Accelerated exponential parameterization of T2 relaxation with model-driven low rank and sparsity priors (MORASA)

QRAGE-Simultaneous multiparametric quantitative MRI of water content, T1, T2*, and magnetic susceptibility at ultrahigh field strength

PURPOSE

To introduce quantitative rapid gradient-echo (QRAGE), a novel approach for the simultaneous mapping of multiple quantitative MRI parameters, including water content, T1, T2*, and magnetic susceptibility at ultrahigh field strength.

METHODS

QRAGE leverages a newly developed multi-echo MPnRAGE sequence, facilitating the acquisition of 171 distinct contrast images across a range of TI and TE points. To maintain a short acquisition time, we introduce MIRAGE2, a novel model-based reconstruction method that exploits prior knowledge of temporal signal evolution, represented as damped complex exponentials. MIRAGE2 minimizes local Block-Hankel and Casorati matrices. Parameter maps are derived from the reconstructed contrast images through postprocessing steps. We validate QRAGE through extensive simulations, phantom studies, and in vivo experiments, demonstrating its capability for high-precision imaging.

RESULTS

In vivo brain measurements show the promising performance of QRAGE, with test-retest SDs and deviations from reference methods of < 0.8% for water content, < 17 ms for T1, and < 0.7 ms for T2*. QRAGE achieves whole-brain coverage at a 1-mm isotropic resolution in just 7 min and 15 s, comparable to the acquisition time of an MP2RAGE scan. In addition, QRAGE generates a contrast image akin to the UNI image produced by MP2RAGE.

CONCLUSION

QRAGE is a new, successful approach for simultaneously mapping multiple MR parameters at ultrahigh field.

Ultrafast T2 and T2* mapping using single-shot spatiotemporally encoded MRI with reduced field of view and spiral out-in-out-in trajectory

BACKGROUND

T2 and T2* mapping are crucial components of quantitative magnetic resonance imaging, offering valuable insights into tissue characteristics and pathology. Single-shot methods can achieve ultrafast T2 or T2* mapping by acquiring multiple readout echo trains. However, the extended echo trains pose challenges, such as compromised image quality and diminished quantification accuracy.

PURPOSE

In this study, we develop a single-shot method for ultrafast T2 and T2* mapping with reduced echo train length.

METHODS

The proposed method is based on ultrafast single-shot spatiotemporally encoded (SPEN) MRI combined with reduced field of view (FOV) and spiral out-in-out-in (OIOI) trajectory. Specifically, a biaxial SPEN excitation scheme was employed to excite the spin signal into the spatiotemporal encoding domain. The OIOI trajectory with high acquisition efficiency was employed to acquire signals within targeted reduced FOV. Through non-Cartesian super-resolved (SR) reconstruction, 12 aliasing-free images with different echo times were obtained within 150 ms. These images were subsequently fitted to generate T2 or T2* mapping simultaneously using a derived model.

RESULTS

Accurate and co-registered T2 and T2* maps were generated, closely resembling the reference maps. Numerical simulations demonstrated substantial consistency (R2 > 0.99) with the ground truth values. A mean difference of 0.6% and 1.7% was observed in T2 and T2*, respectively, in in vivo rat brain experiments compared to the reference. Moreover, the proposed method successfully obtained T2 and T2* mappings of rat kidney in free-breathing mode, demonstrating its superiority over multishot methods lacking respiratory navigation.

CONCLUSIONS

The results suggest that the proposed method can achieve ultrafast and accurate T2 and T2* mapping, potentially facilitating the application of T2 and T2* mapping in scenarios requiring high temporal resolution.

Fast and High-Resolution T2 Mapping Based on Echo Merging Plus k-t Undersampling with Reduced Refocusing Flip Angles (TEMPURA) as Methods for Human Renal MRI

PURPOSE

To develop a highly accelerated multi-echo spin-echo method, TEMPURA, for reducing the acquisition time and/or increasing spatial resolution for kidney T2 mapping.

METHODS

TEMPURA merges several adjacent echoes into one k-space by either combining independent echoes or sharing one echo between k-spaces. The combined k-space is reconstructed based on compressed sensing theory. Reduced flip angles are used for the refocusing pulses, and the extended phase graph algorithm is used to correct the effects of indirect echoes. Two sequences were developed: a fast breath-hold sequence; and a high-resolution sequence. The performance was evaluated prospectively on a phantom, 16 healthy subjects, and two patients with different types of renal tumors.

RESULTS

The fast TEMPURA method reduced the acquisition time from 3-5 min to one breath-hold (18 s). Phantom measurements showed that fast TEMPURA had a mean absolute percentage error (MAPE) of 8.2%, which was comparable to a standardized respiratory-triggered sequence (7.4%), but much lower than a sequence accelerated by purely k-t undersampling (21.8%). High-resolution TEMPURA reduced the in-plane voxel size from 3 × 3 to 1 × 1 mm2, resulting in improved visualization of the detailed anatomical structure. In vivo T2 measurements demonstrated good agreement (fast: MAPE = 1.3%-2.5%; high-resolution: MAPE = 2.8%-3.3%) and high correlation coefficients (fast: R = 0.85-0.98; high-resolution: 0.82-0.96) with the standardized method, outperforming k-t undersampling alone (MAPE = 3.3-4.5%, R = 0.57-0.59).

CONCLUSION

TEMPURA provides fast and high-resolution renal T2 measurements. It has the potential to improve clinical throughput and delineate intratumoral heterogeneity and tissue habitats at unprecedented spatial resolution.

