Multidimensional compressed sensing MRI using tensor decomposition-based sparsifying transform

Multidimensional compressed sensing to advance 23 Na multi-quantum coherences MRI

PURPOSE

Sodium (23 Na) multi-quantum coherences (MQC) MRI was accelerated using three-dimensional (3D) and a dedicated five-dimensional (5D) compressed sensing (CS) framework for simultaneous Cartesian single (SQ) and triple quantum (TQ) sodium imaging of in vivo human brain at 3.0 and 7.0 T.

THEORY AND METHODS

3D 23 Na MQC MRI requires multi-echo paired with phase-cycling and exhibits thus a multidimensional space. A joint reconstruction framework to exploit the sparsity in all imaging dimensions by extending the conventional 3D CS framework to 5D was developed. 3D MQC images of simulated brain, phantom and healthy brain volunteers obtained from 3.0 T and 7.0 T were retrospectively and prospectively undersampled. Performance of the CS models were analyzed by means of structural similarity index (SSIM), root mean squared error (RMSE), signal-to-noise ratio (SNR) and signal quantification of tissue sodium concentration and TQ/SQ ratio.

RESULTS

It was shown that an acceleration of three-fold, leading to less than2 × 10 $$ 2\times 10 $$ min of scan time with a resolution of8 × 8 × 20   mm 3 $$ 8\times 8\times 20\;{\mathrm{mm}}^3 $$ at 3.0 T, are possible. 5D CS improved SSIM by 3%, 5%, 1% and reduced RMSE by 50%, 30%, 8% for in vivo SQ, TQ, and TQ/SQ ratio maps, respectively. Furthermore, for the first time prospective undersampling enabled unprecedented high resolution from8 × 8 × 20   mm 3 $$ 8\times 8\times 20\;{\mathrm{mm}}^3 $$ to6 × 6 × 10   mm 3 $$ 6\times 6\times 10\;{\mathrm{mm}}^3 $$ MQC images of in vivo human brain at 7.0 T without extending acquisition time.

CONCLUSION

5D CS proved to allow up to three-fold acceleration retrospectively on 3.0 T data. 2-fold acceleration was demonstrated prospectively at 7.0 T to reach higher spatial resolution of 23 Na MQC MRI.

A three-dimensional Magnetic Resonance Spin Tomography in Time-domain protocol for high-resolution multiparametric quantitative magnetic resonance imaging

Magnetic Resonance Spin TomogrAphy in Time-domain (MR-STAT) is a multiparametric quantitative MR framework, which allows for simultaneously acquiring quantitative tissue parameters such as T1, T2, and proton density from one single short scan. A typical two-dimensional (2D) MR-STAT acquisition uses a gradient-spoiled, gradient-echo sequence with a slowly varying RF flip-angle train and Cartesian readouts, and the quantitative tissue maps are reconstructed by an iterative, model-based optimization algorithm. In this work, we design a three-dimensional (3D) MR-STAT framework based on previous 2D work, in order to achieve better image signal-to-noise ratio, higher though-plane resolution, and better tissue characterization. Specifically, we design a 7-min, high-resolution 3D MR-STAT sequence, and the corresponding two-step reconstruction algorithm for the large-scale dataset. To reduce the long acquisition time, Cartesian undersampling strategies such as SENSE are adopted in our transient-state quantitative framework. To reduce the computational burden, a data-splitting scheme is designed for decoupling the 3D reconstruction problem into independent 2D reconstructions. The proposed 3D framework is validated by numerical simulations, phantom experiments, and in vivo experiments. High-quality knee quantitative maps with 0.8 × 0.8 × 1.5 mm3 resolution and bilateral lower leg maps with 1.6 mm isotropic resolution can be acquired using the proposed 7-min acquisition sequence and the 3-min-per-slice decoupled reconstruction algorithm. The proposed 3D MR-STAT framework could have wide clinical applications in the future.

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.

A Hybrid Volume-Surface Integral Equation Method for Rapid Electromagnetic Simulations in MRI

OBJECTIVE

We developed a hybrid volume surface integral equation (VSIE) method based on domain decomposition to perform fast and accurate magnetic resonance imaging (MRI) simulations that include both remote and local conductive elements.

