锥束CT的改进FDK算法及加速实现

锥束CT成像中,FDK重建算法得到广泛应用。提出一种可以扩大锥束CT旋转轴方向重建体积的FDK方法。在反投影步骤中,对重建物体的每个体素点被反投影的总次数进行计算,之后进行权重计算,最终得到三维重建图像。同时,采用CUDA技术,利用GPU对改进的FDK算法进行并行计算加速实现,提高重建效率。实验结果表明,改进的FDK算法可以增大重建体积,重建更多物体信息,采用CUDA技术后,速度大幅度提升。     

基于硬件实现的锥束CT图像重建系统的存储机制设计

为了实现三维锥束CT图像重建加速系统的小型化,建立了基于FPGA的三维图像重建系统。并对该系统中所采用的FDK重建算法所需的数据存储量和数据传输量以及由SDRAM、SRAM和FPGA内部缓存组成的存储系统的数据吞吐率进行了研究。首先,根据FDK算法的滤波与反投影两个步骤介绍了三维锥束CT图像重建系统的数据规模。接着,介绍了一种以SDRAM为外部主存,以SRAM为外部缓存和以FPGA内部SRAM资源作为内部高速缓存的存储机制。然后,介绍了该存储机制的实现方法以及测试方法。最后对该三维图像重建系统的数据吞吐能力进行了测试,并将之与FDK算法所需的数据传输量进行了对比分析。试验结果表明:该存储机制的数据连续存取速度为151.9MB/s,数据随机存取速度为100MB/s,基本满足小规模的三维图像重建的数据存储与传输带宽的要求。     

螺旋CT三种近似方法重建效果研究

针对螺旋CT的三种近似重建算法FDK、Short-Scan FDK和PI-ORIGINAL,在相对螺距逐渐增大过程中的重建效果作了比较。仿真实验结果表明,在螺距较大的情况下,相对其他两种方法,PI-ORIGINAL方法优势明显。采用的仿真实验模型为3-D Shepp模型和Turbell＇s Cloclg型。     

基于平板探测器投影数据预处理的三维CT重构算法研究

大面积非晶硅平板探测器(flat panel detector-FPD)在工业透射射线成像领域得到越来越多的应用。基于FPD的圆轨道FDK型三维计算机层析成像技术(Computed Tomography,3D-CT)检测速度快,但成像质量不及2D-CT。为发挥3D-CT速度优势,抑制噪声同时提高图像重建的质量。以由平板探测器得到的二维投影数据为研究对象,提出了一种对投影数据分别进行高频和低频两次滤波的投影预处理方法,然后将分别重建的图像叠加最终得到高质量的重建图像。由算法的仿真实验结果表明,重建图像质量得到明显改善,系统噪声得到抑制。     

基于现代GPU的实时锥束重建算法研究

FDK算法是一种被广泛应用的小锥角近似三维重建算法,但其运算量大,重建时间长。因此,本文提出了一种基于现代GPU实现的实时FDK加速算法。该方法充分结合现代GPU设备,通过灵活有效的并行策略减少反投影所需要的计算量;并利用一种新的基于角度相关性的优化方案进一步提升该算法的性能。大量实验表明该算法在不牺牲重建质量的前提下可以获得更高的加速性能。     

基于FDK的任意轨迹重建算法研究

为克服工业CT扫描较大工件时CT成像系统有效透照厚度受限,在FDK算法的基础上,突破常规的直线、圆和螺旋轨迹扫描模式,研究推导了任意轨迹的扫描模式。并将FDK算法推广到任意轨迹上,弥补了投影数据的缺失,实现了复杂结构件三维CT重构的任意轨迹重建算法。进行了倾斜圆、马鞍线等扫描轨迹的重建,结果表明:该方法具有扫描速度快、时间短的特点,更能提高长宽比较大的结构件重建质量,是医学CT和工业CT常用的算法,且适用于不同设备各种扫描轨迹。     

基于异构多GPU的锥束CT图像重建研究

针对锥束CT图像重建系统中GPU型号不一致问题,提出了基于异构多GPU的重建模型。该模型基于FDK算法进行重建,采用了按计算能力进行任务分配的方法,确保各GPU计算平衡。采用数据流分解的方法,实现了海量数据的图像重建。给出了该重建模型基于CUDA的实现方法,包括采用流管理和异步函数来实现多GPU并行计算以及滤波和反投影核函数的流程设计。利用高精度工业CT系统进行模型的实验验证。结果表明：所建立的重建模型正确有效,能充分发挥系统中异构多GPU的计算能力,执行效率高。     