Cartilage compositional MRI-a narrative review of technical development and clinical applications over the past three decades

Articular cartilage damage and degeneration are among hallmark manifestations of joint injuries and arthritis, classically osteoarthritis. Cartilage compositional MRI (Cart-C MRI), a quantitative technique, which aims to detect early-stage cartilage matrix changes that precede macroscopic alterations, began development in the 1990s. However, despite the significant advancements over the past three decades, Cart-C MRI remains predominantly a research tool, hindered by various technical and clinical hurdles. This paper will review the technical evolution of Cart-C MRI, delve into its clinical applications, and conclude by identifying the existing gaps and challenges that need to be addressed to enable even broader clinical application of Cart-C MRI.

Highly accelerated parameter mapping using model-based alternating reconstruction coupling fitting

Objective.A model-based alternating reconstruction coupling fitting, termed Model-based Alternating Reconstruction COupling fitting (MARCO), is proposed for accurate and fast magnetic resonance parameter mapping.Approach.MARCO utilizes the signal model as a regularization by minimizing the bias between the image series and the signal produced by the suitable signal model based on iteratively updated parameter maps when reconstructing. The technique can incorporate prior knowledge of both image series and parameters by adding sparsity constraints. The optimization problem is decomposed into three subproblems and solved through three alternating steps involving reconstruction and nonlinear least-square fitting, which can produce both contrast-weighted images and parameter maps simultaneously.Main results.The algorithm is applied toT2mapping with extended phase graph algorithm integrated and validated on undersampled multi-echo spin-echo data from both phantom and in vivo sources. Compared with traditional compressed sensing and model-based methods, the proposed approach yields more accurateT2maps with more details at high acceleration factors.Significance.The proposed method provides a basic framework for quantitative MR relaxometry, theoretically applicable to all quantitative MR relaxometry. It has the potential to improve the diagnostic utility of quantitative imaging techniques.

Learning Disentangled Representation for Multidimensional MR Image Reconstruction

We proposed a new way to represent and reconstruct multidimensional MR images. Specifically, a representation capable of disentangling different types of features in high-dimensional images was learned via training an autoencoder with separated sets of latent spaces for image style transfer, e.g., contrast or geometry transfer. A latent diffusion model was introduced to capture the distributions of the disentangled latents for constrained reconstruction. A new formulation was developed to integrate the pre-learned representation with other complementary constraints for reconstruction from sparse data. We demonstrated the ability of our model to disentangle contrast and geometry features in multicontrast MR images, and its effectiveness in accelerated T1 and T2 mapping.

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.

High-Dimensional MR Reconstruction Integrating Subspace and Adaptive Generative Models

OBJECTIVE

To develop a new method that integrates subspace and generative image models for high-dimensional MR image reconstruction.

METHODS

We proposed a formulation that synergizes a low-dimensional subspace model of high-dimensional images, an adaptive generative image prior serving as spatial constraints on the sequence of "contrast-weighted" images or spatial coefficients of the subspace model, and a conventional sparsity regularization. A special pretraining plus subject-specific network adaptation strategy was proposed to construct an accurate generative-network-based representation for images with varying contrasts. An iterative algorithm was introduced to jointly update the subspace coefficients and the multi-resolution latent space of the generative image model that leveraged an recently proposed intermediate layer optimization technique for network inversion.

RESULTS

We evaluated the utility of the proposed method for two high-dimensional imaging applications: accelerated MR parameter mapping and high-resolution MR spectroscopic imaging. Improved performance over state-of-the-art subspace-based methods was demonstrated in both cases.

CONCLUSION

The proposed method provided a new way to address high-dimensional MR image reconstruction problems by incorporating an adaptive generative model as a data-driven spatial prior for constraining subspace reconstruction.

SIGNIFICANCE

Our work demonstrated the potential of integrating data-driven and adaptive generative priors with canonical low-dimensional modeling for high-dimensional imaging problems.

Strategically Acquired Gradient Echo (STAGE) Imaging, part IV: Constrained Reconstruction of White Noise (CROWN) Processing as a Means to Improve Signal-to-Noise in STAGE Imaging at 3 Tesla

Increasing the signal-to-noise ratio (SNR) has always been of critical importance for magnetic resonance imaging. Although increasing field strength provides a linear increase in SNR, it is more and more costly as field strength increases. Therefore, there is a major effort today to use signal processing methods to improve SNR since it is more efficient and economical. There are a variety of methods to improve SNR such as averaging the data at the expense of imaging time, or collecting the data with a lower resolution, all of these methods, including imaging processing methods, usually come at the expense of loss of image detail or image blurring. Therefore, we developed a new mathematical approach called CROWN (Constrained Reconstruction of White Noise) to enhance SNR without loss of structural detail and without affecting scanning time. In this study, we introduced and tested the concept behind CROWN specifically for STAGE (strategically acquired gradient echo) imaging. The concept itself is presented first, followed by simulations to demonstrate its theoretical effectiveness. Then the SNR improvement on proton spin density (PSD) and R2⁎ maps was investigated using brain STAGE data acquired from 10 healthy controls (HCs) and 10 patients with Parkinson's disease (PD). For the PSD and R2* maps, the SNR and CNR between white matter and gray matter were improved by a factor of 1.87 ± 0.50 and 1.72 ± 0.88, respectively. The white matter hyperintensity lesions in PD patients were more clearly defined after CROWN processing. Using these improved maps, simulated images for any repeat time, echo time or flip angle can be created with improved SNR. The potential applications of this technology are to trade off the increased SNR for higher resolution images and/or faster imaging.