METHODS

We separated the conductive surfaces present in MRI setups into two domains and optimized electromagnetic (EM) modeling for each case. Specifically, interactions between the body and EM waves originating from local radiofrequency (RF) coils were modeled with the precorrected fast Fourier transform, whereas the interactions with remote conductive surfaces (RF shield, scanner bore) were modeled with a novel cross tensor train-based algorithm. We compared the hybrid-VSIE with other VSIE methods for realistic MRI simulation setups.

RESULTS

The hybrid-VSIE was the only practical method for simulation using 1 mm voxel isotropic resolution (VIR). For 2 mm VIR, our method could be solved at least 23 times faster and required 760 times lower memory than traditional VSIE methods.

CONCLUSION

The hybrid-VSIE demonstrated a marked improvement in terms of convergence times of the numerical EM simulation compared to traditional approaches in multiple realistic MRI scenarios.

SIGNIFICANCE

The efficiency of the novel hybrid-VSIE method could enable rapid simulations of complex and comprehensive MRI setups.

Active Sampling for Accelerated MRI with Low-Rank Tensors

Magnetic resonance imaging (MRI) is a powerful imaging modality that revolutionizes medicine and biology. The imaging speed of high -dimensional MRI is often limited, which constrains its practical utility. Recently, low-rank tensor models have been exploited to enable fast MR imaging with sparse sampling. Most existing methods use some pre-defined sampling design, and active sensing has not been explored for low-rank tensor imaging. In this paper, we introduce an active low-rank tensor model for fast MR imaging. We propose an active sampling method based on a Query-by-Committee model, making use of the benefits of low-rank tensor structure. Numerical experiments on a 3-D MRI data set with Cartesian sampling designs demonstrate the effectiveness of the proposed method.

Compressed sensing based dynamic MR image reconstruction by using 3D-total generalized variation and tensor decomposition: k-t TGV-TD

PURPOSE

Compressed Sensing Magnetic Resonance Imaging (CS-MRI) is a promising technique to accelerate dynamic cardiac MR imaging (DCMRI). For DCMRI, the CS-MRI usually exploits image signal sparsity and low-rank property to reconstruct dynamic images from the undersampled k-space data. In this paper, a novel CS algorithm is investigated to improve dynamic cardiac MR image reconstruction quality under the condition of minimizing the k-space recording.

METHODS

The sparse representation of 3D cardiac magnetic resonance data is implemented by synergistically integrating 3D total generalized variation (3D-TGV) algorithm and high order singular value decomposition (HOSVD) based Tensor Decomposition, termed k-t TGV-TD method. In the proposed method, the low rank structure of the 3D dynamic cardiac MR data is performed with the HOSVD method, and the localized image sparsity is achieved by the 3D-TGV method. Moreover, the Fast Composite Splitting Algorithm (FCSA) method, combining the variable splitting with operator splitting techniques, is employed to solve the low-rank and sparse problem. Two different cardiac MR datasets (cardiac perfusion and cine MR datasets) are used to evaluate the performance of the proposed method.

RESULTS

Compared with the state-of-art methods, such as k-t SLR, 3D-TGV, HOSVD based tensor decomposition and low-rank plus sparse method, the proposed k-t TGV-TD method can offer improved reconstruction accuracy in terms of higher peak SNR (PSNR) and structural similarity index (SSIM). The proposed k-t TGV-TD method can achieve significantly better and stable reconstruction results than state-of-the-art methods in terms of both PSNR and SSIM, especially for cardiac perfusion MR dataset.

CONCLUSIONS

This work proved that the k-t TGV-TD method was an effective sparse representation way for DCMRI, which was capable of significantly improving the reconstruction accuracy with different acceleration factors.

