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.     

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 inherited parallel acquisition (KIPA): application on dynamic magnetic resonance imaging thermometry

In this study, a novel method for dynamic parallel image acquisition and reconstruction is presented. In this method, called k-space inherited parallel acquisition (KIPA), localized reconstruction coefficients are used to achieve higher reduction factors, and lower noise and artifact levels compared to that of generalized autocalibrating partially parallel acquisition (GRAPPA) reconstruction. In KIPA, the full k-space for the first frame and the partial k-space for later frames are required to reconstruct a whole series of images. Reconstruction coefficients calculated for different segments of k-space from the first frame data set are used to estimate missing k-space lines in corresponding k-space segments of other frames. The local determination of KIPA reconstruction coefficients is essential to adjusting them according to the local signal-to-noise ratio characteristics of k-space data. The proposed algorithm is applicable to dynamic imaging with arbitrary k-space sampling trajectories. Simulations of magnetic resonance thermometry using the KIPA method with a reduction factor of 6 and using dynamic imaging studies of human subjects with reduction factors of 4 and 6 have been performed to prove the feasibility of our method and to show apparent improvement in image quality in comparison with GRAPPA for dynamic imaging.     

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.     

Composite MR image reconstruction and unaliasing for general trajectories using neural networks

In rapid parallel magnetic resonance imaging, the problem of image reconstruction is challenging. Here, a novel image reconstruction technique for data acquired along any general trajectory in neural network framework, called “Composite Reconstruction And Unaliasing using Neural Networks” (CRAUNN), is proposed. CRAUNN is based on the observation that the nature of aliasing remains unchanged whether the undersampled acquisition contains only low frequencies or includes high frequencies too. Here, the transformation needed to reconstruct the alias-free image from the aliased coil images is learnt, using acquisitions consisting of densely sampled low frequencies. Neural networks are made use of as machine learning tools to learn the transformation, in order to obtain the desired alias-free image for actual acquisitions containing sparsely sampled low as well as high frequencies. CRAUNN operates in the image domain and does not require explicit coil sensitivity estimation. It is also independent of the sampling trajectory used, and could be applied to arbitrary trajectories as well. As a pilot trial, the technique is first applied to Cartesian trajectory-sampled data. Experiments performed using radial and spiral trajectories on real and synthetic data, illustrate the performance of the method. The reconstruction errors depend on the acceleration factor as well as the sampling trajectory. It is found that higher acceleration factors can be obtained when radial trajectories are used. Comparisons against existing techniques are presented. CRAUNN has been found to perform on par with the state-of-the-art techniques. Acceleration factors of up to 4, 6 and 4 are achieved in Cartesian, radial and spiral cases, respectively.     

Reconstruction in image space using basis functions for partially parallel imaging

General theory of a new reconstruction technique for partially parallel imaging (PPI) is presented in this study. Reconstruction in Image space using Basis functions (RIB) is based on the general principle that the PPI reconstruction in image space can be represented by a pixel-wise weighted summation of the aliased images directly from undersampled data. By assuming that these weighting coefficients for unaliasing can be approximated from the linear combination of a few predefined basis functions, RIB is capable of reconstructing the image within an arbitrary region. This paper discusses the general theory of RIB and its relationship to the classical reconstruction method, GRAPPA. The presented experiments demonstrate RIB with several MRI applications. It is shown that the performance of RIB is comparable to that of GRAPPA. In some cases, RIB shows advantages of increasing reconstruction efficiency, suppressing artifacts and alleviating the nonuniformity of noise distribution. It is anticipated that RIB would be especially useful for cardiac and prostate imaging, where the field of view during data acquisition is required to be much larger than the region of interest.     