Feasibility of transient nuclear Overhauser effect imaging in brain at 7 T

PURPOSE

The nuclear Overhauser effect (NOE) quantification from the steady-state NOE imaging suffers from multiple confounding non-NOE-specific sources, including direct saturation, magnetization transfer, and relevant chemical exchange species, and is affected by B₀ and B₁ ⁺ inhomogeneities. The B₀ -dependent and B₁ ⁺ -dependent data needed for deconvolving these confounding effects would increase the scan time substantially, leading to other issues such as patient tolerability. Here, we demonstrate the feasibility of brain lipid mapping using an easily implementable transient NOE (tNOE) approach.

METHODS

This 7T study used a frequency-selective inversion pulse at a range of frequency offsets between 1.0 and 5.0 parts per million (ppm) and -5.0 and -1.0 ppm relative to bulk water peak. This was followed by a fixed/variable mixing time and then a single-shot 2D turbo FLASH readout. The feasibility of tNOE measurements is demonstrated on bovine serum albumin phantoms and healthy human brains.

RESULTS

The tNOE measurements from bovine serum albumin phantoms were found to be independent of physiological pH variations. Both bovine serum albumin phantoms and human brains showed broad tNOE contributions centered at approximately -3.5 ppm relative to water peak, with presumably aliphatic moieties in lipids and proteins being the dominant contributors. Less prominent tNOE contributions of approximately +2.5 ppm relative to water, presumably from aromatic moieties, were also detected. These aromatic signals were free from any CEST signals.

CONCLUSION

In this study, we have demonstrated the feasibility of tNOE in human brain at 7 T. This method is more scan-time efficient than steady-state NOE and provides NOE measurement with minimal confounders.

LARO: Learned acquisition and reconstruction optimization to accelerate quantitative susceptibility mapping

Quantitative susceptibility mapping (QSM) involves acquisition and reconstruction of a series of images at multi-echo time points to estimate tissue field, which prolongs scan time and requires specific reconstruction technique. In this paper, we present our new framework, called Learned Acquisition and Reconstruction Optimization (LARO), which aims to accelerate the multi-echo gradient echo (mGRE) pulse sequence for QSM. Our approach involves optimizing a Cartesian multi-echo k-space sampling pattern with a deep reconstruction network. Next, this optimized sampling pattern was implemented in an mGRE sequence using Cartesian fan-beam k-space segmenting and ordering for prospective scans. Furthermore, we propose to insert a recurrent temporal feature fusion module into the reconstruction network to capture signal redundancies along echo time. Our ablation studies show that both the optimized sampling pattern and proposed reconstruction strategy help improve the quality of the multi-echo image reconstructions. Generalization experiments show that LARO is robust on the test data with new pathologies and different sequence parameters. Our code is available at https://github.com/Jinwei1209/LARO-QSM.git.

SuperMAP: Deep ultrafast MR relaxometry with joint spatiotemporal undersampling

PURPOSE

To develop an ultrafast and robust MR parameter mapping network using deep learning.

THEORY AND METHODS

We design a deep learning framework called SuperMAP that directly converts a series of undersampled (both in k-space and parameter-space) parameter-weighted images into several quantitative maps, bypassing the conventional exponential fitting procedure. We also present a novel technique to simultaneously reconstruct T1rho and T2 relaxation maps within a single scan. Full data were acquired and retrospectively undersampled for training and testing using traditional and state-of-the-art techniques for comparison. Prospective data were also collected to evaluate the trained network. The performance of all methods is evaluated using the parameter qualification errors and other metrics in the segmented regions of interest.

RESULTS

SuperMAP achieved accurate T1rho and T2 mapping with high acceleration factors (R = 24 and R = 32). It exploited both spatial and temporal information and yielded low error (normalized mean square error of 2.7% at R = 24 and 2.8% at R = 32) and high resemblance (structural similarity of 97% at R = 24 and 96% at R = 32) to the gold standard. The network trained with retrospectively undersampled data also works well for the prospective data (with a slightly lower acceleration factor). SuperMAP is also superior to conventional methods.

CONCLUSION

Our results demonstrate the feasibility of generating superfast MR parameter maps through very few undersampled parameter-weighted images. SuperMAP can simultaneously generate T1rho and T2 relaxation maps in a short scan time.

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.

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.

Reducing the Effects of Motion Artifacts in fMRI: A Structured Matrix Completion Approach

Functional MRI (fMRI) is widely used to study the functional organization of normal and pathological brains. However, the fMRI signal may be contaminated by subject motion artifacts that are only partially mitigated by motion correction strategies. These artifacts lead to distance-dependent biases in the inferred signal correlations. To mitigate these spurious effects, motion-corrupted volumes are censored from fMRI time series. Censoring can result in discontinuities in the fMRI signal, which may lead to substantial alterations in functional connectivity analysis. We propose a new approach to recover the missing entries from censoring based on structured low rank matrix completion. We formulated the artifact-reduction problem as the recovery of a super-resolved matrix from unprocessed fMRI measurements. We enforced a low rank prior on a large structured matrix, formed from the samples of the time series, to recover the missing entries. The recovered time series, in addition to being motion compensated, are also slice-time corrected at a fine temporal resolution. To achieve a fast and memory-efficient solution for our proposed optimization problem, we employed a variable splitting strategy. We validated the algorithm with simulations, data acquired under different motion conditions, and datasets from the ABCD study. Functional connectivity analysis showed that the proposed reconstruction resulted in connectivity matrices with lower errors in pair-wise correlation than non-censored and censored time series based on a standard processing pipeline. In addition, seed-based correlation analyses showed improved delineation of the default mode network. These demonstrate that the method can effectively reduce the adverse effects of motion in fMRI analysis.

