Real-time imaging with radial GRAPPA: Implementation on a heterogeneous architecture for low-latency reconstructions

Combination of non-Cartesian trajectories with parallel MRI permits to attain unmatched acceleration rates when compared to traditional Cartesian MRI during real-time imaging. However, computationally demanding reconstructions of such imaging techniques, such as k-space domain radial generalized auto-calibrating partially parallel acquisitions (radial GRAPPA) and image domain conjugate gradient sensitivity encoding (CG-SENSE), lead to longer reconstruction times and unacceptable latency for online real-time MRI on conventional computational hardware. Though CG-SENSE has been shown to work with low-latency using a general purpose graphics processing unit (GPU), to the best of our knowledge, no such effort has been made for radial GRAPPA. Radial GRAPPA reconstruction, which is robust even with highly undersampled acquisitions, is not iterative, requiring only significant computation during initial calibration while achieving good image quality for low-latency imaging applications. In this work, we present a very fast, low-latency, reconstruction framework based on a heterogeneous system using multi-core CPUs and GPUs. We demonstrate an implementation of radial GRAPPA that permits reconstruction times on par with or faster than acquisition of highly accelerated datasets in both cardiac and dynamic musculoskeletal imaging scenarios. Acquisition and reconstruction times are reported.     

Correlation imaging with arbitrary sampling trajectories

The presented work aims to develop a generalized linear approach to image reconstruction with arbitrary sampling trajectories for high-speed MRI. This approach is based on a previously developed image reconstruction framework, “correlation imaging”. In the presented work, correlation imaging with arbitrary sampling trajectories is implemented in a multi-dimensional hybrid space that is formed from the physical sampling space and a virtually defined space. By introducing an undersampling trajectory with both uniformity and randomness in the hybrid space, correlation imaging may take advantage of multiple image reconstruction mechanisms including coil sensitivity encoding, data sparsity and information sharing. This hybrid-space implementation is demonstrated in multi-slice 2D imaging, multi-scan imaging, and radial dynamic imaging. Since more information is used in image reconstruction, it is found that hybrid-space correlation imaging outperforms several conventional techniques. The presented approach will benefit clinical MRI by enabling correlation imaging to be used to accelerate multi-scan clinical protocols that need different sampling trajectories in different scans.     

Improved matrix inversion in image plane parallel MRI

A new 3D parallel magnetic resonance imaging (MRI) method named Generalized Unaliasing Incorporating Support constraint and sensitivity Encoding (GUISE) is presented. GUISE allows direct image recovery from arbitrary Cartesian k-space trajectories. However, periodic k-space sampling patterns are considered for reconstruction efficiency. Image recovery methods such as 2D SENSE (SENSitivity Encoding) and 2D CAIPIRINHA (Controlled Aliasing In Parallel Imaging Results IN Higher Acceleration) are special instances of GUISE where specific restrictions are placed on the k-space sampling patterns used. It is shown that the sampling pattern has large impacts on the image reconstruction error due to noise. An efficient sampling pattern design method that incorporates prior knowledge of object support and coil sensitivity profile is proposed. It requires no experimental trials and could be used in clinical imaging. Comparison of the proposed sampling pattern design method with 2D SENSE and 2D CAIPIRINHA are made based on both simulation and experiment results. It is seen that this new adaptive sampling pattern design method results in a lower noise level in reconstructions due to better exploitation of the coil sensitivity variation and object support constraint. In addition, elimination of the non-object region from reconstruction potentially allows an acceleration factor higher than the number of receiver coils used.     