一种结合并行成像和压缩感知的快速磁共振成像新方法

压缩感知（CS）技术和并行成像技术（主要是SENSE技术、GRAPPA技术等）都能通过减少k空间数据的采集量来加快磁共振成像速度,目前已有一些将两种方法相结合进一步加速磁共振成像速度的方法（例如CS-GRAPPA）.本文针对数据采集和重建这两方面对现有CS-GRAPPA方法进行了改进,采集方式上采用了局部等间隔采集模板以满足GRAPPA重建的要求,并对采集模板进行随机放置以满足CS重建的要求;数据重建时,根据自动校正数据估算GRAPPA算法中欠采行的重建误差,并利用误差的大小确定在CS算法中保真的程度.不同磁共振图像重建实验的结果表明：与现有方法相比,本文方法能够更好地保留原有图像细节并有效减少伪影.     

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.     

Sparsity-constrained SENSE reconstruction: An efficient implementation using a fast composite splitting algorithm

Parallel imaging and compressed sensing have been arguably the most successful and widely used techniques for fast magnetic resonance imaging (MRI). Recent studies have shown that the combination of these two techniques is useful for solving the inverse problem of recovering the image from highly under-sampled k-space data. In sparsity-enforced sensitivity encoding (SENSE) reconstruction, the optimization problem involves data fidelity (L2-norm) constraint and a number of L1-norm regularization terms (i.e. total variation or TV, and L1 norm). This makes the optimization problem difficult to solve due to the non-smooth nature of the regularization terms. In this paper, to effectively solve the sparsity-regularized SENSE reconstruction, we utilize a new optimization method, called fast composite splitting algorithm (FCSA), which was developed for compressed sensing MRI. By using a combination of variable splitting and operator splitting techniques, the FCSA algorithm decouples the large optimization problem into TV and L1 sub-problems, which are then, solved efficiently using existing fast methods. The operator splitting separates the smooth terms from the non-smooth terms, so that both terms are treated in an efficient manner. The final solution to the SENSE reconstruction is obtained by weighted solutions to the sub-problems through an iterative optimization procedure. The FCSA-based parallel MRI technique is tested on MR brain image reconstructions at various acceleration rates and with different sampling trajectories. The results indicate that, for sparsity-regularized SENSE reconstruction, the FCSA-based method is capable of achieving significant improvements in reconstruction accuracy when compared with the state-of-the-art reconstruction method.     

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.     

Respiratory motion compensation using data binning in dynamic contrast enhanced golden-angle radial MRI

GRASP (Golden-Angle Radial Sparse Parallel MRI) is a data acquisition and reconstruction technique that combines parallel imaging and golden-angle radial sampling. The continuously acquired free breathing Dynamic Contrast Enhanced (DCE) golden-angle radial MRI data of liver and abdomen has artifacts due to respiratory motion, resulting in low vessel-tissue contrast that makes GRASP reconstructed images less suitable for diagnosis. In this paper, DCE golden-angle radial MRI data of abdomen and liver perfusion is sorted into different motion states using the self-gating property of radial acquisition and then reconstructed using GRASP. Three methods of amplitude-based data binning namely uniform binning, adaptive binning and optimal binning are applied on the DCE golden-angle radial data to extract different motion states and a comparison is performed with the conventional GRASP reconstruction. Also, a comparison among the amplitude-based data binning techniques is performed and benefits of each of these binning techniques are discussed from a clinical perspective. The image quality assessment in terms of hepatic vessel clarity, liver edge sharpness, contrast enhancement clarity and streaking artifacts is performed by a certified radiologist. The results show that DCE golden-angle radial trajectories benefit from all the three types of amplitude-based data binning methods providing improved reconstruction results. The choice of binning technique depends upon the clinical application e.g. uniform and adaptive binning are helpful for a detailed analysis of lesion characteristic and contrast enhancement in different motion states while optimal binning can be used when clinical analysis requires a single image per contrast enhancement phase with no motion blurring artifacts.     