Deep learning-enhanced T1 mapping with spatial-temporal and physical constraint

PURPOSE

To propose a reconstruction framework to generate accurate T₁ maps for a fast MR T₁ mapping sequence.

METHODS

A deep learning-enhanced T₁ mapping method with spatial-temporal and physical constraint (DAINTY) was proposed. This method explicitly imposed low-rank and sparsity constraints on the multiframe T₁ -weighted images to exploit the spatial-temporal correlation. A deep neural network was used to efficiently perform T₁ mapping as well as denoise and reduce undersampling artifacts. Additionally, the physical constraint was used to build a bridge between low-rank and sparsity constraint and deep learning prior, so the benefits of constrained reconstruction and deep learning can be both available. The DAINTY method was trained on simulated brain data sets, but tested on real acquired phantom, 6 healthy volunteers, and 7 atherosclerosis patients, compared with the narrow-band k-space-weighted image contrast filter conjugate-gradient SENSE (NK-CS) method, kt-sparse-SENSE (kt-SS) method, and low-rank plus sparsity (L+S) method with least-squares T₁ fitting and direct deep learning mapping.

RESULTS

The DAINTY method can generate more accurate T₁ maps and higher-quality T₁ -weighted images compared with other methods. For atherosclerosis patients, the intraplaque hemorrhage can be successfully detected. The computation speed of DAINTY was 10 times faster than traditional methods. Meanwhile, DAINTY can reconstruct images with comparable quality using only 50% of k-space data.

CONCLUSION

The proposed method can provide accurate T₁ maps and good-quality T₁ -weighted images with high efficiency.

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.

Resolution-dependent influences of compressed sensing in quantitative T2 mapping of articular cartilage

This study evaluates the resolution-dependent influences of compressed sensing (CS) in MRI quantification of T2 mapping in articular cartilage with osteoarthritis (OA). T2-weighed 2D experiments of healthy and OA cartilage were fully sampled in k-space with five echo times at both 17.6 μm and 195.3 μm in-plane resolutions; termed as microscopic MRI (μMRI) and macroscopic MRI (mMRI) respectively. These fully sampled k-space data were under-sampled at various 2D CS accelerating factors (AF = 4-32). The under-sampled data were reconstructed individually into 2D images using nonlinear reconstruction, which were used to calculate the T2 maps. The bulk and zonal variations of T2 values in cartilage were evaluated at different AFs. The study finds that the T2 images at AFs up to 8 preserved major visual information and produced negligible artifacts for μMRI. The T2 values remained accurate for different sub-tissue zones at various AFs. The absolute difference between the CS (AF up to 32) and the Ground Truth (i.e., using 100% of the k-space data) of the mean T2 values through the whole tissue depth was higher in mMRI versus μMRI. For mMRI (where the resolution mimics the clinical MRI of human cartilage), the quantitative T2 mapping at AFs up to 4 showed negligible variations. This study demonstrates that both clinical MRI and μMRI can benefit from the use of CS in image acquisition, and μMRI benefits more from the use of CS by acquiring much less data, without losing significant accuracy in the quantification of T2 maps in osteoarthritic cartilage.

Quantitative T2 mapping using accelerated 3D stack-of-spiral gradient echo readout

PURPOSE

To develop a rapid T2 mapping protocol using optimized spiral acquisition, accelerated reconstruction, and model fitting.

MATERIALS AND METHODS

A T2-prepared stack-of-spiral gradient echo (GRE) pulse sequence was applied. A model-based approach joined with compressed sensing was compared with the two methods applied separately for accelerated reconstruction and T2 mapping. A 2-parameter-weighted fitting method was compared with 2- or 3-parameter models for accurate T2 estimation under the influences of noise and B1 inhomogeneity. The performance was evaluated using both digital phantoms and healthy volunteers. Mitigating partial voluming with cerebrospinal fluid (CSF) was also tested.

RESULTS

Simulations demonstrates that the 2-parameter-weighted fitting approach was robust to a large range of B1 scales and SNR levels. With an in-plane acceleration factor of 5, the model-based compressed sensing-incorporated method yielded around 8% normalized errors compared to references. The T2 estimation with and without CSF nulling was consistent with literature values.

CONCLUSION

This work demonstrated the feasibility of a T2 quantification technique with 3D high-resolution and whole-brain coverage in 2-3 min. The proposed iterative reconstruction method, which utilized the model consistency, data consistency and spatial sparsity jointly, provided reasonable T2 estimation. The technique also allowed mitigation of CSF partial volume effect.