Deep Learning-Based Diffusion-Weighted Magnetic Resonance Imaging in the Diagnosis of Ischemic Penumbra in Early Cerebral Infarction

The prefiltered image was imported into the local higher-order singular value decomposition (HOSVD) denoising algorithm (GL-HOSVD)-optimized diffusion-weighted imaging (DWI) image, which was compared with the deviation correction nonlocal mean (NL mean) and low-level edge algorithm (LR + edge). Regarding the peak signal-to-noise ratio (PSNR), root mean square error (RMSE), sensitivity, specificity, accuracy, and consistency, the application effect of the GL-HOSVD algorithm in DWI was investigated, and its adoption effect in the examination of ischemic penumbra (IP) of early acute cerebral infarction (ACI) patients was evaluated. A total of 210 patients with ACI were selected as the research subjects, who were randomly rolled into two groups. Those who were checked by conventional DWI were set as the control group, and those who used DWI based on the GL-HOSVD denoising algorithm were set as the observation group, with 105 people in each. Positron emission tomography (PET) test results were set as the gold standard to evaluate the application value of the two examination methods. It was found that under different noise levels, the peak signal-to-noise ratio (PSNR) of the GL-HOSVD algorithm and the root mean square error (RMSE) of the FA parameter were better than those of the nonlocal means (NL-means) of deviation correction and low-rank edge algorithm (LR + edge). The sensitivity, specificity, accuracy, and consistency (8.76%, 81.25%, 87.62%, and 0.52) of the observation group were higher than those of the control group (57.78%, 53.33%, 57.14%, and 0.35) (P < 0.05). Moreover, the apparent diffusion coefficient (ADC) of the DWI images of the observation group was basically consistent with that of the PET images, while the control group had a poor display effect and low definition. In summary, under different noise levels, the GL-HOSVD algorithm had a good denoising effect and greatly reduced fringe artifacts. DWI after denoising had high sensitivity, specificity, accuracy, and consistency in the detection of IP, which was worthy of clinical application and promotion.

A review on deep learning MRI reconstruction without fully sampled k-space

BACKGROUND

Magnetic resonance imaging (MRI) is an effective auxiliary diagnostic method in clinical medicine, but it has always suffered from the problem of long acquisition time. Compressed sensing and parallel imaging are two common techniques to accelerate MRI reconstruction. Recently, deep learning provides a new direction for MRI, while most of them require a large number of data pairs for training. However, there are many scenarios where fully sampled k-space data cannot be obtained, which will seriously hinder the application of supervised learning. Therefore, deep learning without fully sampled data is indispensable.

MAIN TEXT

In this review, we first introduce the forward model of MRI as a classic inverse problem, and briefly discuss the connection of traditional iterative methods to deep learning. Next, we will explain how to train reconstruction network without fully sampled data from the perspective of obtaining prior information.

CONCLUSION

Although the reviewed methods are used for MRI reconstruction, they can also be extended to other areas where ground-truth is not available. Furthermore, we may anticipate that the combination of traditional methods and deep learning will produce better reconstruction results.

Accelerating quantitative susceptibility and R2* mapping using incoherent undersampling and deep neural network reconstruction

Quantitative susceptibility mapping (QSM) and R2* mapping are MRI post-processing methods that quantify tissue magnetic susceptibility and transverse relaxation rate distributions. However, QSM and R2* acquisitions are relatively slow, even with parallel imaging. Incoherent undersampling and compressed sensing reconstruction techniques have been used to accelerate traditional magnitude-based MRI acquisitions; however, most do not recover the full phase signal, as required by QSM, due to its non-convex nature. In this study, a learning-based Deep Complex Residual Network (DCRNet) is proposed to recover both the magnitude and phase images from incoherently undersampled data, enabling high acceleration of QSM and R2* acquisition. Magnitude, phase, R2*, and QSM results from DCRNet were compared with two iterative and one deep learning methods on retrospectively undersampled acquisitions from six healthy volunteers, one intracranial hemorrhage and one multiple sclerosis patients, as well as one prospectively undersampled healthy subject using a 7T scanner. Peak signal to noise ratio (PSNR), structural similarity (SSIM), root-mean-squared error (RMSE), and region-of-interest susceptibility and R2* measurements are reported for numerical comparisons. The proposed DCRNet method substantially reduced artifacts and blurring compared to the other methods and resulted in the highest PSNR, SSIM, and RMSE on the magnitude, R2*, local field, and susceptibility maps. Compared to two iterative and one deep learning methods, the DCRNet method demonstrated a 3.2% to 9.1% accuracy improvement in deep grey matter susceptibility when accelerated by a factor of four. The DCRNet also dramatically shortened the reconstruction time of single 2D brain images from 36-140 seconds using conventional approaches to only 15-70 milliseconds.