K-space trajectory mapping and its application for ultrashort Echo time imaging

MR images are affected by system delays and gradient field imperfections which induce discrepancies between prescribed and actual k-space trajectories. This could be even more critical for non-Cartesian data acquisitions where even a small deviation from the assumed k-space trajectory results in severe image degradation and artifacts. Knowledge of the actual k-space trajectories is therefore crucial and can be incorporated in the reconstruction of high quality non-Cartesian images. A novel MR method for the calibration of actual gradient waveforms was developed using a combination of phase encoding increments and subsequent detection of the exact time point at which the corresponding trajectory is crossing the k-space origin. The measured sets of points were fitted to a parametrical model to calculate the complete actual acquisition trajectory. Measurements performed on phantoms and volunteers, positioned both in- and off-isocenter of the magnet, clearly demonstrate the improvement in reconstructed ultrashort echo time (UTE) images, when information from calibration of k-space sampling trajectories is employed in the MR image reconstruction procedure. The unique feature of the proposed method is its robustness and simple experimental setup, making it suitable for quick acquisition trajectory calibration procedures e.g. for non-Cartesian radial fast imaging.     

Cardiac magnetic resonance imaging using radial k-space sampling and self-calibrated partial parallel reconstruction

Radial sampling has been demonstrated to be potentially useful in cardiac magnetic resonance imaging because it is less susceptible to motion than Cartesian sampling. Nevertheless, its capability of imaging acceleration remains limited by undersampling-induced streaking artifacts. In this study, a self-calibrated reconstruction method was developed to suppress streaking artifacts for highly accelerated parallel radial acquisitions in cardiac magnetic resonance imaging. Two- (2D) and three-dimensional (3D) radial k-space data were collected from a phantom and healthy volunteers. Images reconstructed using the proposed method and the conventional regridding method were compared based on statistical analysis on a four-point scale imaging scoring. It was demonstrated that the proposed method can effectively remove undersampling streaking artifacts and significantly improve image quality (P<.05). With the use of the proposed method, image score (1–4, 1=poor, 2=good, 3=very good, 4=excellent) was improved from 2.14 to 3.34 with the use of an undersampling factor of 4 and from 1.09 to 2.5 with the use of an undersampling factor of 8. Our study demonstrates that the proposed reconstruction method is effective for highly accelerated cardiac imaging applications using parallel radial acquisitions without calibration data.     

Reduced aliasing artifacts using shaking projection k-space sampling trajectory

Radial imaging techniques, such as projection-reconstruction （PR）, are used in magnetic resonance imaging （MRI） for dynamic imaging, angiography, and short-T2 imaging. They are less sensitive to flow and motion artifacts, and support fast imaging with short echo times. However, aliasing and streaking artifacts are two main sources which degrade radial imaging quality. For a given fixed number of k-space projections, data distributions along radial and angular directions will influence the level of aliasing and streaking artifacts. Conventional radial k-space sampling trajectory introduces an aliasing artifact at the first principal ring of point spread function （PSF）. In this paper, a shaking projection （SP） k-space sampling trajectory was proposed to reduce aliasing artifacts in MR images. SP sampling trajectory shifts the projection alternately along the k-space center, which separates k-space data in the azimuthal direction. Simulations based on conventional and SP sampling trajectories were compared with the same number projections. A significant reduction of aliasing artifacts was observed using the SP sampling trajectory. These two trajectories were also compared with different sampling frequencies. ASP trajectory has the same aliasing character when using half sampling frequency （or half data） for reconstruction. SNR comparisons with different white noise levels show that these two trajectories have the same SNR character. In conclusion, the SP trajectory can reduce the aliasing artifact without decreasing SNR and also provide a way for undersampling recon- struction. Furthermore, this method can be applied to three-dimensional （3D） hybrid or spherical radial k-space sampling for a more efficient reduction of aliasing artifacts.     