Accelerated MR-STAT Reconstructions Using Sparse Hessian Approximations

MR-STAT is a quantitative magnetic resonance imaging framework for obtaining multi-parametric quantitative tissue parameter maps using data from single short scans. A large-scale optimization problem is solved in which spatial localization of signal and estimation of tissue parameters are performed simultaneously by directly fitting a Bloch-based volumetric signal model to measured time-domain data. In previous work, a highly parallelized, matrix-free Gauss-Newton reconstruction algorithm was presented that can solve the large-scale optimization problem for high-resolution scans. The main computational bottleneck in this matrix-free method is solving a linear system involving (an approximation to) the Hessian matrix at each iteration. In the current work, we analyze the structure of the Hessian matrix in relation to the dynamics of the spin system and derive conditions under which the (approximate) Hessian admits a sparse structure. In the case of Cartesian sampling patterns with smooth RF trains we demonstrate how exploiting this sparsity can reduce MR-STAT reconstruction times by approximately an order of magnitude.

A multi-scale residual network for accelerated radial MR parameter mapping

A deep learning MR parameter mapping framework which combines accelerated radial data acquisition with a multi-scale residual network (MS-ResNet) for image reconstruction is proposed. The proposed supervised learning strategy uses input image patches from multi-contrast images with radial undersampling artifacts and target image patches from artifact-free multi-contrast images. Subspace filtering is used during pre-processing to denoise input patches. For each anatomy and relaxation parameter, an individual network is trained. in vivo T1 mapping results are obtained on brain and abdomen datasets and in vivo T2 mapping results are obtained on brain and knee datasets. Quantitative results for the T2 mapping of the knee show that MS-ResNet trained using either fully sampled or undersampled data outperforms conventional model-based compressed sensing methods. This is significant because obtaining fully sampled training data is not possible in many applications. in vivo brain and abdomen results for T1 mapping and in vivo brain results for T2 mapping demonstrate that MS-ResNet yields contrast-weighted images and parameter maps that are comparable to those achieved by model-based iterative methods while offering two orders of magnitude reduction in reconstruction times. The proposed approach enables recovery of high-quality contrast-weighted images and parameter maps from highly accelerated radial data acquisitions. The rapid image reconstructions enabled by the proposed approach makes it a good candidate for routine clinical use.

MULTI-ECHO RECOVERY WITH FIELD INHOMOGENEITY COMPENSATION USING STRUCTURED LOW-RANK MATRIX COMPLETION

Echo-planar imaging (EPI), which is the main workhorse of functional MRI, suffers from field inhomogeneity-induced geometric distortions. The amount of distortion is proportional to the readout duration, which restricts the maximum achievable spatial resolution. The spatially varying nature of the T 2 * decay makes it challenging for EPI schemes with a single echo time to obtain good sensitivity to functional activations in different brain regions. Despite the use of parallel MRI and multislice acceleration, the number of different echo times that can be acquired in a reasonable TR is limited. The main focus of this work is to introduce a rosette-based acquisition scheme and a structured low-rank reconstruction algorithm to overcome the above challenges. The proposed scheme exploits the exponential structure of the time series to recover distortion-free images from several echoes simultaneously.

Structured Low-Rank Algorithms: Theory, Magnetic Resonance Applications, and Links to Machine Learning

In this survey, we provide a detailed review of recent advances in the recovery of continuous domain multidimensional signals from their few non-uniform (multichannel) measurements using structured low-rank matrix completion formulation. This framework is centered on the fundamental duality between the compactness (e.g., sparsity) of the continuous signal and the rank of a structured matrix, whose entries are functions of the signal. This property enables the reformulation of the signal recovery as a low-rank structured matrix completion, which comes with performance guarantees. We will also review fast algorithms that are comparable in complexity to current compressed sensing methods, which enables the application of the framework to large-scale magnetic resonance (MR) recovery problems. The remarkable flexibility of the formulation can be used to exploit signal properties that are difficult to capture by current sparse and low-rank optimization strategies. We demonstrate the utility of the framework in a wide range of MR imaging (MRI) applications, including highly accelerated imaging, calibration-free acquisition, MR artifact correction, and ungated dynamic MRI.

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.

Accelerated mono- and biexponential 3D-T1ρ relaxation mapping of knee cartilage using golden angle radial acquisitions and compressed sensing

PURPOSE

To use golden-angle radial sampling and compressed sensing (CS) for accelerating mono- and biexponential 3D spin-lattice relaxation time in the rotating frame (T_1ρ ) mapping of knee cartilage.

METHODS

Golden-angle radial stack-of-stars and Cartesian 3D-T_1ρ -weighted knee cartilage datasets (n = 12) were retrospectively undersampled by acceleration factors (AFs) 2-10. CS-based reconstruction using 8 different sparsifying transforms were compared for mono- and biexponential T_1ρ -mapping of knee cartilage, including spatio-temporal finite differences, wavelets, dictionary from principal component analysis, and exponential decay models, and also low rank and low rank plus sparse models (L+S). Complex-valued fitting was used and Marchenko-Pastur principal component analysis filtering also tested.

RESULTS

Most CS methods performed well for an AF of 2, with relative median normalized absolute deviation below 10% for monoexponential and biexponential mapping. For monoexponential mapping, radial sampling obtained a median normalized absolute deviation below 10% up to AF of 10, while Cartesian obtained this level of error only up to AF of 4. Radial sampling was also better with biexponential T_1ρ mapping, with median normalized absolute deviation below 10% up to AF of 6.

CONCLUSION

Golden-angle radial acquisitions combined with CS outperformed Cartesian acquisitions for 3D-T_1ρ mapping of knee cartilage, being it is a good alternative to Cartesian sampling for reducing scan time and/or improving image and mapping quality. The methods exponential decay models, spatio-temporal finite differences, and low rank obtained the best results for radial sampling patterns.

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.

