evaluated with human brain MR data and compared to the traditional single-slice simultaneous autocalibrating and k-space estimation reconstruction.

RESULTS

The proposed multislice block-wise Hankel tensor completion approach robustly reconstructed highly undersampled multislice 2D spiral and Cartesian data. It produced substantially lower level of artifacts compared to the traditional single-slice simultaneous autocalibrating and k-space estimation reconstruction. Quantitative evaluation using error maps and root mean square error demonstrated its significantly improved performance in terms of residual artifacts and root mean square error.

CONCLUSION

Our proposed multislice block-wise Hankel tensor completion method exploits the similar coil sensitivity and image content within multislice MR data through a tensor completion framework. It offers a new and effective approach to acquire and reconstruct highly undersampled multislice MR data in a calibrationless manner.

Accelerated T2 Mapping of the Lumbar Intervertebral Disc: Highly Undersampled K-Space Data for Robust T2 Relaxation Time Measurement in Clinically Feasible Acquisition Times

T2 mapping of the intervertebral disc (IVD) can depict quantitative changes reflecting biochemical change due to loss of glycosaminoglycan content. Conventional T2 mapping is usually performed using a 2-dimensional multi-echo-spin echo sequence (2D-MESE) with long acquisition times that are generally not compatible with clinical routine. This study investigates the applicability of GRAPPATINI, a T2 mapping sequence combining undersampling, model-based reconstruction, and parallel imaging, to offer clinically feasible acquisition times in T2 mapping of the lumbar IVD.

MATERIALS AND METHODS

Fifty-eight individuals (26 female; mean age, 23.3 ± 8.1 years) were prospectively studied at 3 T. GRAPPATINI was conducted with the same parameters as the 2D-MESE while shortening the acquisition time from 13:18 to 2:27 minutes. The setup was also validated in a phantom experiment using a 6.48-hour-long single echo-spin echo sequence as reference. The IVDs were manually segmented on 4 central slices.

RESULTS

The median nucleus pulposus showed a strong Pearson correlation coefficient between T2GRAPPATINI and T2MESE (rp = 0.919; P < 0.001). There was also a significant correlation for the ventral (rp = 0.241; P < 0.001) and posterior (rp = 0.418; P < 0.001) annular regions.In the single spin-echo phantom experiment, the most accurate T2 estimation was achieved using T2GRAPPATINI with a median absolute deviation of 15.3 milliseconds as compared with T2MESE with 26.5 milliseconds.

CONCLUSIONS

GRAPPATINI facilitates precise T2 mapping at 3 T in accordance with clinical standards and reference methods using the same parameters while shortening acquisition times from 13:18 to 2:27 minutes with the same parameters.

High-dimensional embedding network derived prior for compressive sensing MRI reconstruction

Although recent deep learning methodology has shown promising performance in fast imaging, the network needs to be retrained for specific sampling patterns and ratios. Therefore, how to explore the network as a general prior and leverage it into the observation constraint flexibly is urgent. In this work, we present a multi-channel enhanced Deep Mean-Shift Prior (MEDMSP) to address the highly under-sampled magnetic resonance imaging reconstruction problem. By extending the naive DMSP via integration of multi-model aggregation and multi-channel network learning, a high-dimensional embedding network derived prior is formed. Then, we apply the learned prior to single-channel image reconstruction via variable augmentation technique. The resulting model is tackled by proximal gradient descent and alternative iteration. Experimental results under various sampling trajectories and acceleration factors consistently demonstrated the superiority of the proposed prior.