High resolution dynamic cardiac MRI using partial separability of spatiotemporal signals with a novel sampling scheme

The partial separability (PS) of spatiotemporal signals has been exploited to accelerate dynamic cardiac MRI by sampling two datasets (training and imaging datasets) without breath-holding or ECG triggering. According to the theory of partially separable functions, the wider the range of spatial frequency components covered by the training dataset, the more accurate the temporal constraint imposed by the PS model. Therefore, it is necessary to develop a new sampling scheme for the PS model in order to cover a wider range of spatial frequency components. In this paper, we propose the use of radial sampling trajectories for collecting the training dataset and Cartesian sampling trajectories for collecting the imaging dataset. In vivo high resolution cardiac MRI experiments demonstrate that the proposed data sampling scheme can significantly improve the image quality. The image quality using the PS model with the proposed sampling scheme is comparable to that of a commercial method using retrospective cardiac gating and breath-holding. The success of this study demonstrates great potential for high-quality, high resolution dynamic cardiac MRI without ECG gating or breath-holding through use of the PS model and the novel data sampling scheme.     

Real-time exercise stress cardiac MRI with Fourier-series reconstruction from golden-angle radial data

Magnetic resonance imaging (MRI) can measure cardiac response to exercise stress for evaluating and managing heart patients in the practice of clinical cardiology. However, exercise stress cardiac MRI have been clinically limited by the ability of available MRI techniques to quantitatively measure fast and unstable cardiac dynamics during exercise. The presented work is to develop a new real-time MRI technique for improved quantitative performance of exercise stress cardiac MRI. This technique seeks to represent real-time cardiac images as a sparse Fourier-series along the time. With golden-angle radial acquisition, parallel imaging and compressed sensing can be integrated into a linear system of equations for resolving Fourier coefficients that are in turn used to generate real-time cardiac images from the Fourier-series representation. Fourier-series reconstruction from golden-angle radial data can effectively address data insufficiency due to MRI speed limitation, providing a real-time approach to exercise stress cardiac MRI. To demonstrate the feasibility, an exercise stress cardiac MRI experiment was run to investigate biventricular response to in-scanner biking exercise in a cohort of sixteen healthy volunteers. It was found that Fourier-series reconstruction from golden-angle radial data effectively detected exercise-induced increase in stroke volume and ejection fraction in a healthy heart. The presented work will improve the applications of exercise stress cardiac MRI in the practice of clinical cardiology.     

基于同时多层激发和并行成像的心脏磁共振电影成像

磁共振成像（MRI）无创无害、对比度多、可以任意剖面成像的特点特别适合用于心脏成像,却因扫描时间长限制了其在临床上的应用.为了解决心脏磁共振电影成像屏气扫描时间过长的问题,该文提出了一种基于同时多层激发的多倍加速心脏磁共振电影成像及其影像重建的方法,该方法将相位调制多层激发（CAIPIRINHA）技术与并行加速（PPA）技术相结合,运用到分段采集心脏电影成像序列中,实现了在相位编码方向和选层方向的四倍加速,并使用改进的SENSE/GRAPPA算法对图像进行重建.分别在水模以及人体上进行了实验,将加速序列图像与不加速序列图像进行对比,结果验证了重建算法的有效性,表明该方法可以在保障图像质量以及准确测量心脏功能的前提下成倍节省扫描时间.     

基于图像压缩传感的自动式光学单点成像系统

基于图像压缩传感理论,在手动式光学单点成像系统的基础上研究了自动式光学单点成像系统。主要介绍了系统中自动编码转盘的设计以及编码块的获取,采用一系列优化的编码块图案作为测量矩阵,并利用最小均方差线性估计（MMSE）重构算法进行实验。实验研究表明,通过7.8% 低采样率即可实现对字符样本的重构。该自动编码转盘系统自动化程度较高,误差较小,而且可随意改变测量次数。     

一种基于时空变换和压缩感知的磁共振螺旋采样的图像重建算法

螺旋采样磁共振快速成像在功能性成像、并行成像和动态成像等领域发挥着越来越重要的作用.螺旋采样图像重建的传统算法是用核函数将螺旋状分布的k空间数据插值到均匀网格中,再利用傅里叶变换和最小二乘法进行重建.但是基于网格化的算法对核函数过于依赖,在网格化过程中产生难以避免的误差.该文提出了基于时空变换和压缩感知的l1范数的最优化模型和重建算法.时空变换矩阵描述了空间上的磁共振图像与采集到的时域信号间的关系,使得算法直接使用采集到的数据作为保真约束项,避免了网格化过程产生的误差.此外,基于图像处理单元的并行计算被用来提高时空变换矩阵的运算速度,使得算法具有较强的应用价值.     