High-dimensionality undersampled patch-based reconstruction (HD-PROST) for accelerated multi-contrast MRI

PURPOSE

To develop a new high-dimensionality undersampled patch-based reconstruction (HD-PROST) for highly accelerated 2D and 3D multi-contrast MRI.

METHODS

HD-PROST jointly reconstructs multi-contrast MR images by exploiting the highly redundant information, on a local and non-local scale, and the strong correlation shared between the multiple contrast images. This is achieved by enforcing multi-dimensional low-rank in the undersampled images. 2D magnetic resonance fingerprinting (MRF) phantom and in vivo brain acquisitions were performed to evaluate the performance of HD-PROST for highly accelerated simultaneous T1 and T2 mapping. Additional in vivo experiments for reconstructing multiple undersampled 3D magnetization transfer (MT)-weighted images were conducted to illustrate the impact of HD-PROST for high-resolution multi-contrast 3D imaging.

RESULTS

In the 2D MRF phantom study, HD-PROST provided accurate and precise estimation of the T1 and T2 values in comparison to gold standard spin echo acquisitions. HD-PROST achieved good quality maps for the in vivo 2D MRF experiments in comparison to conventional low-rank inversion reconstruction. T1 and T2 values of white matter and gray matter were in good agreement with those reported in the literature for MRF acquisitions with reduced number of time point images (500 time point images, ~2.5 s scan time). For in vivo MT-weighted 3D acquisitions (6 different contrasts), HD-PROST achieved similar image quality than the fully sampled reference image for an undersampling factor of 6.5-fold.

CONCLUSION

HD-PROST enables multi-contrast 2D and 3D MR images in a short acquisition time without compromising image quality. Ultimately, this technique may increase the potential of conventional parameter mapping.

Calibration-Free B0 Correction of EPI Data Using Structured Low Rank Matrix Recovery

We introduce a structured low rank algorithm for the calibration-free compensation of field inhomogeneity artifacts in echo planar imaging (EPI) MRI data. We acquire the data using two EPI readouts that differ in echo-time. Using time segmentation, we reformulate the field inhomogeneity compensation problem as the recovery of an image time series from highly undersampled Fourier measurements. The temporal profile at each pixel is modeled as a single exponential, which is exploited to fill in the missing entries. We show that the exponential behavior at each pixel, along with the spatial smoothness of the exponential parameters, can be exploited to derive a 3-D annihilation relation in the Fourier domain. This relation translates to a low rank property on a structured multi-fold Toeplitz matrix, whose entries correspond to the measured k-space samples. We introduce a fast two-step algorithm for the completion of the Toeplitz matrix from the available samples. In the first step, we estimate the null space vectors of the Toeplitz matrix using only its fully sampled rows. The null space is then used to estimate the signal subspace, which facilitates the efficient recovery of the time series of images. We finally demonstrate the proposed approach on spherical MR phantom data and human data and show that the artifacts are significantly reduced.

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.

Rapid compositional mapping of knee cartilage with compressed sensing MRI

More than a decade after the introduction of compressed sensing (CS) in MRI, researchers are still working on ways to translate it into different research and clinical applications. The greatest advantage of CS in MRI is the reduced amount of k-space data needed to reconstruct images, which can be exploited to reduce scan time or to improve spatial resolution and volumetric coverage. Efficient data acquisition using CS is extremely important for compositional mapping of the musculoskeletal system in general and knee cartilage mapping techniques in particular. High-resolution quantitative information about tissue biochemical composition could be obtained in just a few minutes using CS MRI. However, in order to make this goal a reality, some issues still need to be addressed. In this article we review the current state of the art of CS methods for rapid compositional mapping of knee cartilage. Specifically, data acquisition strategies, image reconstruction algorithms, and data fitting models are discussed. Different CS studies for T2 and T1ρ mapping of knee cartilage are reviewed, with illustrative results. Future directions, opportunities, and challenges of rapid compositional mapping techniques are also discussed. Level of Evidence: 4 Technical Efficacy: Stage 6 J. Magn. Reson. Imaging 2018;47:1185-1198.

Compressed sensing acceleration of biexponential 3D-T1ρ relaxation mapping of knee cartilage

PURPOSE

Use compressed sensing (CS) for 3D biexponential spin-lattice relaxation time in the rotating frame (T_1ρ ) mapping of knee cartilage, reducing the total scan time and maintaining the quality of estimated biexponential T_1ρ parameters (short and long relaxation times and corresponding fractions) comparable to fully sampled scans.

METHODS

Fully sampled 3D-T_1ρ -weighted data sets were retrospectively undersampled by factors 2-10. CS reconstruction using 12 different sparsifying transforms were compared for biexponential T_1ρ -mapping of knee cartilage, including temporal and spatial wavelets and finite differences, dictionary from principal component analysis (PCA), k-means singular value decomposition (K-SVD), exponential decay models, and also low rank and low rank plus sparse models. Synthetic phantom (N = 6) and in vivo human knee cartilage data sets (N = 7) were included in the experiments. Spatial filtering before biexponential T_1ρ parameter estimation was also tested.

RESULTS

Most CS methods performed satisfactorily for an acceleration factor (AF) of 2, with relative median normalized absolute deviation (MNAD) around 10%. Some sparsifying transforms, such as low rank with spatial finite difference (L + S SFD), spatiotemporal finite difference (STFD), and exponential dictionaries (EXP) significantly improved this performance, reaching MNAD below 15% with AF up to 10, when spatial filtering was used.