Parallel imaging with 3D TPI trajectory: SNR and acceleration benefits

Three-dimensional (3D) twisted projection imaging (TPI) trajectory has a unique advantage in sodium (²³Na) imaging on clinical MRI scanners at 1.5 or 3 T, generating a high signal-to-noise ratio (SNR) with a short acquisition time (∼10 min). Parallel imaging with an array of coil elements transits SNR benefits from small coil elements to acquisition efficiency by sampling partial k-space. This study investigates the feasibility of parallel sodium imaging with emphases on SNR and acceleration benefits provided by the 3D TPI trajectory. Computer simulations were used to find available acceleration factors and noise amplification. Human head studies were performed on clinical 1.5/3-T scanners with four-element coil arrays to verify simulation outcomes. In in vivo studies, proton (¹H) data, however, were acquired for concept–proof purpose. The sensitivity encoding (SENSE) method with the conjugate gradient algorithm was used to reconstruct images from accelerated TPI-SENSE data sets. Self-calibration was employed to estimate coil sensitivities. Noise amplification in TPI-SENSE was evaluated using multiple noise trials. It was found that the acceleration factor was as high as 5.53 (corresponding to acceleration number 2×3, ring-by-rotation), with a small image error of 6.9% when TPI projections were reduced in both polar (ring) and azimuthal (rotation) directions. The average noise amplification was as low as 98.7%, or 27% lower than Cartesian SENSE at that acceleration factor. The 3D nature of both TPI trajectory and coil sensitivities might be responsible for the high acceleration and low noise amplification. Consequently, TPI-SENSE may have potential advantages for parallel sodium imaging.     

O-space with high resolution readouts outperforms radial imaging

PurposeWhile O-Space imaging is well known to accelerate image acquisition beyond traditional Cartesian sampling, its advantages compared to undersampled radial imaging, the linear trajectory most akin to O-Space imaging, have not been detailed. In addition, previous studies have focused on ultrafast imaging with very high acceleration factors and relatively low resolution. The purpose of this work is to directly compare O-Space and radial imaging in their potential to deliver highly undersampled images of high resolution and minimal artifacts, as needed for diagnostic applications. We report that the greatest advantages to O-Space imaging are observed with extended data acquisition readouts.Theory and methodsA sampling strategy that uses high resolution readouts is presented and applied to compare the potential of radial and O-Space sequences to generate high resolution images at high undersampling factors. Simulations and phantom studies were performed to investigate whether use of extended readout windows in O-Space imaging would increase k-space sampling and improve image quality, compared to radial imaging.ResultsExperimental O-Space images acquired with high resolution readouts show fewer artifacts and greater sharpness than radial imaging with equivalent scan parameters. Radial images taken with longer readouts show stronger undersampling artifacts, which can cause small or subtle image features to disappear. These features are preserved in a comparable O-Space image.ConclusionsHigh resolution O-Space imaging yields highly undersampled images of high resolution and minimal artifacts. The additional nonlinear gradient field improves image quality beyond conventional radial imaging.     

Spiral MRI和图像处理

介绍了在Bruker Biospec 47/30 超导核磁共振成象仪(4.7 T)上实现Spiral快速成像及图像处理系统. 图像处理系统基于PC技术构建而成,主要功能包括：1） 将以Spiral形式采集到的时域磁共振信号转化为适用于快速傅立叶变换的笛卡尔网格(Cartesian)形式（网格化处理）;2）二维快速傅立叶变换(2D-FFT,图像重建);3）由化学位移偏置或磁场不均匀引起得偏共振效应(off-resonance effect)的校正;4）图像分析. 该软件适用于包括以多片多回波在内的各种采样方式得到的Spiral图像的重建和分析,也适用于常规成像数据的重建和分析. 所得到的图像可以以数据方式保存以供再次读入,也能够以TIF、GIF、JPG、BM等格式辅出为图像文件.     

Real-time dynamic vocal tract imaging using an accelerated spiral GRE sequence and low rank plus sparse reconstruction

