A constrained Gauss-Seidel method for correction of point spread function effect in MR spectroscopic imaging

Magnetic resonance spectroscopic imaging is limited by a low signal-to-noise ratio, so a compromise between spatial resolution and examination time is needed in clinical application. The reconstruction of truncated signal introduces a Point Spread Function that considerably affects the spatial resolution. In order to reduce spatial contamination, three methods, applied after Fourier transform image reconstruction, based on deconvolution or iterative techniques are tested to decrease Point Spread Function contamination. A Gauss-Seidel (GS) algorithm is used for iterative techniques with and without a non-negative constraint (GS+). Convergence and noise dependence studies of the GS algorithm have been done. The linear property of contamination was validated on a point sample phantom. A significant decrease of contamination without broadening the spatial resolution was obtained with GS+ method compared to a conventional apodization. This post-processing method can provide a contrast enhancement of clinical spectroscopic images without changes in acquisition time.     

Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization

Sparse-view x-ray computed tomography(CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform(NUFFT) is presented in this work along with advanced total variation(TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively.     

Undersampled MRI reconstruction with patch-based directional wavelets

Compressed sensing has shown great potential in reducing data acquisition time in magnetic resonance imaging (MRI). In traditional compressed sensing MRI methods, an image is reconstructed by enforcing its sparse representation with respect to a preconstructed basis or dictionary. In this paper, patch-based directional wavelets are proposed to reconstruct images from undersampled k-space data. A parameter of patch-based directional wavelets, indicating the geometric direction of each patch, is trained from the reconstructed image using conventional compressed sensing MRI methods and incorporated into the sparsifying transform to provide the sparse representation for the image to be reconstructed. A reconstruction formulation is proposed and solved via an efficient alternating direction algorithm. Simulation results on phantom and in vivo data indicate that the proposed method outperforms conventional compressed sensing MRI methods in preserving the edges and suppressing the noise. Besides, the proposed method is not sensitive to the initial image when training directions.     

ANTHEM: anatomically tailored hexagonal MRI

PURPOSE: This study aimed to investigate the use of anatomically tailored hexagonal sampling for scan-time and error reduction in MRI. MATERIALS AND METHODS: Anatomically tailored hexagonal MRI (ANTHEM), a method that combines hexagonal sampling with specific symmetry in anatomical geometry, is proposed. By using hexagonal sampling, aliasing artifacts are moved to regions where, due to the nature of the anatomy, aliasing is inconsequential. This can be used to either reduce scan time while maintaining spatial resolution or reduce residual errors in speedup techniques like UNFOLD and k-t BLAST/SENSE, which undersample k-space and unwrap fold-over artifacts during reconstruction. Computer simulations as well as phantom and volunteer studies were used to validate the theory. A simplified reconstruction algorithm for hexagonally sampled and subsampled k-space data was also used. RESULTS: A reduction in sampling density of 13.4% and 25% in each hexagonally sampled dimension was achieved for spherical and conical geometries without aliasing or reduction in spatial resolution. Optimal subsampling schemes that can be utilized by UNFOLD and k-t BLAST/SENSE were derived using hexagonal subsampling, which resulted in maximal, isotropic dispersal of the aliases. In combination with UNFOLD, ANTHEM was shown to move residual aliasing artifacts to the corners of the field of view, yielding reduced artifacts in CINE reconstructions. CONCLUSIONS: ANTHEM was successful in reducing acquisition time in conventional MRI and in reducing errors in UNFOLD imaging.     

Detection of pseudoperiodic patterns using partial acquisition of magnetic resonance images

Improving the resolution of magnetic resonance imaging (MRI), or, alternatively, reducing the acquisition time, can be quite beneficial for many applications. The main motivation of this work is the assumption that any information that is a priori available on the target image could be used to achieve this goal. In order to demonstrate this approach, we present a novel partial acquisition strategy and reconstruction algorithm, suitable for the special case of detection of pseudoperiodic patterns. Pseudoperiodic patterns are frequently encountered in the cerebral cortex due to its columnar functional organization (best exemplified by orientation columns and ocular dominance columns of the visual cortex). We present a new MRI research methodology, in which we seek an activity pattern, and a pattern-specific experiment is devised to detect it. Such specialized experiments extend the limits of conventional MRI experiments by substantially reducing the scan time. Using the fact that pseudoperiodic patterns are localized in the Fourier domain, we present an optimality criterion for partial acquisition of the MR signal and a strategy for obtaining the optimal discrete Fourier transform (DFT) coefficients. A by-product of this strategy is an optimal linear extrapolation estimate. We also present a nonlinear spectral extrapolation algorithm, based on projections onto convex sets (POCSs), used to perform the actual reconstruction. The proposed strategy was tested and analyzed on simulated signals and in MRI phantom experiments.     