CONCLUSION

Accelerating biexponential 3D-T_1ρ mapping of knee cartilage with CS is feasible. The best results were obtained by STFD, EXP, and L + S SFD regularizers combined with spatial prefiltering. These 3 CS methods performed satisfactorily on synthetic phantom as well as in vivo knee cartilage for AFs up to 10, with median error below 15%.

SCOPE: signal compensation for low-rank plus sparse matrix decomposition for fast parameter mapping

Magnetic resonance (MR) parameter mapping is useful for many clinical applications. However, its practical utility is limited by the long scan time. To address this problem, this paper developed a novel image reconstruction method for fast MR parameter mapping. The proposed method (SCOPE) used a low-rank plus sparse model to reconstruct the parameter-weighted images from highly undersampled acquisitions. A signal compensation strategy was introduced to promote low rankness along the parametric direction and thus improve the reconstruction accuracy. Specifically, compensation was performed by multiplying the original signal by the inversion of the mono-exponential decay at each voxel. The performance of SCOPE was evaluated via quantitative T _1ρ mapping. The results of the simulation and in vivo experiments with acceleration factors from 3 to 5 are shown. The performance of SCOPE was verified via comparisons with several low-rank and sparsity-based methods. The experimental results showed that the T _1ρ maps obtained using SCOPE were more accurate than those obtained using competing methods and were comparable to the reference, even when the acceleration factor reached 5. SCOPE can greatly reduce the scan time of parameter mapping while still achieving high accuracy. This technique might therefore help facilitate fast MR parameter mapping in clinical use.

Accelerated MR parameter mapping with a union of local subspaces constraint

PURPOSE

A new reconstruction method for multi-contrast imaging and parameter mapping based on a union of local subspaces constraint is presented.

THEORY

Subspace constrained reconstructions use a predetermined subspace to explicitly constrain the relaxation signals. The choice of subspace size ( K ) impacts the approximation error vs noise-amplification tradeoff associated with these methods. A different approach is used in the model consistency constraint (MOCCO) framework to leverage the subspace model to enforce a softer penalty. Our proposed method, MOCCO-LS, augments the MOCCO model with a union of local subspaces (LS) approach. The union of local subspaces model is coupled with spatial support constraints and incorporated into the MOCCO framework to regularize the contrast signals in the scene.

METHODS

The performance of the MOCCO-LS method was evaluated in vivo on T₁ and T₂ mapping of the human brain and with Monte-Carlo simulations and compared against MOCCO and the explicit subspace constrained models.

RESULTS

The results demonstrate a clear improvement in the multi-contrast images and parameter maps. We sweep across the model order space ( K ) to compare the different reconstructions and demonstrate that the reconstructions have different preferential operating points. Experiments on T₂ mapping show that the proposed method yields substantial improvements in performance even when operating at very high acceleration rates.

CONCLUSIONS

The use of a union of local subspace constraints coupled with a sparsity promoting penalty leads to improved reconstruction quality of multi-contrast images and parameter maps.

Joint sparse reconstruction of multi-contrast MRI images with graph based redundant wavelet transform

Background

Multi-contrast images in magnetic resonance imaging (MRI) provide abundant contrast information reflecting the characteristics of the internal tissues of human bodies, and thus have been widely utilized in clinical diagnosis. However, long acquisition time limits the application of multi-contrast MRI. One efficient way to accelerate data acquisition is to under-sample the k-space data and then reconstruct images with sparsity constraint. However, images are compromised at high acceleration factor if images are reconstructed individually. We aim to improve the images with a jointly sparse reconstruction and Graph-based redundant wavelet transform (GBRWT).

Methods

First, a sparsifying transform, GBRWT, is trained to reflect the similarity of tissue structures in multi-contrast images. Second, joint multi-contrast image reconstruction is formulated as a ℓ_{2, 1} norm optimization problem under GBRWT representations. Third, the optimization problem is numerically solved using a derived alternating direction method.

Results

Experimental results in synthetic and in vivo MRI data demonstrate that the proposed joint reconstruction method can achieve lower reconstruction errors and better preserve image structures than the compared joint reconstruction methods. Besides, the proposed method outperforms single image reconstruction with joint sparsity constraint of multi-contrast images.

Conclusions

The proposed method explores the joint sparsity of multi-contrast MRI images under graph-based redundant wavelet transform and realizes joint sparse reconstruction of multi-contrast images. Experiment demonstrate that the proposed method outperforms the compared joint reconstruction methods as well as individual reconstructions. With this high quality image reconstruction method, it is possible to achieve the high acceleration factors by exploring the complementary information provided by multi-contrast MRI.

Accelerating 3D-T1ρ mapping of cartilage using compressed sensing with different sparse and low rank models

PURPOSE

To evaluate the feasibility of using compressed sensing (CS) to accelerate 3D-T_1ρ mapping of cartilage and to reduce total scan times without degrading the estimation of T_1ρ relaxation times.

METHODS

Fully sampled 3D-T_1ρ datasets were retrospectively undersampled by factors 2-10. CS reconstruction using 12 different sparsifying transforms were compared, including finite differences, temporal and spatial wavelets, learned transforms using principal component analysis (PCA) and K-means singular value decomposition (K-SVD), explicit exponential models, low rank and low rank plus sparse models. Spatial filtering prior to T_1ρ parameter estimation was also tested. Synthetic phantom (n = 6) and in vivo human knee cartilage datasets (n = 7) were included.