PurposeTo develop a real-time dynamic vocal tract imaging method using an accelerated spiral GRE sequence and low rank plus sparse reconstruction.MethodsSpiral k-space sampling has high data acquisition efficiency and thus is suited for real-time dynamic imaging; further acceleration can be achieved by undersampling k-space and using a model-based reconstruction. Low rank plus sparse reconstruction is a promising method with fast computation and increased robustness to global signal changes and bulk motion, as the images are decomposed into low rank and sparse terms representing different dynamic components. However, the combination with spiral scanning has not been well studied. In this study an accelerated spiral GRE sequence was developed with an optimized low rank plus sparse reconstruction and compared with L1-SPIRiT and XD-GRASP methods. The off-resonance was also corrected using a Chebyshev approximation method to reduce blurring on a frame-by-frame basis.ResultsThe low rank plus sparse reconstruction method is sensitive to the weights of the low rank and sparse terms. The optimized reconstruction showed advantages over other methods with reduced aliasing and improved SNR. With the proposed method, spatial resolution of 1.3*1.3 mm² with 150 mm field-of-view (FOV) and temporal resolution of 30 frames-per-second (fps) was achieved with good image quality. Blurring was reduced using the Chebyshev approximation method.ConclusionThis work studies low rank plus sparse reconstruction using the spiral trajectory and demonstrates a new method for dynamic vocal tract imaging which can benefit studies of speech disorders.     

Incorporating prior knowledge via volumetric deep residual network to optimize the reconstruction of sparsely sampled MRI

For sparse sampling that accelerates magnetic resonance (MR) image acquisition, non-linear reconstruction algorithms have been developed, which incorporated patient specific a prior information. More generic a prior information could be acquired via deep learning and utilized for image reconstruction. In this study, we developed a volumetric hierarchical deep residual convolutional neural network, referred to as T-Net, to provide a data-driven end-to-end mapping from sparsely sampled MR images to fully sampled MR images, where cartilage MR images were acquired using an Ultra-short TE sequence and retrospectively undersampled using pseudo-random Cartesian and radial acquisition schemes. The network had a hierarchical architecture that promoted the sparsity of feature maps and increased the receptive field, which were valuable for signal synthesis and artifact suppression. Relatively dense local connections and global shortcuts were established to facilitate residual learning and compensate for details lost in hierarchical processing. Additionally, volumetric processing was adopted to fully exploit spatial continuity in three-dimensional space. Data consistency was further enforced. The network was trained with 336 three-dimensional images (each consisting of 32 slices) and tested by 24 images. The incorporation of a priori information acquired via deep learning facilitated high acceleration factors (as high as 8) while maintaining high image fidelity (quantitatively evaluated using the structural similarity index measurement). The proposed T-Net had an improved performance as compared to several state-of-the-art networks.     

SEnD NMR: Sensitivity Enhanced n-Dimensional NMR

Sparse sampling offers tremendous potential for overcoming the time limitations imposed by traditional Cartesian sampling of indirectly detected dimensions of multidimensional NMR data. However, in many instances sensitivity rather than time remains of foremost importance when collecting data on protein samples. Here we explore how to optimize the collection of radial sampled multidimensional NMR data to achieve maximal signal-to-noise. A method is presented that exploits a rigorous definition of the minimal set of radial sampling angles required to resolve all peaks of interest in combination with a fundamental statistical property of radial sampled data. The approach appears general and can achieve a substantial sensitivity advantage over Cartesian sampling for the same total data acquisition time. Termed Sensitivity Enhanced n-Dimensional or SEnD NMR, the method involves three basic steps. First, data collection is optimized using routines to determine a minimal set of radial sampling angles required to resolve frequencies in the radially sampled chemical shift evolution dimensions. Second, appropriate combinations of experimental parameters (transients and increments) are defined by simple statistical considerations in order to optimize signal-to-noise in single angle frequency domain spectra. Finally, the data is processed with a direct multidimensional Fourier transform and a statistical artifact and noise removal step is employed.     

Robust GRAPPA reconstruction using sparse multi-kernel learning with least squares support vector regression

Accuracy of interpolation coefficients fitting to the auto-calibrating signal data is crucial for k-space-based parallel reconstruction. Both conventional generalized autocalibrating partially parallel acquisitions (GRAPPA) reconstruction that utilizes linear interpolation function and nonlinear GRAPPA (NLGRAPPA) reconstruction with polynomial kernel function are sensitive to interpolation window and often cannot consistently produce good results for overall acceleration factors. In this study, sparse multi-kernel learning is conducted within the framework of least squares support vector regression to fit interpolation coefficients as well as to reconstruct images robustly under different subsampling patterns and coil datasets. The kernel combination weights and interpolation coefficients are adaptively determined by efficient semi-infinite linear programming techniques. Experimental results on phantom and in vivo data indicate that the proposed method can automatically achieve an optimized compromise between noise suppression and residual artifacts for various sampling schemes. Compared with NLGRAPPA, our method is significantly less sensitive to the interpolation window and kernel parameters.     