MRISim:磁共振成像仿真实验软件包

本文基于数值计算模拟技术,开发了模拟磁共振成像（MRI）数据采集与图像重建的仿真软件包——MRISim.虚拟数据采集部分通过对设备硬件、样品（标样或人体部位）进行物理数学建模后,构建原始模拟信号,并填充k空间,然后再基于k空间数据实现磁共振图像重建.该软件可以通过参数的任意调节对影响磁共振图像质量的因素进行可视化分析,包括11种常见伪影的特征和成因分析.我们的研究表明应用该仿真软件可以弥补台式MRI扫描仪价格昂贵、实验时间长等不足之处,实现对相关科技人员的批量化、规模化的实践操作培训.     

A novel phantom and method for comprehensive 3-dimensional measurement and correction of geometric distortion in magnetic resonance imaging

A phantom that can be used for mapping geometric distortion in magnetic resonance imaging (MRI) is described. This phantom provides an array of densely distributed control points in three-dimensional (3D) space. These points form the basis of a comprehensive measurement method to correct for geometric distortion in MR images arising principally from gradient field non-linearity and magnet field inhomogeneity. The phantom was designed based on the concept that a point in space can be defined using three orthogonal planes. This novel design approach allows for as many control points as desired. Employing this novel design, a highly accurate method has been developed that enables the positions of the control points to be measured to sub-voxel accuracy. The phantom described in this paper was constructed to fit into a body coil of a MRI scanner, (external dimensions of the phantom were: 310 mm x 310 mm x 310 mm), and it contained 10,830 control points. With this phantom, the mean errors in the measured coordinates of the control points were on the order of 0.1 mm or less, which were less than one tenth of the voxel's dimensions of the phantom image. The calculated three-dimensional distortion map, i.e., the differences between the image positions and true positions of the control points, can then be used to compensate for geometric distortion for a full image restoration. It is anticipated that this novel method will have an impact on the applicability of MRI in both clinical and research settings, especially in areas where geometric accuracy is highly required, such as in MR neuro-imaging.     

An improved gridding method for spiral MRI using nonuniform fast Fourier transform

The algorithm of Liu and Nguyen [IEEE Microw. Guided Wave Lett. 8 (1) (1998) 18; SIAM J. Sci. Comput. 21 (1) (1999) 283] for nonuniform fast Fourier transform (NUFFT) has been extended to two dimensions to reconstruct images using spiral MRI. The new gridding method, called LS_NUFFT, minimizes the reconstruction approximation error in the Least Square sense by generated convolution kernels that fit for the spiral k-space trajectories. For analytical comparison, the LS_NUFFT has been fitted into a consistent framework with the conventional gridding methods using Kaiser-Bessel gridding and a recently proposed generalized FFT (GFFT) approach. Experimental comparison was made by assessing the performance of the LS_NUFFT with that of the standard direct summation method and the Kaiser-Bessel gridding method, using both digital phantom data and in vivo experimental data. Because of the explicitly optimized convolution kernel in LS_NUFFT, reconstruction results showed that the LS_NUFFT yields smaller reconstruction approximation error than the Kaiser-Bessel gridding method, but with the same computation complexity.     

The accuracy of signal intensity measurements in magnetic resonance imaging as evaluated within the knee.

Quantitative signal intensity measurements are being utilized in both clinical and research magnetic resonance imaging protocols. This paper addresses three questions in quantitative MRI measurements as evaluated within the knee: 1) the accuracy of quantitative measurements; 2) improvement of accuracy by phantom normalization; and 3) the amount of signal change that is clinically significant. Seven normal subjects were imaged on three different days within a 1-wk period. Test-tube phantoms of manganous chloride (MnCl2) were imaged posterior to the knee and were used to normalize each image. The variation in signal intensity within the same subject averaged 20% for both the anterior cruciate ligament (ACL) and the posterior cruciate ligament (PCL). The phantom variation was approximately 18%. Signal intensity normalization by background subtraction, background division, phantom division, or a combination of subtraction and division did not significantly improve either the phantom variation or the ligament variation. Given that an individual ligament intensity will be measured with standard errors of +/- 20% of its value, we calculated the minimum increase in signal intensity to be considered abnormal relative to a normal ligament. A relative signal increase of 46% can be considered pathologic with 95% confidence. These findings emphasize that quantitative measurements must be carefully assessed when being applied in clinical settings.     