RESULTS

Most CS methods performed satisfactorily for an acceleration factor (AF) of 2, with relative T_1ρ error lower than 4.5%. Some sparsifying transforms, such as spatiotemporal finite difference (STFD), exponential dictionaries (EXP) and low rank combined with spatial finite difference (L+S SFD) significantly improved this performance, reaching average relative T_1ρ error below 6.5% on T_1ρ relaxation times with AF up to 10, when spatial filtering was used before T_1ρ fitting, at the expense of smoothing the T_1ρ maps. The STFD achieved 5.1% error at AF = 10 with spatial filtering prior to T_1ρ fitting.

CONCLUSION

Accelerating 3D-T_1ρ mapping of cartilage with CS is feasible up to AF of 10 when using STFD, EXP or L+S SFD regularizers. These three best CS methods performed satisfactorily on synthetic phantom and in vivo knee cartilage for AFs up to 10, with T_1ρ error of 6.5%.

Shuffled magnetization-prepared multicontrast rapid gradient-echo imaging

PURPOSE

To develop a novel acquisition and reconstruction method for magnetization-prepared 3-dimensional multicontrast rapid gradient-echo imaging, using Hankel matrix completion in combination with compressed sensing and parallel imaging.

METHODS

A random k-space shuffling strategy was implemented in simulation and in vivo human experiments at 7 T for 3-dimensional inversion recovery, T₂ /diffusion preparation, and magnetization transfer imaging. We combined compressed sensing, based on total variation and spatial-temporal low-rank regularizations, and parallel imaging with pixel-wise Hankel matrix completion, allowing the reconstruction of tens of multicontrast 3-dimensional images from 3- or 6-min scans.

RESULTS

The simulation result showed that the proposed method can reconstruct signal-recovery curves in each voxel and was robust for typical in vivo signal-to-noise ratio with 16-times acceleration. In vivo studies achieved 4 to 24 times accelerations for inversion recovery, T₂ /diffusion preparation, and magnetization transfer imaging. Furthermore, the contrast was improved by resolving pixel-wise signal-recovery curves after magnetization preparation.

CONCLUSIONS

The proposed method can improve acquisition efficiencies for magnetization-prepared MRI and tens of multicontrast 3-dimensional images could be recovered from a single scan. Furthermore, it was robust against noise, applicable for recovering multi-exponential signals, and did not require any previous knowledge of model parameters. Magn Reson Med 79:62-70, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Recovery of Damped Exponentials Using Structured Low Rank Matrix Completion

We introduce a structured low rank matrix completion algorithm to recover a series of images from their under-sampled measurements, where the signal along the parameter dimension at every pixel is described by a linear combination of exponentials. We exploit the exponential behavior of the signal at every pixel, along with the spatial smoothness of the exponential parameters to derive an annihilation relation in the Fourier domain. This relation translates to a low-rank property on a structured matrix constructed from the Fourier samples. We enforce the low-rank property of the structured matrix as a regularization prior to recover the images. Since the direct use of current low rank matrix recovery schemes to this problem is associated with high computational complexity and memory demand, we adopt an iterative re-weighted least squares algorithm, which facilitates the exploitation of the convolutional structure of the matrix. Novel approximations involving 2-D fast Fourier transforms are introduced to drastically reduce the memory demand and computational complexity, which facilitates the extension of structured low-rank methods to large scale 3-D problems. We demonstrate our algorithm in the MR parameter mapping setting and show improvement over the state-of-the-art methods.

Improved magnetic resonance fingerprinting reconstruction with low-rank and subspace modeling

PURPOSE

This article introduces a constrained imaging method based on low-rank and subspace modeling to improve the accuracy and speed of MR fingerprinting (MRF).

THEORY AND METHODS

A new model-based imaging method is developed for MRF to reconstruct high-quality time-series images and accurate tissue parameter maps (e.g., T₁ , T₂ , and spin density maps). Specifically, the proposed method exploits low-rank approximations of MRF time-series images, and further enforces temporal subspace constraints to capture magnetization dynamics. This allows the time-series image reconstruction problem to be formulated as a simple linear least-squares problem, which enables efficient computation. After image reconstruction, tissue parameter maps are estimated via dictionary-based pattern matching, as in the conventional approach.

RESULTS

The effectiveness of the proposed method was evaluated with in vivo experiments. Compared with the conventional MRF reconstruction, the proposed method reconstructs time-series images with significantly reduced aliasing artifacts and noise contamination. Although the conventional approach exhibits some robustness to these corruptions, the improved time-series image reconstruction in turn provides more accurate tissue parameter maps. The improvement is pronounced especially when the acquisition time becomes short.

CONCLUSIONS

The proposed method significantly improves the accuracy of MRF, and also reduces data acquisition time. Magn Reson Med 79:933-942, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

NOVEL STRUCTURED LOW-RANK ALGORITHM TO RECOVER SPATIALLY SMOOTH EXPONENTIAL IMAGE TIME SERIES

We propose a structured low rank matrix completion algorithm to recover a time series of images consisting of linear combination of exponential parameters at every pixel, from undersampled Fourier measurements. The spatial smoothness of these parameters is exploited along with the exponential structure of the time series at every pixel, to derive an annihilation relation in the k - t domain. This annihilation relation translates into a structured low rank matrix formed from the k-t samples. We demonstrate the algorithm in the parameter mapping setting and show significant improvement over state of the art methods.