Deep artifact suppression for spiral real-time phase contrast cardiac magnetic resonance imaging in congenital heart disease

PurposeReal-time spiral phase contrast MR (PCMR) enables rapid free-breathing assessment of flow. Target spatial and temporal resolutions require high acceleration rates often leading to long reconstruction times. Here we propose a deep artifact suppression framework for fast and accurate flow quantification.MethodsU-Nets were trained for deep artifact suppression using 520 breath-hold gated spiral PCMR aortic datasets collected in congenital heart disease patients. Two spiral trajectories (uniform and perturbed) and two losses (Mean Absolute Error -MAE- and average structural similarity index measurement -SSIM-) were compared in synthetic data in terms of MAE, peak SNR (PSNR) and SSIM. Perturbed spiral PCMR was prospectively acquired in 20 patients. Stroke Volume (SV), peak mean velocity and edge sharpness measurements were compared to Compressed Sensing (CS) and Cartesian reference.ResultsIn synthetic data, perturbed spiral consistently outperformed uniform spiral for the different image metrics. U-Net MAE showed better MAE and PSNR while U-Net SSIM showed higher SSIM based metrics.In-vivo, there were no significant differences in SV between any of the real-time reconstructions and the reference standard Cartesian data. However, U-Net SSIM had better image sharpness and lower biases for peak velocity when compared to U-Net MAE. Reconstruction of 96 frames took ~59 s for CS and 3.9 s for U-Nets.ConclusionDeep artifact suppression of complex valued images using an SSIM based loss was successfully demonstrated in a cohort of congenital heart disease patients for fast and accurate flow quantification.     

Phase-constrained parallel MR image reconstruction

A generalized method for phase-constrained parallel MR image reconstruction is presented that combines and extends the concepts of partial-Fourier reconstruction and parallel imaging. It provides a framework for reconstructing images employing either or both techniques and for comparing image quality achieved by varying k-space sampling schemes. The method can be used as a parallel image reconstruction with a partial-Fourier reconstruction built in. It can also be used with trajectories not readily handled by straightforward combinations of partial-Fourier and SENSE-like parallel reconstructions, including variable-density, and non-Cartesian trajectories. The phase constraint specifies a better-conditioned inverse problem compared to unconstrained parallel MR reconstruction alone. This phase-constrained parallel MRI reconstruction offers a one-step alternative to the standard combination of homodyne and SENSE reconstructions with the added benefit of flexibility of sampling trajectory. The theory of the phase-constrained approach is outlined, and its calibration requirements and limitations are discussed. Simulations, phantom experiments, and in vivo experiments are presented.     

Point spread functions of the T(2) decay in k-space trajectories with long echo train

T(2) decay during long echo trains of magnetic resonance (MR) imaging pulse sequences is known to cause a blurring effect, due to the peak broadening of the point spread function (PSF). In contrast, the simultaneous amplitude-loss effect, led by the peak reduction of the PSF, has gained much less attention. In this report, we analyzed the PSFs of both the truncation and T(2) decay for Cartesian (linear profile ordering and low-high ordering) and spiral trajectories, respectively. Then, we derived simple formulas to characterize both the blurring and amplitude-loss effects, which are functions of the ratios of the echo train duration (T(k)) over T(2) (T(k)/T(2)). Signal-to-noise ratio (SNR) per unit time was thus analyzed considering both the amplitude-loss effect induced by the T(2) decay and the SNR gain from the long acquisition duration based on MR sampling theory. Optimum T(k)/T(2) ratios to achieve maximum SNR per unit time were 1.2 for the Cartesian trajectory and 0.8 for the spiral trajectory.     