Simultaneous Multi-VENC and Simultaneous Multi-Slice Phase Contrast Magnetic Resonance Imaging

This work develops a novel, simultaneous multi-VENC and simultaneous multi-slice (SMV+SMS) imaging in a single acquisition for robust phase contrast (PC) MRI. To this end, the pulse sequence was designed to permit concurrent acquisition of multiple VENCs as well as multiple slices on a shared frequency encoding gradient, in which each effective echo time for multiple VENCs was controlled by adjusting net gradient area while multiple slices were simultaneously excited by employing multiband resonance frequency (RF) pulses. For VENC and slice separation, RF phase cycling and gradient blip were applied to create both inter-VENC and inter-slice shifts along phase encoding direction, respectively. With an alternating RF phase cycling that generates oscillating steady-state with low and high signal amplitude, the acquired multi-VENC k-space was reformulated into 3D undersampled k-space by generating a virtual dimension along VENC direction for modulation induced artifact reduction. In vivo studies were conducted to validate the feasibility of the proposed method in comparison with conventional PC MRI. The proposed method shows comparable performance to the conventional method in delineating both low and high flow velocities across cardiac phases with high spatial coverage without apparent artifacts. In the presence of high flow velocity that is above the VENC value, the proposed method exhibits clear depiction of flow signals over conventional method, thereby leading to high VNR image with improved velocity dynamic range.

Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning

The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems. These methods are typically fast, but have suboptimal properties such as poor resolution-noise trade-off for CT. A second type is iterative reconstruction methods based on more complete models for the imaging system physics and, where appropriate, models for the sensor statistics. These iterative methods improved image quality by reducing noise and artifacts. The FDA-approved methods among these have been based on relatively simple regularization models. A third type of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose. These methods typically involve mathematical image models involving assumptions such as sparsity or low-rank. A fourth type of methods replaces mathematically designed models of signals and systems with data-driven or adaptive models inspired by the field of machine learning. This paper focuses on the two most recent trends in medical image reconstruction: methods based on sparsity or low-rank models, and data-driven methods based on machine learning techniques.

Improved MUSSELS reconstruction for high-resolution multi-shot diffusion weighted imaging

PURPOSE

MUSSELS is a one-step iterative reconstruction method for multishot diffusion weighted (msDW) imaging. The current work presents an efficient implementation, termed IRLS MUSSELS, that enables faster reconstruction to enhance its utility for high-resolution diffusion MRI studies.

METHODS

The recently proposed MUSSELS reconstruction belongs to a new class of parallel imaging-based methods that recover artifact-free DWIs from msDW data without needing phase compensation. The reconstruction is achieved via structured low-rank matrix completion algorithms, which are computationally demanding due to the large size of the Hankel matrices and their associated computations involving singular value decompositions. Because of this, computational demands of the MUSSELS reconstruction scales as the matrix size and the number of shots increases, which hinders its practical utility for high-resolution applications. In this work, we derive a computationally efficient MUSSELS formulation by modifying the iterative reweighted least squares (IRLS) method that were proposed earlier to solve such problems. Using whole-brain in vivo data, we show the utility of the IRLS MUSSELS for routine high-resolution studies with reduced computational burden.

RESULTS

IRLS MUSSELS provides about five times faster reconstruction for matrix sizes 192 × 192 and 256 × 256 compared to the earlier MUSSELS implementation. The widely employed conjugate symmetry priors can also be incorporated into IRLS MUSSELS to reduce blurring of the partial Fourier acquisitions, without incurring much computational burden.

CONCLUSIONS

The proposed method is observed to be computationally efficient to enable routine high-resolution studies. The computational complexity matches the traditional msDWI reconstruction methods and provides improved reconstruction results with the additional constraints.

Bio-SCOPE: fast biexponential T1ρ mapping of the brain using signal-compensated low-rank plus sparse matrix decomposition

PURPOSE

To develop and evaluate a fast imaging method based on signal-compensated low-rank plus sparse matrix decomposition to accelerate data acquisition for biexponential brain T_1ρ mapping (Bio-SCOPE).

METHODS

Two novel strategies were proposed to improve reconstruction performance. A variable-rate undersampling scheme was used with a varied acceleration factor for each k-space along the spin-lock time direction, and a modified nonlinear thresholding scheme combined with a feature descriptor was used for Bio-SCOPE reconstruction. In vivo brain T_1ρ mappings were acquired from 4 volunteers. The fully sampled k-space data acquired from 3 volunteers were retrospectively undersampled by net acceleration rates (R) of 4.6 and 6.1. Reference values were obtained from the fully sampled data. The agreement between the accelerated T_1ρ measurements and reference values was assessed with Bland-Altman analyses. Prospectively undersampled data with R = 4.6 and R = 6.1 were acquired from 1 volunteer.