Towards a general framework for fast and feasible k-space trajectories for MRI based on projection methods

The design of feasible trajectories to traverse the k-space for sampling in magnetic resonance imaging (MRI) is important while considering ways to reduce the scan time. Over the recent years, non-Cartesian trajectories have been observed to result in benign artifacts and being less sensitive to motion. In this paper, we propose a generalized framework that encompasses projection-based methods to generate feasible non-Cartesian k-space trajectories. This framework allows to construct feasible trajectories from both random or structured initial trajectories, e.g., based on the traveling salesman problem (TSP). We evaluate the performance of the proposed methods by simulating the reconstruction of 128 × 128 and 256 × 256 phantom and brain MRI images in terms of structural similarity (SSIM) index and peak signal-to-noise ratio (PSNR) using compressed sensing techniques. It is observed that the TSP-based trajectories from the proposed projection method with constant acceleration parameterization (CAP) result in better reconstruction compared to the projection method with constant velocity parameterization (CVP) and this for a similar read-out time. Further, random-like trajectories are observed to be better than TSP-based trajectories as they reduce the read-out time while providing better reconstruction quality. A reduction in read-out time by upto 67% is achieved using the proposed projection with permutation (PP) method.     

鬼成像中一些数学问题

鬼成像是一种与传统成像方式不同的通过光场涨落的高阶关联获得图像信息的新型成像方式。近年来,相比传统成像方式,鬼成像所拥有的一些优点如高灵敏度、超分辨能力、抗散射等,使其在遥感、多光谱成像、热X射线衍射成像等领域得到广泛研究。随着对鬼成像的广泛研究,数学理论和方法在其中发挥的作用愈显突出。例如,基于压缩感知理论,可以进行鬼成像系统采样方式优化、图像重构算法设计及图像重构质量分析等研究工作。本文旨在探索鬼成像中的一些有趣的数学问题,主要包括:系统预处理方法、光场优化及相位恢复问题。对这些问题的研究既可以丰富鬼成像理论,又能推动它在实际应用中的发展。     

Retrospective cardiac gating: a review of technical aspects and future directions

The advent of short TR gradient-echo imaging has made it possible to acquire cine images of the heart with conventional whole body MRI scanners. In this paper, technical details of the data collection and image reconstruction process for cine MRI using retrospective cardiac gating are presented. Specifically, the following issues are discussed: data sorting and interpolation; time resolution; motion compensation and phase information; the type of steady state sequence including optimal flip angle; respiratory motion and correction; and the potential of 3D imaging.     

Triple-D network for efficient undersampled magnetic resonance images reconstruction

Compressed sensing (CS) theory can help accelerate magnetic resonance imaging (MRI) by sampling partial k-space measurements. However, conventional optimization-based CS-MRI methods are often time-consuming and are based on fixed transform or shallow image dictionaries, which limits modeling capabilities. Recently, deep learning models have been used to solve the CS-MRI problem. However, recent researches have focused on modeling in image domain, and the potential of k-space modeling capability has not been utilized seriously. In this paper, we propose a deep model called Dual Domain Dense network (Triple-D network), which consisted of some k-space and image domain sub-network. These sub-networks are connected with dense connections, which can utilize feature maps at different levels to enhance performance. To further promote model capabilities, we use two strategies: multi-supervision strategies, which can avoid loss of supervision information; channel-wise attention layer (CA layer), which can adaptively adjust the weight of the feature map. Experimental results show that the proposed Triple-D network provides promising performance in CS-MRI, and it can effectively work on different sampling trajectories and noisy settings.