利用CUDA技术实现锥束CT图像快速重建

锥束CT三维重建算法的计算量和传输量巨大,仅利用CPU来计算,无法满足实时、快速、准确重建的要求,根据图形处理器运算能力强、存储带宽大的特点,研究了一种不需要学习图形API,就可以在图形处理器上实现三维重建算法的快速运算的方法。该方法采用基于统一计算设备架构的图形处理器,通过这种新架构的编程模式,利用图形处理器中的流处理器来加快滤波和反投影计算,实现了FDK算法的重建加速,与利用图形API的重建方法相比,开发门槛较低。对于尺寸为5123的单精度浮点数据格式的图像,重建时间可以缩短到一分钟以内,并且GPU与计算机的传输时间小于1秒。实验结果表明与仅利用CPU的重建方法相比,本文提出的图像加速方法得到了较高的时间加速比。     

中间函数法CT图像重建算法研究

CT自从被发明以来其技术已发生了很大的变化.这些变化不仅体现在计算机技术、探测器技术和X线技术方面,同时CT的图像重建算法也在不断地发展.本文提出的中间函数重建算法,是一种可以应用于扇束和锥束扫描的图像重建算法.研究它的目的是为将来的锥束扫描提供直接重建算法.     

具有加速因子的OSEM重建算法用于X射线荧光CT研究

有序子集最大期望值算法(Ordered Subsets Expectation Maximization,OSEM)具有较高的图像重建质量和较短的计算时间,已经被应用于内源CT(如SPECT、PET、同步辐射X射线荧光CT)的图像重建中。本文提出了一种具有加速因子的OSEM算法应用于X射线荧光CT的图像重建,通过引入加速因子h来调制校正因子的步长加快OSEM算法的收敛速度,研究了不同加速因子和不同子集数的AOSEM算法对重建图像质量的影响。计算机模拟及实验结果表明,在获得同等质量重建图像的同时,具有加速因子的OSEM算法的重建速度是常规OSEM的两倍。     

Three-dimensional weighting reconstruction algorithm for circular cone-beam CT under large scan angles

Improving imaging quality of cone-beam CT under large cone angle scan has been an important area of CT imaging research. Considering the idea of conjugate rays and making up missing data, we propose a three-dimensional(3D) weighting reconstruction algorithm for cone-beam CT. The 3D weighting function is added in the back-projection process to reduce the axial density drop and improve the accuracy of FDK algorithm. Having a simple structure, the algorithm can be implemented easily without rebinning the native cone-beam data into coneparallel beam data. Performance of the algorithm is evaluated using two computer simulations and a real industrial component, and the results show that the algorithm achieves better performance in reduction of axial intensity drop artifacts and has a wide range of application.     

Performance evaluation of the backprojection filtered （BPF） algorithm in circular fan-beam and cone-beam CT

In this article we introduce an exact backprojection filtered （BPF） type reconstruction algorithm for cone-beam scans based on Zou and Pan＇s work. The algorithm can reconstruct images using only the projection data passing through the parallel PI-line segments in reduced scans. Computer simulations and practical experiments are carded out to evaluate this algorithm. The BPF algorithm has a higher computational efficiency than the famous FDK algorithm. The BPF algorithm is evaluated using the practical CT projection data on a 450 keV X-ray CT system with a flat-panel detector （FPD）. From the practical experiments, we get the spatial resolution of this CT system. The algorithm could achieve the spatial resolution of 2.4 lp/mm and satisfies the practical applications in industrial CT inspection.     

A fully three-dimensional reconstruction algorithm with thenonstationary filter for improved single-orbit cone beam SPECT

Conventional single-orbit cone beam tomography suffers from incomplete sampling and an inadequate three-dimensional (3D) reconstruction algorithm. The commonly used Feldkamp reconstruction algorithm simply extends the two-dimensional (2D) fan beam algorithm to 3D cone beam geometry. A truly 3D reconstruction formulation based on the 3D Fourier slice theorem is derived for a single-orbit cone beam SPECT. In the formulation, a nonstationary filter which depends on the distance from the central plane of the cone beam is derived and applied to the 2D projection data in directions along and normal to the axis of rotation. This algorithm was evaluated using both computer simulation and experimental measurements. Significant improvement in image quality was demonstrated in terms of decreased artifacts and distortions in cone beam reconstructed images. However, compared with the Feldkamp algorithm, a fivefold increase in processing time is required     

Derivative-Hilbert-Backprojection based image reconstruction from truncated projections in helical cone-beam CT