Multilinear Compressive Learning

Compressive learning (CL) is an emerging topic that combines signal acquisition via compressive sensing (CS) and machine learning to perform inference tasks directly on a small number of measurements. Many data modalities naturally have a multidimensional or tensorial format, with each dimension or tensor mode representing different features such as the spatial and temporal information in video sequences or the spatial and spectral information in hyperspectral images. However, in existing CL frameworks, the CS component utilizes either random or learned linear projection on the vectorized signal to perform signal acquisition, thus discarding the multidimensional structure of the signals. In this article, we propose multilinear CL (MCL), a framework that takes into account the tensorial nature of multidimensional signals in the acquisition step and builds the subsequent inference model on the structurally sensed measurements. Our theoretical complexity analysis shows that the proposed framework is more efficient compared to its vector-based counterpart in both memory and computation requirement. With extensive experiments, we also empirically show that our MCL framework outperforms the vector-based framework in object classification and face recognition tasks, and scales favorably when the dimensionalities of the original signals increase, making it highly efficient for high-dimensional multidimensional signals.

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.

High-Resolution Oscillating Steady-State fMRI Using Patch-Tensor Low-Rank Reconstruction

The goals of fMRI acquisition include high spatial and temporal resolutions with a high signal to noise ratio (SNR). Oscillating Steady-State Imaging (OSSI) is a new fMRI acquisition method that provides large oscillating signals with the potential for high SNR, but does so at the expense of spatial and temporal resolutions. The unique oscillation pattern of OSSI images makes it well suited for high-dimensional modeling. We propose a patch-tensor low-rank model to exploit the local spatial-temporal low-rankness of OSSI images. We also develop a practical sparse sampling scheme with improved sampling incoherence for OSSI. With an alternating direction method of multipliers (ADMM) based algorithm, we improve OSSI spatial and temporal resolutions with a factor of 12 acquisition acceleration and 1.3 mm isotropic spatial resolution in prospectively undersampled experiments. The proposed model yields high temporal SNR with more activation than other low-rank methods. Compared to the standard grad- ient echo (GRE) imaging with the same spatial-temporal resolution, 3D OSSI tensor model reconstruction demonstrates 2 times higher temporal SNR with 2 times more functional activation.

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.

Online Tensor Sparsifying Transform based on Temporal Superpixels from Compressive Spectral Video Measurements

Spectral videos contain highly redundant information across spatial, spectral and temporal axes which can be exploited through a temporal-data-learned sparsifying basis. However, in compressive spectral video acquisition, tackling dictionary learning is time-consuming since it increases the computational complexity and presents drawbacks for realtime processing, where offline learning is required. This paper introduces a tensor-decomposition learning (TenDL) framework for simultaneous online sparsifying and recovering the spatialspectral- temporal information of a spectral video performed on several temporal superpixels (TSP-TenDL) for time processing reduction. The framework is composed of two main stages: preprocessing and joint estimation. The preprocessing stage includes a strategy for a grayscale approximation of the video to provide a suitable initialization of the sparsifying basis to be learned. To fully exploit the high signal correlation, a set of temporal superpixels is estimated from the grayscale approximation, reducing the reconstruction time of the large-scale data. Then, the outcome of the first stage is used to estimate the basis and the signal coefficients, where an optimization problem is solved to learn and reconstruct the basis and the signal, respectively, following a block-descent coordinate strategy. The proposed approach is compared from simulations with an offline-learned based method, traditional matrix-based recovery algorithms and the tensor-based recovery, the two latter using a fixed basis, where TSP-TenDL exhibits higher image quality results and lower computation time. Specifically, our methodology gains up to 7dB in terms of PSNR and a speedup of up to 6.6× compared with state-of-the-art counterparts.