Autocalibrated parallel imaging reconstruction with sampling pattern optimization for GRASE: APIR4GRASE

PurposeTo reduce artifacts and scan time of GRASE imaging by selecting an optimal sampling pattern and jointly reconstructing gradient echo and spin echo images.MethodsWe jointly reconstruct images for the different echo types by considering these as additional virtual coil channels in the novel Autocalibrated Parallel Imaging Reconstruction with Sampling Pattern Optimization for GRASE (APIR4GRASE) method. Besides image reconstruction, we identify optimal sampling patterns for the acquisition. The selected optimal patterns were validated on phantom and in-vivo acquisitions. Comparison to the conventional GRASE without acceleration, and to the GRAPPA reconstruction with a single echo type was also performed.ResultsUsing identified optimal sampling patterns, APIR4GRASE eliminated modulation artifacts in both phantom and in-vivo experiments; mean square error (MSE) was reduced by 78% and 94%, respectively, compared to the conventional GRASE with similar scan time. Both artifacts and g-factor were reduced compared to the GRAPPA reconstruction with a single echo type.ConclusionAPIR4GRASE substantially improves the speed and quality of GRASE imaging over the state-of-the-art, and is able to reconstruct both spin echo and gradient echo images.     

Centric scan SPRITE magnetic resonance imaging

Two rapid, pure phase encode, centric scan, Single Point Ramped Imaging with T₁-Enhancement (SPRITE) MRI methods are described. Each retains the benefits of the standard SPRITE method, most notably the ability to image short T₂^* systems, while increasing the sensitivity and generality of the technique. The Spiral-SPRITE method utilizes a modified Archimedean spiral k-space trajectory. The Conical-SPRITE method utilizes a system of spirals mapped to conical surfaces to sample the k-space cube. The sampled k-space points are naturally Cartesian grid points, eliminating the requirement of a re-gridding procedure prior to image reconstruction. The effects of transient state behaviour on image resolution and signal/noise are explored.     

Retrospective intra-scan motion correction

This paper analyzes the effects of intra-scan motion and demonstrates the possibility of correcting them directly in k-space with a new automatic retrospective method. The method is presented for series of 2D acquisitions with Cartesian sampling. Using a reference k-space acquisition (corrected for translations) within the series, intra-scan motion parameters are accurately estimated for each trajectory in k-space of each data set in the series resulting in pseudo-random sample positions. The images are reconstructed with a Bayesian estimator that can handle sparse arbitrary sampling in k-space and reduces intra-scan rotation artefacts to the noise level. The method has been assessed by means of a Monte Carlo study on axial brain images for different signal-to-noise ratios. The accuracy of motion estimates is better than 0.1 degrees for rotation, and 0.1 and 0.05 pixel, respectively, for translation along the read and phase directions for signal-to-noise ratios higher than 6 of the signals on each trajectory. An example of reconstruction from experimental data corrupted by head motion is also given.     

基于改进空间频率域采样的天文光干涉望远镜阵列优化

提出一种基于改进空间频率域(UV)采样的阵列评价函数,用于长基线天文光干涉望远镜阵列几何结构的优化。该评价函数将UV采样区域沿径向和角度方向分别进行划分,统计划分所得区域中UV采样点数目并计算UV采样点密度,以UV采样点密度偏离理想高斯分布的大小作为评价依据。在具体的优化技术上,利用遗传算法的全局收敛特性,降低了传统算法对初始结构的依赖,采用该评价函数对6孔径望远镜阵列进行优化设计,并与国际主流天文光干涉阵列CHARA进行了性能对比。分析结果表明:优化所得Array-6阵列UV采样点密度分布具有径向连续覆盖和低频强调的特点,有利于对轮廓信息的恢复;双星模拟成像实验中Array-6阵列重构图像相对于原始图像的误差为21.34,相比CHARA阵列降低了18.16%,具有更高的成像质量。该优化算法具备优化大孔径数目阵列的能力,对于射电波段望远镜阵列的优化设计亦有一定的参考意义。