RESULTS

T_1ρ -weighted images were successfully reconstructed using Bio-SCOPE for R = 4.6 and 6.1 with signal-to-noise ratio variations <1 dB and normalized root mean square errors <4%. Accelerated and reference T_1ρ measurements were in good agreement for R = 4.6 (T_{1ρ s} : 18.6651 ± 1.7786 ms; T_{1ρ l} : 88.9603 ± 1.7331 ms) and R = 6.1 (T_{1ρ s} : 17.8403 ± 3.3302 ms; T_{1ρ l} : 88.0275 ± 4.9606 ms) in the Bland-Altman analyses. T_1ρ parameter maps from prospectively undersampled data also show reasonable image quality using the Bio-SCOPE method.

CONCLUSION

Bio-SCOPE achieves a high net acceleration rate for biexponential T_1ρ mapping and improves reconstruction quality by using a variable-rate undersampling data acquisition scheme and a modified soft-thresholding algorithm in image reconstruction.

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.

Quantitative susceptibility map reconstruction using annihilating filter-based low-rank Hankel matrix approach

PURPOSE

Quantitative susceptibility mapping (QSM) inevitably suffers from streaking artifacts caused by zeros on the conical surface of the dipole kernel in k-space. This work proposes a novel and accurate QSM reconstruction method based on k-space low-rank Hankel matrix constraint, avoiding the over-smoothing problem and streaking artifacts.

THEORY AND METHODS

Based on the recent theory of annihilating filter-based low-rank Hankel matrix approach (ALOHA), QSM is formulated as deconvolution under low-rank Hankel matrix constraint in the k-space. The computational complexity and the high memory burden were reduced by successive reconstruction of 2-D planes along 3 independent axes of the 3-D phase image in Fourier domain. Feasibility of the proposed method was tested on a simulated phantom and human data and were compared with existing QSM reconstruction methods.

RESULTS

The proposed ALOHA-QSM effectively reduced streaking artifacts and accurately estimated susceptibility values in deep gray matter structures, compared to the existing QSM methods.

CONCLUSIONS

The suggested ALOHA-QSM algorithm successfully solves the 3-dimensional QSM dipole inversion problem using k-space low rank property with no anatomical constraint. ALOHA-QSM can provide detailed brain structures and accurate susceptibility values with no streaking artifacts.

k-Space deep learning for reference-free EPI ghost correction

PURPOSE

Nyquist ghost artifacts in echo planar imaging (EPI) are originated from phase mismatch between the even and odd echoes. However, conventional correction methods using reference scans often produce erroneous results especially in high-field MRI due to the nonlinear and time-varying local magnetic field changes. Recently, it was shown that the problem of ghost correction can be reformulated as k-space interpolation problem that can be solved using structured low-rank Hankel matrix approaches. Another recent work showed that data driven Hankel matrix decomposition can be reformulated to exhibit similar structures as deep convolutional neural network. By synergistically combining these findings, we propose a k-space deep learning approach that immediately corrects the phase mismatch without a reference scan in both accelerated and non-accelerated EPI acquisitions.

THEORY AND METHODS

To take advantage of the even and odd-phase directional redundancy, the k-space data are divided into 2 channels configured with even and odd phase encodings. The redundancies between coils are also exploited by stacking the multi-coil k-space data into additional input channels. Then, our k-space ghost correction network is trained to learn the interpolation kernel to estimate the missing virtual k-space data. For the accelerated EPI data, the same neural network is trained to directly estimate the interpolation kernels for missing k-space data from both ghost and subsampling.

RESULTS

Reconstruction results using 3T and 7T in vivo data showed that the proposed method outperformed the image quality compared to the existing methods, and the computing time is much faster.

CONCLUSIONS

The proposed k-space deep learning for EPI ghost correction is highly robust and fast, and can be combined with acceleration, so that it can be used as a promising correction tool for high-field MRI without changing the current acquisition protocol.