Low-Rank Tensor Models for Improved Multi-Dimensional MRI: Application to Dynamic Cardiac T 1 Mapping

Multi-dimensional, multi-contrast magnetic resonance imaging (MRI) has become increasingly available for comprehensive and time-efficient evaluation of various pathologies, providing large amounts of data and offering new opportunities for improved image reconstructions. Recently, a cardiac phase-resolved myocardial T 1 mapping method has been introduced to provide dynamic information on tissue viability. Improved spatio-temporal resolution in clinically acceptable scan times is highly desirable but requires high acceleration factors. Tensors are well-suited to describe inter-dimensional hidden structures in such multi-dimensional datasets. In this study, we sought to utilize and compare different tensor decomposition methods, without the use of auxiliary navigator data. We explored multiple processing approaches in order to enable high-resolution cardiac phase-resolved myocardial T 1 mapping. Eight different low-rank tensor approximation and processing approaches were evaluated using quantitative analysis of accuracy and precision in T 1 maps acquired in six healthy volunteers. All methods provided comparable T 1 values. However, the precision was significantly improved using local processing, as well as a direct tensor rank approximation. Low-rank tensor approximation approaches are well-suited to enable dynamic T 1 mapping at high spatio-temporal resolutions.

[High quality reconstruction algorithm for cardiac magnetic resonance images based on multiscale low rank modeling]

Taking advantages of the sparsity or compressibility inherent in real world signals, compressed sensing (CS) can collect compressed data at the sampling rate much lower than that needed in Shannon's theorem. The combination of CS and low rank modeling is used to medical imaging techniques to increase the scanning speed of cardiac magnetic resonance (CMR), alleviate the patients' suffering and improve the images quality. The alternating direction method of multipliers (ADMM) algorithm is proposed for multiscale low rank matrix decomposition of CMR images. The algorithm performance is evaluated quantitatively by the peak signal to noise ratio (PSNR) and relative l 2 norm error (RLNE), with the human visual system and the local region magnification as the qualitative comparison. Compared to L + S, kt FOCUSS, k-t SPARSE SENSE algorithms, experimental results demonstrate that the proposed algorithm can achieve the best performance indices, and maintain the most detail features and edge contours. The proposed algorithm can encourage the development of fast imaging techniques, and improve the diagnoses values of CMR in clinical applications.

Compressive Color Pattern Detection using Partial Orthogonal Circulant Sensing Matrix

One key issue in compressive sensing is to design a sensing matrix that is random enough to have a good signal reconstruction quality and that also enjoys some desirable properties such that orthogonality or being circulant. The classic method to construct such sensing matrices is to first generate a full orthogonal circulant matrix and then select only a few rows. In this paper, we propose a refined construction of orthogonal circulant sensing matrices that generates a circulant matrix where only a given subset of its rows are orthogonal. That way, the generation method is a lot less constrained leading to better sensing matrices and we still have the desired properties. The proposed partial shift-orthogonal sensing matrix is compared to random and learned sensing matrices in the frame of signal reconstruction. This sensing matrix is pattern-dependent and thus efficient to detect color patterns and edges from the measurements of a color image.

Orthogonal tensor dictionary learning for accelerated dynamic MRI

A direct application of the compressed sensing (CS) theory to dynamic magnetic resonance imaging (MRI) reconstruction needs vectorization or matricization of the dynamic MRI data, which is composed of a stack of 2D images and can be naturally regarded as a tensor. This 1D/2D model may destroy the inherent spatial structure property of the data. An alternative way to exploit the multidimensional structure in dynamic MRI is to employ tensor decomposition for dictionary learning, that is, learning multiple dictionaries along each dimension (mode) and sparsely representing the multidimensional data with respect to the Kronecker product of these dictionaries. In this work, we introduce a novel tensor dictionary learning method under an orthonormal constraint on the elementary matrix of the tensor dictionary for dynamic MRI reconstruction. The proposed algorithm alternates sparse coding, tensor dictionary learning, and updating reconstruction, and each corresponding subproblem is efficiently solved by a closed-form solution. Numerical experiments on phantom and synthetic data show significant improvements in reconstruction accuracy and computational efficiency obtained by the proposed scheme over the existing method that uses the 1D/2D model with overcomplete dictionary learning. Graphical abstract Fig. 1 Comparison between (a) the traditional method and (b) the proposed method based on dictionary learning for dynamic MRI reconstruction.