In helical cone-beam computed tomography(CT), Feldkamp-Davis-Kress(FDK) based image reconstruction algorithms are by far the most popular. However, artifacts are commonly met in the presence of lateral projection truncation. The reason is that the ramp filter is global. To restrain the truncation artifacts, an approximate reconstruction formula is proposed based on the Derivative-Hilbert-Backprojection(DHB) framework. In the method, the first order derivative filter is followed by the Hilbert transform. Since the filtered projection values are almost zero by the first order derivative filter, the following Hilbert transform has little influence on the projection values, even though the projections are laterally truncated. The proposed method has two main advantages. First, it has comparable computational efficiency and image quality as well as the conventional helical FDK algorithm for non-truncated projections. The second advantage is that images can be reconstructed with acceptable quality and much lower computational cost in comparison to the Laplace operator based algorithm in cases with truncated projections. To point out the advantages of our method, simulations on the computer and real data experiments on our laboratory industrial cone-beam CT are conducted. The simulated and experimental results demonstrate that the method is feasible for image reconstruction in the case of projection truncation.     

3D image reconstruction for a Compton SPECT camera model

Proposes a 3D image reconstruction algorithm for a 3D Compton camera being developed at the University of Michigan. The authors present a mathematical model of the transition matrix of the camera which exploits symmetries by using an adapted spatial sampling pattern in the object domain. For each projection angle, the sampling pattern is uniform over a set of equispaced nested hemispheres. By using this sampling pattern the system matrix is reduced to a product of a (approximately) block circulant matrix and a sparse interpolation matrix. This representation reduces the very high storage and computation requirement inherent to 3D reconstruction using transition matrix inversion methods. The authors geometrically optimize their hemispherical sampling and propose a 3D volumetric interpolation. Finally, the authors present a 3D image reconstruction method which uses the Gauss-Seidel algorithm to minimize a penalized least square objective     

Comparison of 3D OS-EM and 4D MAP-RBI-EM reconstruction algorithms for cardiac motion abnormality classification using a motion observer

Using a heart motion observer, we compared the performance of two image reconstruction techniques, a 3D OS-EM algorithm with post Butterworth spatial filtering and a 4D MAP-RBI-EM algorithm. The task was to classify gated myocardial perfusion (GMP) SPECT images of beating hearts with or without regional motion abnormalities. Noise-free simulated GMP SPECT projection data was generated from two 4D NCAT beating heart phantom models, one with normal motion and the other with a 50% motion defect in a pie-shaped wedge region-of-interest (ROI) in the anterior-lateral left ventricular wall. The projection data were scaled to clinical GMP SPECT count level before Poisson noise was simulated to generate 40 noise realizations. The noise-free and noisy projection data were reconstructed using the two reconstruction algorithms, parameters chosen to optimize the tradeoff between image bias and noise. As a motion observer, a 3D motion estimation method previously developed was applied to estimate the radial motion on the ROI from two adjacent gates. The receiver operating characteristic (ROC) curves were computed for radial motion magnitudes corresponding to each reconstruction technique. The area under the ROC curve (AUC) was calculated as an index for classification of regional motion. The reconstructed images with better bias and noise tradeoff were found to offer better classification for hearts with or without regional motion defects. The 3D cardiac motion estimation algorithm, serving as a heart motion observer, was better able to distinguish the abnormal from the normal regional motion in GMP SPECT images obtained from the 4D MAP-RBI-EM algorithm than from the 3D OS-EM algorithm with post Butterworth spatial filtering.     

TTPIXAN — the 4th generation

During the past six years the computer code TTPIXAN [I. Orlić et al., NIMB 49 (1990) 166] went through many changes and developments. From its infant stage when it was developed for a simple quantitative broad beam PIXE analysis, through a more sophisticated version [K.K. Loh et al., NIMB 77 (1993) 132] suited for applications in Nuclear Microscopy (NM). At present, the program is finally reaching its mature stage or its 4th metamorphosis [S.C. Liew et al., NIMB 104 (1995) 222]. It is now capable of not only simulating NM elemental images but also performing quantitative analysis and reconstruction of a complex 3D elemental composition encountered in NM applications. From a given initial 3D elemental distributions the program calculates exact elemental maps, compares them with the corresponding measured maps and by using a very efficient iterative Maximum-Likelihood Expectation-Maximisation (MLEM) algorithm, it calculates a new 3D elemental distributions. Energy loss of the incident particles and attenuation of the X-ray photons are incorporated into the reconstruction algorithm by using the most up-to date data base. The reconstruction algorithm has been successfully tested on several samples such as thin tungsten wire coated with paint, integrated circuits, and single aerosol particles. The computer code is briefly described and future plans outlined.