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.     

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.     

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.     

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.     

Calibration-less multi-coil MR image reconstruction

In parallel magnetic resonance imaging (MRI), the problem is to reconstruct an image given the partial K-space scans from all the receiver coils. Depending on its position within the scanner, each coil has a different sensitivity profile. All existing parallel MRI techniques require estimation of certain parameters pertaining to the sensitivity profile, e.g., the sensitivity map needs to be estimated for the SENSE and SMASH and the interpolation weights need to be calibrated for GRAPPA and SPIRiT. The assumption is that the estimated parameters are applicable at the operational stage. This assumption does not always hold, consequently the reconstruction accuracies of existing parallel MRI methods may suffer. We propose a reconstruction method called Calibration-Less Multi-coil (CaLM) MRI. As the name suggests, our method does not require estimation of any parameters related to the sensitivity maps and hence does not require a calibration stage. CaLM MRI is an image domain method that produces a sensitivity encoded image for each coil. These images are finally combined by the sum-of-squares method to yield the final image. It is based on the theory of Compressed Sensing (CS). During reconstruction, the constraint that "all the coil images should appear similar" is introduced within the CS framework. This leads to a CS optimization problem that promotes group-sparsity. The results from our proposed method are comparable (at least for the data used in this work) with the best results that can be obtained from state-of-the-art methods.     

Tailored utilization of acquired k-space points for GRAPPA reconstruction

The generalized auto-calibrating partially parallel acquisition (GRAPPA) is an auto-calibrating parallel imaging technique which incorporates multiple blocks of data to derive the missing signals. In the original GRAPPA reconstruction algorithm only the data points in phase encoding direction are incorporated to reconstruct missing points in k-space. It has been recognized that this scheme can be extended so that data points in readout direction are also utilized and the points are selected based on a k-space locality criterion. In this study, an automatic subset selection strategy is proposed which can provide a tailored selection of source points for reconstruction. This novel approach extracts a subset of signal points corresponding to the most linearly independent base vectors in the coefficient matrix of fit, effectively preventing incorporating redundant signals which only bring noise into reconstruction with little contribution to the exactness of fit. Also, subset selection in this way has a regularization effect since the vectors corresponding to the smallest singular values are eliminated and consequently the condition of the reconstruction is improved. Phantom and in vivo MRI experiments demonstrate that this subset selection strategy can effectively improve SNR and reduce residual artifacts for GRAPPA reconstruction.     

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.     

数据插值对正电子发射断层成像设备的图像重建影响的研究

正电子发射断层扫描(positron emission computed tomography, PET)是核医学领域最先进的临床检查影像技术. PET技术是目前临床上用于诊断和指导治疗肿瘤的最佳手段之一. 正电子发射断层成像设备探测器采集到的数据需要进行数据处理, 把原始数据转换成正弦图形式的数据才能用于图像重建. 平行束断层重建和扇形束图像重建是图像重建的两种方法, 分别对应平行束和扇形束形式的数据处理方法. 对原始数据的操作不可避免地破坏了原始数据的完整性. 现今, 正电子发射断层设备在重建过程中普遍采用平行束重建的方法. 平行束的数据分离会对PET数据进行插值操作, 扇形束的数据分离不会对PET数据进行插值操作. 本文通过对比平行束图像重建和扇形束图像重建结果, 研究了数据插值对PET图像重建结果的影响. 关键词： 正电子发射计算机断层扫描 数据插值 图像重建 原始数据     