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.     

Compressed sensing MR image reconstruction using a motion-compensated reference

Compressed sensing (CS)-based methods have been proposed for image reconstruction from undersampled magnetic resonance data. Recently, CS-based schemes using reference images have also been proposed to further reduce the sampling requirement. In this study, we propose a new reference-constrained CS reconstruction method that accounts for the misalignment between the reference and the target image to be reconstructed. The proposed method uses a new image model that represents the target image as a linear combination of a motion-dependent reference image and a sparse difference image. We then use an efficient iterative algorithm to jointly estimate the motion parameters and the difference image from sparsely sampled data. Simulation results from a numerical phantom data set and an in vivo data set show that the proposed method can accurately compensate the motion effects between the reference and the target images and improve reconstruction quality. The proposed method should prove useful for several applications such as interventional imaging, longitudinal imaging studies and dynamic contrast-enhanced imaging.     

基于深度神经网络的时空编码磁共振成像超分辨率重建方法

单扫描时空编码磁共振成像是一种新型超快速磁共振成像技术,它对磁场不均匀和化学位移伪影有较强的抵抗性,但是其固有的空间分辨率较低,因此通常需要进行超分辨率重建,以在不增加采样点数的情况下提高时空编码磁共振图像的空间分辨率.然而,现有的重建方法存在迭代求解时间长、重建结果有混叠伪影残留等问题.为此,本文提出了一种基于深度神经网络的单扫描时空编码磁共振成像超分辨率重建方法.该方法采用模拟样本训练深度神经网络,再利用训练好的网络模型对实际采样信号进行重建.数值模拟、水模和活体鼠脑的实验结果表明,该方法能快速重建出无残留混叠伪影、纹理信息清楚的超分辨率时空编码磁共振图像.适当增加训练样本数量以及在训练样本中加入适当的随机噪声水平,有助于改善重建效果.     

基于Gadgetron平台的多GPU分布式磁共振图像重建

为了满足磁共振成像（MRI）临床扫描的需求,磁共振图像重建算法的开发一直在不断进行.目前广泛使用的算法实现方式是利用中央处理器（CPU）对磁共振扫描数据进行数学变换得到图像,随着算法复杂度的提升,计算性能问题逐渐显露.利用CPU在大数据量下执行复杂算法时,计算并行性的缺失以及运算中产生的海量数据的存储负荷会导致计算变得极为缓慢,使得一些算法因为重建时间过长,在临床上面临难以推广的问题,也制约了基础研究中新算法的研发.本文设计并实现了一种新的重建算法执行方式,利用Gadgetron磁共振软件重建平台在多核CPU基础上搭载多块图形处理器（GPU）,将磁共振图像重建以分布式并行计算方式实现,并以重建耗时较长的3D径向数据采集Stack of Star（SOS）的图像重建为实例,展示这种重建的实现方法能以相对低廉的硬件成本极大提升重建的速度.     

Optimizing Image Reconstruction in SENSE Using GPU

Parallel magnetic resonance imaging (MRI) (pMRI) uses multiple receiver coils to reduce the MRI scan time. To accelerate the data acquisition process in MRI, less amount of data is acquired from the scanner which leads to artifacts in the reconstructed images. SENSitivity Encoding (SENSE) is a reconstruction algorithm in pMRI to remove aliasing artifacts from the undersampled multi coil data and recovers fully sampled images. The main limitation of SENSE is computing inverse of the encoding matrix. This work proposes the inversion of encoding matrix using Jacobi singular value decomposition (SVD) algorithm for image reconstruction on GPUs to accelerate the reconstruction process. The performance of Jacobi SVD is compared with Gauss–Jordan algorithm. The simulations are performed on two datasets (brain and cardiac) with acceleration factors 2, 4, 6 and 8. The results show that the graphics processing unit (GPU) provides a speed up to 21.6 times as compared to CPU reconstruction. Jacobi SVD algorithm performs better in terms of acceleration in reconstructions on GPUs as compared to Gauss–Jordan method. The proposed algorithm is suitable for any number of coils and acceleration factors for SENSE reconstruction on real time processing systems.     

