基于虚拟线圈和卷积神经网络的多层同时激发图像重建

本文提出一种基于虚拟共轭线圈（Virtual Coil Concept,VCC）技术和k空间插值鲁棒人工神经网络（Robust Artificial-neural-networks for k-space Interpolation,RAKI）的图像重建方法,用于磁共振多层同时激发成像（Simultaneous Multi-Slice imaging,SMS）,该方法能够有效提升重建图像的质量,被命名为VIRGINIA（VIRtual conjuGate coIls Neural-networks InterpolAtion）.为了得到更高质量的SMS图像,本文提出的VIRGINIA方法利用磁共振线圈数据的复数共轭对称性质扩展了SMS所获取的多通道数据,并将扩展后的数据用于RAKI网络的训练,利用训练后的网络实现高质量的SMS图像重建.本文将VIRGINIA方法和其他SMS图像重建方法（RAKI和Slice-GRAPPA方法）进行了对比,并采用结构相似指数（Structural Similarity Index,SSIM）、峰值信噪比（Peak Signal-to-Noise Ratio,PSNR）和均方根误差（Root Mean Square Error,RMSE）对不同方法的重建图像进行了量化对比分析.结果显示,在相同的SMS加速倍数下,使用VIRGINIA方法进行重建的图像质量均好于RAKI方法,且远好于传统Slice-GRAPPA方法.     

Optimization of hyperparameters for SMS reconstruction

PurposeSimultaneous multi-slice (SMS) imaging accelerates MRI data acquisition by exciting multiple image slices with a single radiofrequency pulse. Overlapping slices encoded in acquired signal are separated using a mathematical model, which requires estimation of image reconstruction kernels using calibration data. Several parameters used in SMS reconstruction impact the quality and fidelity of final images. Therefore, finding an optimal set of reconstruction parameters is critical to ensure that accelerated acquisition does not significantly degrade resulting image quality.MethodsGradient-echo echo planar imaging data were acquired with a range of SMS acceleration factors from a cohort of five volunteers with no known neurological pathology. Images were collected using two available phased-array head coils (a 48-channel array and a reduced diameter 32-channel array) that support SMS. Data from these coils were identically reconstructed offline using a range of coil compression factors and reconstruction kernel parameters. A hybrid space (k-x), externally-calibrated coil-by-coil slice unaliasing approach was used for image reconstruction. The image quality of the resulting reconstructed SMS images was assessed by evaluating correlations with identical echo-planar reference data acquired without SMS. A finger tapping functional MRI (fMRI) experiment was also performed and group analysis results were compared between data sets reconstructed with different coil compression levels.ResultsBetween the two RF coils tested in this study, the 32-channel coil with smaller dimensions clearly outperformed the larger 48-channel coil in our experiments. Generally, a large calibration region (144–192 samples) and small kernel sizes (2–4 samples) in k_y direction improved image quality. Use of regularization in the kernel fitting procedure had a notable impact on the fidelity of reconstructed images and a regularization value 0.0001 provided good image quality. With optimal selection of other hyperparameters in the hybrid space SMS unaliasing algorithm, coil compression caused small reduction in correlation between single-band and SMS unaliased images. Similarly, group analysis of fMRI results did not show a significant influence of coil compression on resulting image quality.ConclusionsThis study demonstrated that the hyperparameters used in SMS reconstruction need to be fine-tuned once the experimental factors such as the RF receive coil and SMS factor have been determined. A cursory evaluation of SMS reconstruction hyperparameter values is therefore recommended before conducting a full-scale quantitative study using SMS technologies.     

Deep learning for radial SMS myocardial perfusion reconstruction using the 3D residual booster U-net