Free-breathing, non-ECG, continuous myocardial T1 mapping with cardiovascular magnetic resonance multitasking

PURPOSE

To evaluate the accuracy and repeatability of a free-breathing, non-electrocardiogram (ECG), continuous myocardial T₁ and extracellular volume (ECV) mapping technique adapted from the Multitasking framework.

METHODS

The Multitasking framework is adapted to quantify both myocardial native T₁ and ECV with a free-breathing, non-ECG, continuous acquisition T₁ mapping method. We acquire interleaved high-spatial resolution image data and high-temporal resolution auxiliary data following inversion-recovery pulses at set intervals and perform low-rank tensor imaging to reconstruct images at 344 inversion times, 20 cardiac phases, and 6 respiratory phases. The accuracy and repeatability of Multitasking T₁ mapping in generating native T₁ and ECV maps are compared with conventional techniques in a phantom, a simulation, 12 healthy subjects, and 10 acute myocardial infarction patients.

RESULTS

In phantoms, Multitasking T₁ mapping correlated strongly with the gold-standard spin-echo inversion recovery (R² = 0.99). A simulation study demonstrated that Multitasking T₁ mapping has similar myocardial sharpness to the fully sampled ground truth. In vivo native T₁ and ECV values from Multitasking T₁ mapping agree well with conventional MOLLI values and show good repeatability for native T₁ and ECV mapping for 60 seconds, 30 seconds, or 15 seconds of data. Multitasking native T₁ and ECV in myocardial infarction patients correlate positively with values from MOLLI.

CONCLUSION

Multitasking T₁ mapping can quantify native T₁ and ECV in the myocardium with free-breathing, non-ECG, continuous scans with good image quality and good repeatability in vivo in healthy subjects, and correlation with MOLLI T₁ and ECV in acute myocardial infarction patients.

Quantitative 3D dynamic contrast-enhanced (DCE) MR imaging of carotid vessel wall by fast T1 mapping using Multitasking

PURPOSE

To develop a dynamic contrast-enhanced (DCE) MRI method capable of high spatiotemporal resolution, 3D carotid coverage, and T1-based quantification of contrast agent concentration for the assessment of carotid atherosclerosis using a newly developed Multitasking technique.

METHODS

5D imaging with 3 spatial dimensions, 1 T1 recovery dimension, and 1 DCE time dimension was performed using MR Multitasking based on low-rank tensor modeling, which allows direct T1 quantification with high spatiotemporal resolution (0.7 mm isotropic and 595 ms, respectively). Saturation recovery preparations followed by 3D segmented fast low angle shot readouts were implemented with Gaussian-density random 3D Cartesian sampling. A bulk motion removal scheme was developed to improve image quality. The proposed protocol was tested in phantom and human studies. In vivo scans were performed on 14 healthy subjects and 7 patients with carotid atherosclerosis. Kinetic parameters including area under the concentration versus time curve (AUC), v_p , K^trans , and v_e were evaluated for each case.

RESULTS

Phantom experiments showed that T1 measurements using the proposed protocol were in good agreement with reference value ( R 2 = 0.96 ). In vivo studies demonstrated that AUC, v_p , and K^trans in the patient group were significantly higher than in the control group (0.63 ± 0.13 versus 0.42 ± 0.12, P < 0.001; 0.14 ± 0.05 versus 0.11 ± 0.03, P = 0.034; and 0.13 ± 0.04 versus 0.08 ± 0.02, P < 0.001, respectively). Results from repeated subjects showed good interscan reproducibility (intraclass correlation coefficient: v_p , 0.83; K^trans , 0.87; v_e , 0.92; AUC, 0.94).

CONCLUSION

Multitasking DCE is a promising approach for quantitatively assessing the vascularity properties of the carotid vessel wall.