SUPER: A blockwise curve-fitting method for accelerating MR parametric mapping with fast reconstruction

PURPOSE

To investigate Shift Undersampling improves Parametric mapping Efficiency and Resolution (SUPER), a novel blockwise curve-fitting method for accelerating parametric mapping with very fast reconstruction.

METHODS

SUPER uses interleaved k-space undersampling, which enables a blockwise decomposition of the otherwise large-scale cost function to improve the reconstruction efficiency. SUPER can be readily combined with SENSE to achieve at least 4-fold acceleration. D-factor, a parametric-mapping counterpart of g-factor, was proposed and formulated to compare spatially heterogeneous noise amplification because of different acceleration methods. As a proof-of-concept, SUPER/SUPER-SENSE was validated using T1 mapping, by comparing them to alternative model-based methods, including MARTINI and GRAPPATINI, via simulations, phantom imaging, and in vivo brain imaging (N = 5), over criteria of normalized root-mean-squares error (NRMSE), average d-factor, and computational time per voxel (TPV). A novel SUPER-SENSE MOLLI cardiac T1 -mapping sequence with improved resolution (1.4 mm × 1.4 mm) was compared to standard MOLLI (1.9 mm × 2.5 mm) in 8 healthy subjects.

RESULTS

In brain imaging, 2-fold SUPER achieved lower NRMSE (0.04 ± 0.02 vs. 0.11 ± 0.02, P < 0.01), lower average d-factor (1.01 ± 0.002 vs. 1.12 ± 0.004, P < 0.001), and lower TPV (4.6 ms ± 0.2 ms vs. 79 ms ± 3 ms, P < 0.001) than 2-fold MARTINI. Similarly, 4-fold SUPER-SENSE achieved lower NRMSE (0.07 ± 0.01 vs. 0.13 ± 0.03, P = 0.02), lower average d-factor (1.15 ± 0.01 vs. 1.20 ± 0.01, P < 0.001), and lower TPV (4.0 ms ± 0.1 ms vs. 72 ms ± 3 ms, P < 0.001) than 4-fold GRAPPATINI. In cardiac T1 mapping, SUPER-SENSE MOLLI yielded similar myocardial T1 (1151 ms ± 63 ms vs. 1159 ms ± 32 ms, P = 0.6), slightly lower blood T1 (1643 ms ± 86 ms vs. 1680 ms ± 79 ms, P = 0.004), but improved spatial resolution compared with standard MOLLI in the same imaging time.

CONCLUSION

SUPER and SUPER-SENSE provide fast model-based reconstruction methods for accelerating parametric mapping and improving its clinical appeal.

Compressed sensing MRI: a review from signal processing perspective

Magnetic resonance imaging (MRI) is an inherently slow imaging modality, since it acquires multi-dimensional k-space data through 1-D free induction decay or echo signals. This often limits the use of MRI, especially for high resolution or dynamic imaging. Accordingly, many investigators has developed various acceleration techniques to allow fast MR imaging. For the last two decades, one of the most important breakthroughs in this direction is the introduction of compressed sensing (CS) that allows accurate reconstruction from sparsely sampled k-space data. The recent FDA approval of compressed sensing products for clinical scans clearly reflect the maturity of this technology. Therefore, this paper reviews the basic idea of CS and how this technology have been evolved for various MR imaging problems.

MANTIS: Model-Augmented Neural neTwork with Incoherent k-space Sampling for efficient MR parameter mapping

PURPOSE

To develop and evaluate a novel deep learning-based image reconstruction approach called MANTIS (Model-Augmented Neural neTwork with Incoherent k-space Sampling) for efficient MR parameter mapping.