PurposeTo develop an end-to-end deep learning solution for quickly reconstructing radial simultaneous multi-slice (SMS) myocardial perfusion datasets with comparable quality to the pixel tracking spatiotemporal constrained reconstruction (PT-STCR) method.MethodsDynamic contrast enhanced (DCE) radial SMS myocardial perfusion data were obtained from 20 subjects who were scanned at rest and/or stress with or without ECG gating using a saturation recovery radial CAIPI turboFLASH sequence. Input to the networks consisted of complex coil combined images reconstructed using the inverse Fourier transform of undersampled radial SMS k-space data. Ground truth images were reconstructed using the PT-STCR pipeline. The performance of the residual booster 3D U-Net was tested by comparing it to state-of-the-art network architectures including MoDL, CRNN-MRI, and other U-Net variants.ResultsResults demonstrate significant improvements in speed requiring approximately 8 seconds to reconstruct one radial SMS dataset which is approximately 200 times faster than the PT-STCR method. Images reconstructed with the residual booster 3D U-Net retain quality of ground truth PT-STCR images (0.963 SSIM/40.238 PSNR/0.147 NRMSE). The residual booster 3D U-Net has superior performance compared to existing network architectures in terms of image quality, temporal dynamics, and reconstruction time.ConclusionResidual and booster learning combined with the 3D U-Net architecture was shown to be an effective network for reconstructing high-quality images from undersampled radial SMS datasets while bypassing the reconstruction time of the PT-STCR method.     

Joint Reconstruction of Multi-contrast Images and Multi-channel Coil Sensitivities

Magnetic resonance imaging (MRI) has an important feature that it provides multiple images with different contrasts for complementary diagnostic information. However, a large amount of data is needed for multi-contrast images depiction, and thus, the scan is time-consuming. Many methods based on parallel magnetic resonance imaging (pMRI) and compressed sensing (CS) are applied to accelerate multi-contrast MR imaging. Nevertheless, the image reconstructed by sophisticated pMRI methods contains residual aliasing artifact that degrades the quality of the image when the acceleration factor is high. Other methods based on CS always suffer the regularization parameter-selecting problem. To address these issues, a new method is presented for joint multi-contrast image reconstruction and coil sensitivity estimation. The coil sensitivities can be shared during the reconstruction due to the identity of coil sensitivity profiles of different contrast images for imaging stationary tissues. The proposed method uses the coil sensitivities as sharable information during the reconstruction to improve the reconstruction quality. As a result, the residual aliasing artifact can be effectively removed in the reconstructed multi-contrast images even if the acceleration factor is high. Besides, as there is no regularization term in the proposed method, the troublesome regularization parameter selection in the CS can also be avoided. Results from multi-contrast in vivo experiments demonstrated that multi-contrast images can be jointly reconstructed by the proposed method with effective removal of the residual aliasing artifact at a high acceleration factor.     

Noise estimation in parallel MRI: GRAPPA and SENSE

Parallel imaging methods allow to increase the acquisition rate via subsampled acquisitions of the k-space. SENSE and GRAPPA are the most popular reconstruction methods proposed in order to suppress the artifacts created by this subsampling. The reconstruction process carried out by both methods yields to a variance of noise value which is dependent on the position within the final image. Hence, the traditional noise estimation methods – based on a single noise level for the whole image – fail. In this paper we propose a novel methodology to estimate the spatial dependent pattern of the variance of noise in SENSE and GRAPPA reconstructed images. In both cases, some additional information must be known beforehand: the sensitivity maps of each receiver coil in the SENSE case and the reconstruction coefficients for GRAPPA.     

Parallel magnetic resonance imaging using coils with localized sensitivities

The purpose of this study was to present clinical examples and illustrate the inefficiencies of a conventional reconstruction using a commercially available phased array coil with localized sensitivities. Five patients were imaged at 1.5 T using a cardiac-synchronized gadolinium-enhanced acquisition and a commercially available four-element phased array coil. Four unique sets of images were reconstructed from the acquired k-space data: (a) sum-of-squares image using four elements of the coil; localized sum-of-squares images from the (b) anterior coils and (c) posterior coils and a (c) local reconstruction. Images were analyzed for artifacts and usable field-of-view. Conventional image reconstruction produced images with fold-over artifacts in all cases spanning a portion of the image (mean 90 mm; range 36-126 mm). The local reconstruction removed fold-over artifacts and resulted in an effective increase in the field-of-view (mean 50%; range 20-70%). Commercially available phased array coils do not always have overlapping sensitivities. Fold-over artifacts can be removed using an alternate reconstruction method. When assessing the advantages of parallel imaging techniques, gains achieved using techniques such as SENSE and SMASH should be gauged against the acquisition time of the localized method rather than the conventional sum-of-squares method.     