Cardiac Motion Evolution Model for Analysis of Functional Changes Using Tensor Decomposition and Cross-Sectional Data

Cardiac disease can reduce the ability of the ventricles to function well enough to sustain long-term pumping efficiency. Recent advances in cardiac motion tracking have led to improvements in the analysis of cardiac function. We propose a method to study cohort effects related to age with respect to cardiac function. The proposed approach makes use of a recent method for describing cardiac motion of a given subject using a polyaffine model, which gives a compact parameterization that reliably and accurately describes the cardiac motion across populations. Using this method, a data tensor of motion parameters is extracted for a given population. The partial least squares method for higher order arrays is used to build a model to describe the motion parameters with respect to age, from which a model of motion given age is derived. Based on the cross-sectional statistical analysis with the data tensor of each subject treated as an observation along time, the left ventricular motion over time of Tetralogy of Fallot patients is analysed to understand the temporal evolution of functional abnormalities in this population compared to healthy motion dynamics.

SVD-based Tensor-Completion Technique for Background Initialization

Extracting the background from a video in the presence of various moving patterns is the focus of several background-initialization approaches. To model the scene background using rank-one matrices, this paper proposes a background-initialization technique that relies on the singular-value decomposition (SVD) of spatiotemporally extracted slices from the video tensor. The proposed method is referred to as spatiotemporal slice-based SVD (SS-SVD). To determine the SVD components that best model the background, a depth analysis of the computation of the left/right singular vectors and singular values is performed, and the relationship with tensor-tube fibers is determined. The analysis proves that a rank-1 matrix extracted from the first left and right singular vectors and singular value represents an efficient model of the scene background. The performance of the proposed SS-SVD method is evaluated using 93 complex video sequences of different challenges, and the method is compared with state-of-the-art tensor/matrix completion-based methods, statistical-based methods, search-based methods, and labeling-based methods. The results not only show better performance over most of the tested challenges, but also demonstrate the capability of the proposed technique to solve the background-initialization problem in a less computational time and with fewer frames.

Magnetic resonance multitasking for motion-resolved quantitative cardiovascular imaging

Quantitative cardiovascular magnetic resonance (CMR) imaging can be used to characterize fibrosis, oedema, ischaemia, inflammation and other disease conditions. However, the need to reduce artefacts arising from body motion through a combination of electrocardiography (ECG) control, respiration control, and contrast-weighting selection makes CMR exams lengthy. Here, we show that physiological motions and other dynamic processes can be conceptualized as multiple time dimensions that can be resolved via low-rank tensor imaging, allowing for motion-resolved quantitative imaging with up to four time dimensions. This continuous-acquisition approach, which we name cardiovascular MR multitasking, captures — rather than avoids — motion, relaxation and other dynamics to efficiently perform quantitative CMR without the use of ECG triggering or breath holds. We demonstrate that CMR multitasking allows for T₁ mapping, T₁-T₂ mapping and time-resolved T₁ mapping of myocardial perfusion without ECG information and/or in free-breathing conditions. CMR multitasking may provide a foundation for the development of setup-free CMR imaging for the quantitative evaluation of cardiovascular health.

Improved parallel image reconstruction using feature refinement

PURPOSE

The aim of this study was to develop a novel feature refinement MR reconstruction method from highly undersampled multichannel acquisitions for improving the image quality and preserve more detail information.

THEORY AND METHODS

The feature refinement technique, which uses a feature descriptor to pick up useful features from residual image discarded by sparsity constrains, is applied to preserve the details of the image in compressed sensing and parallel imaging in MRI (CS-pMRI). The texture descriptor and structure descriptor recognizing different types of features are required for forming the feature descriptor. Feasibility of the feature refinement was validated using three different multicoil reconstruction methods on in vivo data.

RESULTS

Experimental results show that reconstruction methods with feature refinement improve the quality of reconstructed image and restore the image details more accurately than the original methods, which is also verified by the lower values of the root mean square error and high frequency error norm.