An iterative image reconstruction algorithm combined with forward and backward diffusion filtering for in‐line X‐ray phase‐contrast computed tomography

In‐line X‐ray phase‐contrast computed tomography (IL‐PCCT) can reveal fine inner structures for low‐Z materials (e.g. biological soft tissues), and shows high potential to become clinically applicable. Typically, IL‐PCCT utilizes filtered back‐projection (FBP) as the standard reconstruction algorithm. However, the FBP algorithm requires a large amount of projection data, and subsequently a large radiation dose is needed to reconstruct a high‐quality image, which hampers its clinical application in IL‐PCCT. In this study, an iterative reconstruction algorithm for IL‐PCCT was proposed by combining the simultaneous algebraic reconstruction technique (SART) with eight‐neighbour forward and backward (FAB8) diffusion filtering, and the reconstruction was performed using the Shepp–Logan phantom simulation and a real synchrotron IL‐PCCT experiment. The results showed that the proposed algorithm was able to produce high‐quality computed tomography images from few‐view projections while improving the convergence rate of the computed tomography reconstruction, indicating that the proposed algorithm is an effective method of dose reduction for IL‐PCCT.     

基于时间分辨测量的近红外光三维层析成像研究

针对近红外漫射光层析成像中的三维成像问题展开了理论和实验研究.利用开发的以强度和平均飞行时间作为数据类型的三维重建算法对数值仿真模型进行了重建,同时采用多通道时间相关单光子计数层析成像系统对固体样品进行了三维成像.结果表明：所发展的算法较忠实地重建出了样品内部的异质体结构;采用的差分重建方法有利于提高重建的抗噪性能;提出的单层测头配置模式对于三维成像具有实际意义.     

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.     

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.     

Restoration of low resolution metabolic images with a priori anatomic information: 23Na MRI in myocardial infarction

A new iterative extrapolation image reconstruction algorithm is presented, which enhances low resolution metabolic magnetic resonance images (MRI) with information about the bounds of signal sources obtained from a priori anatomic proton ((1)H) MRI. The algorithm ameliorates partial volume and ringing artefacts, leaving unchanged local metabolic heterogeneity that is present in the original dataset but not evident at (1)H MRI. Therefore, it is ideally suited to metabolic studies of ischemia, infarction and other diseases where the extent of the abnormality at (1)H MRI is uncertain. The performance of the algorithm is assessed by simulations, MRI of phantoms, and by surface coil 23Na MRI studies of canine myocardial infarction on a clinical scanner where the injury was not evident at (1)H MRI. The algorithm includes corrections for transverse field inhomogeneity, and for the leakage of intense signals into regions of interest such as 23Na MRI signals from ventricular blood ringing into the myocardium. The simulations showed that the algorithm reduced ringing artefacts by 15%, was stable at low SNR ( approximately 7), but is sensitive to the positioning of the (1)H MRI boundaries. The 23Na MRI showed hyperenhancement of regions identified as infarcted at post-mortem histological staining. The areas of hyperenhancement were measured by five independent observers in four 23Na images of infarction reconstructed with and without the algorithm. The infarct areas were correlated with areas determined by post-mortem histological staining with coefficient 0.85 for the enhanced images, compared to 0.58 with the conventional images. The scatter in the amplitude and in the area measurements of ischemia-associated hyper-enhancement in 23Na MRI was reduced by the algorithm by 1.6-fold and by at least 3-fold, respectively, demonstrating its ability to substantially improve quantification of the extent and intensity of metabolic changes in injured tissue that is not evident by (1)H MRI.     

Three-dimensional diffuse optical imaging of hand joints: System description and phantom studies

In this paper we describe a three-dimensional (3D) continuous wave (CW) diffuse optical tomography (DOT) system and present 3D volumetric reconstruction studies using this DOT system with simple phantom models that simulate hand joints. The CCD-based DOT system consists of 64×64 source/detector fiber optic channels, which are arranged in four layers, forming a cylindrical fiber optic/tissue interface. Phantom experiments are used to evaluate system performance with respective to axial spatial resolution, optical contrast and target position for detection of osteoarthritis where cartilage is the primary target region of interest. These phantom studies suggest that we are able to quantitatively resolve a 2 mm thick “cartilage” and qualitatively resolve a 1 mm thick “cartilage” using our 3D reconstruction approach. Our results also show that optical contrast of 3:1–7:1 between the “disease cartilage” and normal cartilage can be quantitatively recovered. Finally, the target position along axial direction on image reconstruction is studied. All the images are obtained using our 3D finite-element-based reconstruction algorithm.