A mixed waveform protocol for reduction of the cardiac motion artifact in black-blood diffusion-weighted imaging of the liver

ObjectiveDiffusion-weighted imaging (DWI) in the liver suffers from signal loss due to the cardiac motion artifact, especially in the left liver lobe. The purpose of this work was to improve the image quality of liver DWI in terms of cardiac motion artifact reduction and achievement of black-blood images in low b-value images.Material and methodsTen healthy volunteers (age 20–31 years) underwent MRI examinations at 1.5 T with a prototype DWI sequence provided by the vendor. Two diffusion encodings (i.e. waveforms), monopolar and flow-compensated, and the b-values 0, 20, 50, 100, 150, 600 and 800 s/mm² were used. Two Likert scales describing the severity of the pulsation artifact and the quality of the black-blood state were defined and evaluated by two experienced radiologists. Regions of interest (ROIs) were manually drawn in the right and left liver lobe in each slice and combined to a volume of interest (VOI). The mean and coefficient of variation were calculated for each normalized VOI-averaged signal to assess the severity of the cardiac motion artifact. The ADC was calculated using two b-values once for the monopolar data and once with mixed data, using the monopolar data for the small and the flow-compensated data for the high b-value. A Wilcoxon rank sum test was used to compare the Likert scores obtained for monopolar and flow-compensated data.ResultsAt b-values from 20 to 150 s/mm², unlike the flow-compensated diffusion encoding, the monopolar encoding yielded black blood in all images with a negligible signal loss due to the cardiac motion artifact. At the b-values 600 and 800 s/mm², the flow-compensated encoding resulted in a significantly reduced cardiac motion artifact, especially in the left liver lobe, and in a black-blood state. The ADC calculated with monopolar data was significantly higher in the left than in the right liver lobe.ConclusionIt is recommendable to use the following mixed waveform protocol: Monopolar diffusion encodings at small b-values and flow-compensated diffusion encodings at high b-values.     

SNR-optimality of sum-of-squares reconstruction for phased-array magnetic resonance imaging

We consider the commonly used "Sum-of-Squares" (SoS) reconstruction method for phased-array magnetic resonance imaging with unknown coil sensitivities. We show that the signal-to-noise ratio (SNR) in the image produced by SoS is asymptotically (as the input SNR--> infinity ) equal to that of maximum-ratio combining, which is the best unbiased reconstruction method when the coil sensitivities are known. Finally, we discuss the implications of this result.     

Dictionary learning based sinogram inpainting for CT sparse reconstruction

In CT (computed tomography), reconstruction from undersampling projection data is often ill-posed and suffers from severe artifact in the reconstructed images. To overcome this problem, this paper proposes a sinogram inpainting method based on recently rising sparse representation technology. In this approach, a dictionary learning based inpainting is used to estimate the missing projection data. The final image can be reconstructed by the analytic filtered back projection (FBP) reconstruction. We conduct experiments using both simulated and real phantom data. Compared to the comparative interpolation method, visual and numerical results validate the clinical potential of the proposed method.     

Detection of explosives by Terahertz synthetic aperture imaging—focusing and spectral classification

In the adaptation of Terahertz (THz) synthetic aperture imaging to stand-off screening of concealed weapons and explosives, the incoming THz wavefronts exhibit significant curvature that must be considered in the image reconstruction. Consequently, the imaging array must be focused at a specific distance to correct for the wavefront curvature. In addition to the focusing correction, detection of explosives requires spectral analysis of the reconstructed THz image. Kohonen self-organizing maps are shown to be promising tools for differentiating the spectral signature of C4 explosive from the reflection spectra of metal and semi-transparent barrier materials. To cite this article: A. Sinyukov et al., C. R. Physique 9 (2008).     

FPGA implementation of real-time SENSE reconstruction using pre-scan and Emaps sensitivities