CONCLUSION

A simple and effective way to preserve more useful detailed information in CS-pMRI is proposed. This technique can effectively improve the reconstruction quality and has superior performance in terms of detail preservation compared with the original version without feature refinement. Magn Reson Med 80:211-223, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Multidimensional encoding of brain connectomes

The ability to map brain networks in living individuals is fundamental in efforts to chart the relation between human behavior, health and disease. Advances in network neuroscience may benefit from developing new frameworks for mapping brain connectomes. We present a framework to encode structural brain connectomes and diffusion-weighted magnetic resonance (dMRI) data using multidimensional arrays. The framework integrates the relation between connectome nodes, edges, white matter fascicles and diffusion data. We demonstrate the utility of the framework for in vivo white matter mapping and anatomical computing by evaluating 1,490 connectomes, thirteen tractography methods, and three data sets. The framework dramatically reduces storage requirements for connectome evaluation methods, with up to 40x compression factors. Evaluation of multiple, diverse datasets demonstrates the importance of spatial resolution in dMRI. We measured large increases in connectome resolution as function of data spatial resolution (up to 52%). Moreover, we demonstrate that the framework allows performing anatomical manipulations on white matter tracts for statistical inference and to study the white matter geometrical organization. Finally, we provide open-source software implementing the method and data to reproduce the results.

Sampling and recovery of MRI data using low rank tensor models

In this paper we investigate the utility of several low-rank models for recovery of Magnetic Resonance Imaging (MRI) data from limited sampling in the k - t space for dynamic imaging. In particular, for 3D temporal (2D space + time) MRI data we employ several tensor factorization techniques and assess the degree of dimensionality reduction, or compressibility, that can be obtained. This algebraic approach is more data adaptive, in contrast to existing compressed sensing (CS) based methods that exploit sparsity in a transform domain, such as wavelets or total variation. Further, we compare these tensor factorization approaches in recovering temporal MRI data under limited sampling. Respecting traditional MRI data acquisition methods, the sampling process is restricted to be uniformly random along only one k space direction. Experimental results on synthetically sub-sampled MRI data show promise in using tensor factorization for sampling and recovery of MRI data.

Dynamic MRI reconstruction from highly undersampled (k, t)-space data using weighted Schatten p-norm regularizer of tensor

Combination of the low-rankness and sparsity has been successfully used to reconstruct desired dynamic magnetic resonance image (MRI) from highly-undersampled (k, t)-space data. However, nuclear norm, as a convex relaxation of the rank function, can cause the solution deviating from the original solution of low-rank problem. Moreover, equally treating different rank component is not flexible to deal with real applications. In this paper, an efficient reconstruction model is proposed to efficiently reconstruct dynamic MRI. First, we treat dynamic MRI as a 3rd-order tensor, and formulate the low-rankness via non-convex Schatten p-norm of matrices unfolded from the tensor. Secondly, we assign different weight for each rank component in Schatten p-norm. Furthermore, we combine the proposed weighted Schatten p-norm of a tensor as low-rank regularizer, and spatiotemporal total variation as sparse regularizer to formulate the reconstruction model for dynamic MRI. Thirdly, to efficiently solve the formulated reconstruction model, we derive an algorithm based on Bregman iterations with alternating direction multiplier. Over two public data sets of dynamic MRI, experiments demonstrate that the proposed method achieves much better quality.

Accelerated High-Dimensional MR Imaging With Sparse Sampling Using Low-Rank Tensors

High-dimensional MR imaging often requires long data acquisition time, thereby limiting its practical applications. This paper presents a low-rank tensor based method for accelerated high-dimensional MR imaging using sparse sampling. This method represents high-dimensional images as low-rank tensors (or partially separable functions) and uses this mathematical structure for sparse sampling of the data space and for image reconstruction from highly undersampled data. More specifically, the proposed method acquires two datasets with complementary sampling patterns, one for subspace estimation and the other for image reconstruction; image reconstruction from highly undersampled data is accomplished by fitting the measured data with a sparsity constraint on the core tensor and a group sparsity constraint on the spatial coefficients jointly using the alternating direction method of multipliers. The usefulness of the proposed method is demonstrated in MRI applications; it may also have applications beyond MRI.