On NUFFT-based gridding for non-Cartesian MRI

For MRI with non-Cartesian sampling, the conventional approach to reconstructing images is to use the gridding method with a Kaiser-Bessel (KB) interpolation kernel. Recently, Sha et al. [L. Sha, H. Guo, A.W. Song, An improved gridding method for spiral MRI using nonuniform fast Fourier transform, J. Magn. Reson. 162(2) (2003) 250-258] proposed an alternative method based on a nonuniform FFT (NUFFT) with least-squares (LS) design of the interpolation coefficients. They described this LS_NUFFT method as shift variant and reported that it yielded smaller reconstruction approximation errors than the conventional shift-invariant KB approach. This paper analyzes the LS_NUFFT approach in detail. We show that when one accounts for a certain linear phase factor, the core of the LS_NUFFT interpolator is in fact real and shift invariant. Furthermore, we find that the KB approach yields smaller errors than the original LS_NUFFT approach. We show that optimizing certain scaling factors can lead to a somewhat improved LS_NUFFT approach, but the high computation cost seems to outweigh the modest reduction in reconstruction error. We conclude that the standard KB approach, with appropriate parameters as described in the literature, remains the practical method of choice for gridding reconstruction in MRI.     

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.     

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.     

Reconstruction of 3D ultrasound images based on Cyclic Regularized Savitzky-Golay filters

This paper presents a new three-dimensional (3D) ultrasound reconstruction algorithm for generation of 3D images from a series of two-dimensional (2D) B-scans acquired in the mechanical linear scanning framework. Unlike most existing 3D ultrasound reconstruction algorithms, which have been developed and evaluated in the freehand scanning framework, the new algorithm has been designed to capitalize the regularity pattern of the mechanical linear scanning, where all the B-scan slices are precisely parallel and evenly spaced. The new reconstruction algorithm, referred to as the Cyclic Regularized Savitzky-Golay (CRSG) filter, is a new variant of the Savitzky-Golay (SG) smoothing filter. The CRSG filter has been improved upon the original SG filter in two respects: First, the cyclic indicator function has been incorporated into the least square cost function to enable the CRSG filter to approximate nonuniformly spaced data of the unobserved image intensities contained in unfilled voxels and reduce speckle noise of the observed image intensities contained in filled voxels. Second, the regularization function has been augmented to the least squares cost function as a mechanism to balance between the degree of speckle reduction and the degree of detail preservation. The CRSG filter has been evaluated and compared with the Voxel Nearest-Neighbor (VNN) interpolation post-processed by the Adaptive Speckle Reduction (ASR) filter, the VNN interpolation post-processed by the Adaptive Weighted Median (AWM) filter, the Distance-Weighted (DW) interpolation, and the Adaptive Distance-Weighted (ADW) interpolation, on reconstructing a synthetic 3D spherical image and a clinical 3D carotid artery bifurcation in the mechanical linear scanning framework. This preliminary evaluation indicates that the CRSG filter is more effective in both speckle reduction and geometric reconstruction of 3D ultrasound images than the other methods.     

Performance Analysis of 2-D GRAPPA and Partial Fourier GRAPPA for 3-D MRI

The acquisition time of three-dimensional magnetic resonance imaging (3-D MRI) is too long to tolerate in many clinical applications. At present, parallel MRI (pMRI) and partial Fourier (PF) with homodyne detection, including 2-D pMRI (two-dimensional pMRI) and PF_pMRI (the combination of PF and pMRI), are often used to accelerate data sampling in 3-D MRI. However, the performances of 2-D pMRI and PF_pMRI have been seldom discussed. In this paper, we choose GRAPPA (generalized auto-calibrating partially parallel acquisition) as a representative pMRI to analyze and compare the performances of 2-D GRAPPA and PF_GRAPPA, including the noise standard deviation (SD), root mean-square error (RMSE) and g factor, through a series of in vitro experiments. A series of phantom experiments show that the SD, RMSE and g-factor values of PF_GRAPPA are lower than those of 2-D GRAPPA under the same acceleration factor. It demonstrates that the performance of PF_GRAPPA is better than that of 2-D GRAPPA. PF_GRAPPA can be used in any thickness of imaging slab, while 2-D GRAPPA can only be used in thick slab due to the difficulties in determination of the fitting coefficients which result from imperfect RF pulse. In vivo brain experiment results also show that the performance of PF_GRAPPA is better than that of 2-D GRAPPA.     