Sensitivity Encoding (SENSE) is a widely used technique in Parallel Magnetic Resonance Imaging (MRI) to reduce scan time. Reconfigurable hardware based architecture for SENSE can potentially provide image reconstruction with much less computation time. Application specific hardware platform for SENSE may dramatically increase the power efficiency of the system and can decrease the execution time to obtain MR images. A new implementation of SENSE on Field Programmable Gate Array (FPGA) is presented in this study, which provides real-time SENSE reconstruction right on the receiver coil data acquisition system with no need to transfer the raw data to the MRI server, thereby minimizing the transmission noise and memory usage. The proposed SENSE architecture can reconstruct MR images using receiver coil sensitivity maps obtained using pre-scan and eigenvector (E-maps) methods. The results show that the proposed system consumes remarkably less computation time for SENSE reconstruction, i.e., 0.164 ms @ 200 MHz, while maintaining the quality of the reconstructed images with good mean SNR (29 + dB), less RMSE (< 5 × 10^− 2) and comparable artefact power (< 9 × 10^− 4) to conventional SENSE reconstruction. A comparison of the center line profiles of the reconstructed and reference images also indicates a good quality of the reconstructed images. Furthermore, the results indicate that the proposed architectural design can prove to be a significant tool for SENSE reconstruction in modern MRI scanners and its low power consumption feature can be remarkable for portable MRI scanners.     

Adaptive fixed-point iterative shrinkage/thresholding algorithm for MR imaging reconstruction using compressed sensing

Recently compressed sensing (CS) has been applied to under-sampling MR image reconstruction for significantly reducing signal acquisition time. To guarantee the accuracy and efficiency of the CS-based MR image reconstruction, it necessitates determining several regularization and algorithm-introduced parameters properly in practical implementations. The regularization parameter is used to control the trade-off between the sparsity of MR image and the fidelity measures of k-space data, and thus has an important effect on the reconstructed image quality. The algorithm-introduced parameters determine the global convergence rate of the algorithm itself. These parameters make CS-based MR image reconstruction a more difficult scheme than traditional Fourier-based method while implemented on a clinical MR scanner. In this paper, we propose a new approach that reveals that the regularization parameter can be taken as a threshold in a fixed-point iterative shrinkage/thresholding algorithm (FPIST) and chosen by employing minimax threshold selection method. No extra parameter is introduced by FPIST. The simulation results on synthetic and real complex-valued MRI data show that the proposed method can adaptively choose the regularization parameter and effectively achieve high reconstruction quality. The proposed method should prove very useful for practical CS-based MRI applications.     

Weighted total variation using split Bregman fast quantitative susceptibility mapping reconstruction method

An ill-posed inverse problem in quantitative susceptibility mapping(QSM) is usually solved using a regularization and optimization solver, which is time consuming considering the three-dimensional volume data. However, in clinical diagnosis, it is necessary to reconstruct a susceptibility map efficiently with an appropriate method. Here, a modified QSM reconstruction method called weighted total variation using split Bregman(WTVSB) is proposed. It reconstructs the susceptibility map with fast computational speed and effective artifact suppression by incorporating noise-suppressed data weighting with split Bregman iteration. The noise-suppressed data weighting is determined using the Laplacian of the calculated local field, which can prevent the noise and errors in field maps from spreading into the susceptibility inversion.The split Bregman iteration accelerates the solution of the L_1-regularized reconstruction model by utilizing a preconditioned conjugate gradient solver. In an experiment, the proposed reconstruction method is compared with truncated k-space division(TKD), morphology enabled dipole inversion(MEDI), total variation using the split Bregman(TVSB) method for numerical simulation, phantom and in vivo human brain data evaluated by root mean square error and mean structure similarity. Experimental results demonstrate that our proposed method can achieve better balance between accuracy and efficiency of QSM reconstruction than conventional methods, and thus facilitating clinical applications of QSM.     

A refined structural analysis of the PTCDA monolayer on the reconstructed Au(1 1 1) surface—“Rigid or distorted carpet?”

The superstructures (H1 and H2) of perylenetetracarboxylicacid-dianhydride (PTCDA) monolayers on the reconstructed Au(1 1 1) surface reported by Mannsfeld et al. [S. Mannsfeld, M. Toerker, T. Schmitz-Hübsch, F. Sellam, T. Fritz, K. Leo, Org. Electron. 2 (2001) 121] are reinvestigated by high resolution low energy electron diffraction (SPALEED). The purpose of this investigation is to elucidate in detail the point-on-line (p-o-l) structural relation of the homogeneous adsorbate layer with respect to the three reconstruction domains of the Au(1 1 1) surface. For the H2 (non-equilibrium) structure, diffraction patterns without a spot splitting are found, indicating an almost perfect undisturbed overgrowth of the domain boundaries of the reconstruction. As a consequence, the superstructure does not follow strictly the p-o-l relation, but only in an averaged manner. Contrary for the H1 phase (equilibrium structure), a spot splitting is observed, which indicates that superstructure domains on different Au(1 1 1) reconstruction domains exhibit slightly different angular orientations, thus adopting p-o-l relations on all Au(1 1 1) reconstruction domains. The PTCDA layer on Au(1 1 1) may be thus considered as a rigid or distorted carpet, depending on the preparation conditions.     