METHODS

MANTIS combines end-to-end convolutional neural network (CNN) mapping, incoherent k-space undersampling, and a physical model as a synergistic framework. The CNN mapping directly converts a series of undersampled images straight into MR parameter maps using supervised training. Signal model fidelity is enforced by adding a pathway between the undersampled k-space and estimated parameter maps to ensure that the parameter maps produced synthesized k-space consistent with the acquired undersampling measurements. The MANTIS framework was evaluated on the T₂ mapping of the knee at different acceleration rates and was compared with 2 other CNN mapping methods and conventional sparsity-based iterative reconstruction approaches. Global quantitative assessment and regional T₂ analysis for the cartilage and meniscus were performed to demonstrate the reconstruction performance of MANTIS.

RESULTS

MANTIS achieved high-quality T₂ mapping at both moderate (R = 5) and high (R = 8) acceleration rates. Compared to conventional reconstruction approaches that exploited image sparsity, MANTIS yielded lower errors (normalized root mean square error of 6.1% for R = 5 and 7.1% for R = 8) and higher similarity (structural similarity index of 86.2% at R = 5 and 82.1% at R = 8) to the reference in the T₂ estimation. MANTIS also achieved superior performance compared to direct CNN mapping and a 2-step CNN method.

CONCLUSION

The MANTIS framework, with a combination of end-to-end CNN mapping, signal model-augmented data consistency, and incoherent k-space sampling, is a promising approach for efficient and robust estimation of quantitative MR parameters.

Accelerated 3D T2 mapping with dictionary-based matching for prostate imaging

PURPOSE

To develop a fast and accurate method for 3D T2 mapping of prostate cancer using undersampled acquisition and dictionary-based fitting.

METHODS

3D high-resolution T2 -weighted images (0.9 × 0.9 × 3 mm3 ) were obtained with a multishot T2 -prepared balanced steady-state free precession (T2 -prep-bSSFP) acquisition sequence using a 3D variable density undersampled Cartesian trajectory. Each T2 -weighted image was reconstructed using total variation regularized sensitivity encoding. A flexible simulation framework based on extended phase graphs generated a dictionary of magnetization signals, which was customized to the proposed sequence. The dictionary was matched to the acquired T2 -weighted images to retrieve quantitative T2 values, which were then compared to gold-standard spin echo acquisition values using monoexponential fitting. The proposed approach was validated in simulations and a T1 /T2 phantom, and feasibility was tested in 8 healthy subjects.

RESULTS

The simulation analysis showed that the proposed T2 mapping approach is robust to noise and typically observed T1 variations. T2 values obtained in the phantom with T2 prep-bSSFP and the acquisition-specific, dictionary-based matching were highly correlated with the gold-standard spin echo method (r = 0.99). Furthermore, no differences were observed with the accelerated acquisition compared to the fully sampled acquisition (r = 0.99). T2 values obtained in prostate peripheral zone, central gland, and muscle in healthy subjects (age, 26 ± 6 years) were 97 ± 14, 76 ± 7, and 36 ± 3 ms, respectively.

CONCLUSION

3D quantitative T2 mapping of the whole prostate can be achieved in 3 minutes.

ENLIVE: An Efficient Nonlinear Method for Calibrationless and Robust Parallel Imaging

Robustness against data inconsistencies, imaging artifacts and acquisition speed are crucial factors limiting the possible range of applications for magnetic resonance imaging (MRI). Therefore, we report a novel calibrationless parallel imaging technique which simultaneously estimates coil profiles and image content in a relaxed forward model. Our method is robust against a wide class of data inconsistencies, minimizes imaging artifacts and is comparably fast, combining important advantages of many conceptually different state-of-the-art parallel imaging approaches. Depending on the experimental setting, data can be undersampled well below the Nyquist limit. Here, even high acceleration factors yield excellent imaging results while being robust to noise and the occurrence of phase singularities in the image domain, as we show on different data. Moreover, our method successfully reconstructs acquisitions with insufficient field-of-view. We further compare our approach to ESPIRiT and SAKE using spin-echo and gradient echo MRI data from the human head and knee. In addition, we show its applicability to non-Cartesian imaging on radial FLASH cardiac MRI data. Using theoretical considerations, we show that ENLIVE can be related to a low-rank formulation of blind multi-channel deconvolution, explaining why it inherently promotes low-rank solutions.