并行MRI图像重建算法比较及软件实现

首先介绍了不加速的并行MRI图像重建方法,然后对加速的并行MRI的4种图像重建算法进行了比较,得出结论：加速因子相同时,重建质量上,GRAPPA和SENSE的重建质量最好,SMASH的重建质量次之, PILS算法对线圈位置要求极高,重建质量最差;重建速度上,SMASH的重建速度最快,其次是SENSE和PILS,GRAPPA的重建速度最慢. 当加速因子变大时,所有算法重建质量都变差. 最后介绍了算法实现软件,该软件可以读入原始数据,显示数据采集轨迹,计算线圈灵敏度,选择图像重建方法,分析和比较重建图像质量. 该软件为我国在MRI成像领域提供了一个学习和进一步研究图像重建算法的有力工具.     

Singular Value Decomposition Using Jacobi Algorithm in pMRI and CS

Parallel magnetic resonance imaging (pMRI) and compressed sensing (CS) have been recently used to accelerate data acquisition process in MRI. Matrix inversion (for rectangular matrices) is required to reconstruct images from the acquired under-sampled data in various pMRI algorithms (e.g., SENSE, GRAPPA) and CS. Singular value decomposition (SVD) provides a mechanism to accurately estimate pseudo-inverse of a rectangular matrix. This work proposes the use of Jacobi SVD algorithm to reconstruct MR images from the acquired under-sampled data both in pMRI and in CS. The use of Jacobi SVD algorithm is proposed in advance MRI reconstruction algorithms, including SENSE, GRAPPA, and low-rank matrix estimation in L + S model for matrix inversion and estimation of singular values. Experiments are performed on 1.5T human head MRI data and 3T cardiac perfusion MRI data for different acceleration factors. The reconstructed images are analyzed using artifact power and central line profiles. The results show that the Jacobi SVD algorithm successfully reconstructs the images in SENSE, GRAPPA, and L + S algorithms. The benefit of using Jacobi SVD algorithm for MRI image reconstruction is its suitability for parallel computation on GPUs, which may be a great help in reducing the image reconstruction time.     

基于高斯核主成分分析的多通道拉曼光谱重建

针对多通道拉曼成像系统常会受荧光背景、噪声等非线性因素的影响而导致拉曼光谱重建结果一般的问题,提出了一种基于高斯核主成分分析的拉曼光谱重建算法.首先利用相似度因子对标定样本数据集进行预处理,其次通过高斯核函数将标定样本以非线性形式映射至高维特征空间,接着在特征空间中对映射后的数据集提取基函数并通过伪逆法求得与之对应的基函数系数.使用聚甲基丙烯酸甲酯作为测试样本,并引入均方根误差来评估拉曼光谱重建结果的准确性.实验结果表明,相比传统的伪逆法与维纳估计法,该算法具有更高的重建精度及抗噪能力,且能有效降低标定样本中不良数据和成像系统中非线性因素对拉曼光谱重建的影响.因此,该算法可以为多通道拉曼快速成像提供一种有效的拉曼光谱重建算法.     

A nonlinear regularization strategy for GRAPPA calibration

A regularization strategy is described for generalized autocalibrating partially parallel acquisition (GRAPPA) that allows successful calibration using a small number of autocalibration signals (ACS). The approach requires certain nonlinear relationships between the GRAPPA coefficients to be satisfied, which increases the redundancy so that fewer ACS need to be acquired.     

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.     

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.     

基于径向基函数神经网络的线性衰减系数的重建算法

层析γ扫描(TGS)技术是非破坏性分析(NDA)中的一项重要技术.在TGS透射测量中,线性衰减系数值的图像重建问题是TGS的难点和核心问题.在文[1]的基础上,提出了将神经网络方法应用于TGS重建线性衰减系数图像的算法.计算机上的仿真模拟结果表明,在一定范围内,径向基函数(RBF)神经网络方法重建的线性衰减系数值与实际值的相对误差小于4%,且具有快速、高精度等优点,表明了此方法的有效性.