A simple application of compressed sensing to further accelerate partially parallel imaging

Compressed sensing (CS) and partially parallel imaging (PPI) enable fast magnetic resonance (MR) imaging by reducing the amount of k-space data required for reconstruction. Past attempts to combine these two have been limited by the incoherent sampling requirement of CS since PPI routines typically sample on a regular (coherent) grid. Here, we developed a new method, “CS+GRAPPA,” to overcome this limitation. We decomposed sets of equidistant samples into multiple random subsets. Then, we reconstructed each subset using CS and averaged the results to get a final CS k-space reconstruction. We used both a standard CS and an edge- and joint-sparsity-guided CS reconstruction. We tested these intermediate results on both synthetic and real MR phantom data and performed a human observer experiment to determine the effectiveness of decomposition and to optimize the number of subsets. We then used these CS reconstructions to calibrate the generalized autocalibrating partially parallel acquisitions (GRAPPA) complex coil weights. In vivo parallel MR brain and heart data sets were used. An objective image quality evaluation metric, Case-PDM, was used to quantify image quality. Coherent aliasing and noise artifacts were significantly reduced using two decompositions. More decompositions further reduced coherent aliasing and noise artifacts but introduced blurring. However, the blurring was effectively minimized using our new edge- and joint-sparsity-guided CS using two decompositions. Numerical results on parallel data demonstrated that the combined method greatly improved image quality as compared to standard GRAPPA, on average halving Case-PDM scores across a range of sampling rates. The proposed technique allowed the same Case-PDM scores as standard GRAPPA using about half the number of samples. We conclude that the new method augments GRAPPA by combining it with CS, allowing CS to work even when the k-space sampling pattern is equidistant.     

Accelerating MRI Using GROG Gridding Followed by ESPIRiT for Non-Cartesian Trajectories

Parallel imaging plays an important role to reduce data acquisition time in magnetic resonance imaging (MRI). Under-sampled non-Cartesian trajectories accelerate the MRI scan time, but the resulting images may have aliasing artifacts. To remove these artifacts, a variety of methods have been developed within the scope of parallel imaging in the recent past. In this paper, the use of Eigen-vector-based iterative Self-consistent Parallel Imaging Reconstruction Technique (ESPIRiT) along with self-calibrated GRAPPA operator gridding (self-calibrated GROG) on radial k-space data for accelerated MR image reconstruction is presented. The proposed method reconstructs the solution image from non-Cartesian k-space data in two steps: First, the acquired radial data is gridded using self-calibrated GROG and then ESPIRIT is applied on this gridded data to get the un-aliased image. The proposed method is tested on human head data and the short-axis cardiac radial data. The quality of the reconstructed images is evaluated using artifact power (AP), root-mean-square error (RMSE) and peak signal-to-noise ratio (PSNR) at different acceleration factors (AF). The results of the proposed method (GROG followed by ESPIRiT) are compared with GROG followed by pseudo-Cartesian GRAPPA reconstruction approach (conventionally used). The results show that the proposed method provides considerable improvement in the reconstructed images as compared to conventionally used pseudo-Cartesian GRAPPA with GROG, e.g., 87, 67 and 82% improvement in terms of AP for 1.5T, 3T human head and short-axis cardiac radial data, 63, 45 and 57% improvement in terms of RMSE for 1.5T, 3T human head and short-axis cardiac radial data, 11, 7 and 9% improvement in terms of PSNR for 1.5T, 3T human head and short-axis cardiac radial data, respectively, at AF = 4.     

Diffusion tensor image up-sampling: a registration-based approach

Diffusion weighted images (DWI), from which the corresponding diffusion tensor images (DTI) are estimated, are commonly acquired with anisotropic discretizations. Traditional methods to up-sample diffusion weighted images generally rely on scene-based interpolation and do not exploit structural information from the images. In this study, a DTI up-sampling framework is presented that incorporates the underlying anatomical shape information by means of non-rigid inter-slice registration. A strategy is proposed to reorient the interpolated tensor in order to maintain its proper orientation. Tests on phantom as well as on real data sets show that the proposed method is able to produce better results compared to scene based interpolation methods in terms of the accuracy of DWI/DTI interpolation, especially when diffusion tensor orientation is taken into account.     

Data consistency criterion for selecting parameters for k-space-based reconstruction in parallel imaging

k-space-based reconstruction in parallel imaging depends on the reconstruction kernel setting, including its support. An optimal choice of the kernel depends on the calibration data, coil geometry and signal-to-noise ratio, as well as the criterion used. In this work, data consistency, imposed by the shift invariance requirement of the kernel, is introduced as a goodness measure of k-space-based reconstruction in parallel imaging and demonstrated. Data consistency error (DCE) is calculated as the sum of squared difference between the acquired signals and their estimates obtained based on the interpolation of the estimated missing data. A resemblance between DCE and the mean square error in the reconstructed image was found, demonstrating DCE's potential as a metric for comparing or choosing reconstructions. When used for selecting the kernel support for generalized autocalibrating partially parallel acquisition (GRAPPA) reconstruction and the set of frames for calibration as well as the kernel support in temporal GRAPPA reconstruction, DCE led to improved images over existing methods. Data consistency error is efficient to evaluate, robust for selecting reconstruction parameters and suitable for characterizing and optimizing k-space-based reconstruction in parallel imaging.     

基于雷诺应力模型的高精度分离涡模拟方法

基于Speziale-Sarkar-Gatski/Launder-Reece-Rodi(SSG/LRR)-ω雷诺应力模型发展了一类分离涡模拟方法,结合高精度加权紧致非线性格式在典型翼型及三角翼算例中进行了验证,并和传统基于线性涡粘模型的分离涡模拟方法进行了对比.结果表明:基于SSG/LRR-ω模型的分离涡模拟方法,提高了原雷诺应力模型对非定常分离湍流的模拟能力;同时相比于传统基于线性涡粘模型的分离涡模拟方法,尤其是在翼型最大升力迎角和三角翼涡破裂迎角附近,该方法在平均气动力预测的准确度、分离湍流模拟的精细度等方面更加优秀.     

Improving dynamic contrast-enhanced MRI of the lung using motion-weighted sparse reconstruction: Initial experiences in patients

PurposeThe purpose of this study was to evaluate the performance of motion-weighted Golden-angle RAdial Sparse Parallel MRI (motion-weighted GRASP) for free-breathing dynamic contrast-enhanced MRI (DCE-MRI) of the lung.MethodsMotion-weighted GRASP incorporates a soft-gating motion compensation algorithm into standard GRASP reconstruction, so that motion-corrupted motion k-space (e.g., k-space acquired in inspiratory phases) contributes less to the final reconstructed images. Lung MR data from 20 patients (mean age = 57.9 ± 13.5) with known pulmonary lesions were retrospectively collected for this study. Each subject underwent a free-breathing DCE-MR scan using a fat-statured T₁-weighted stack-of-stars golden-angle radial sequence and a post-contrast breath-hold MR scan using a Cartesian volumetric-interpolated imaging sequence (BH-VIBE). Each radial dataset was reconstructed using GRASP without motion compensation and motion-weighted GRASP. All MR images were visually evaluated by two experienced radiologists blinded to reconstruction and acquisition schemes independently. In addition, the influence of motion-weighted reconstruction on dynamic contrast-enhancement patterns was also investigated.ResultsFor image quality assessment, motion-weighted GRASP received significantly higher visual scores than GRASP (P < 0.05) for overall image quality (3.68 vs. 3.39), lesion conspicuity (3.54 vs. 3.18) and overall artifact level (3.53 vs. 3.15). There was no significant difference (P > 0.05) between the breath-hold BH-VIBE and motion-weighted GRASP images. For assessment of temporal fidelity, motion-weighted GRASP maintained a good agreement with respect to GRASP.ConclusionMotion-weighted GRASP achieved better reconstruction performance in free-breathing DCE-MRI of the lung compared to standard GRASP, and it may enable improved assessment of pulmonary lesions.