A complete implementation of list-mode reconstruction for PET

Tomography reconstruction algorithm is one of the key components of positron emission tomography (PET) scanners,most PET scanners use statistical iterative reconstruction algorithms from data in sinograms currently. However tomography reconstruction using list-mode data has many unique advantages,in recent years great attention has been paid to it,being in the process of rapid development and improvement.In this paper,using experimental data of small animal PET scanner Eplus-166,exploiting ordinary subsetized list-mode EM(S-LMEM) algorithm and orthogonal distance-based ray-tracer(OD-RT),we eventually achieve list-mode tomography reconstruction.System response matrix(SRM),which establishes mapping relationship between the image and the projection space,is one key problem in iterative reconstruction algorithm.OD-RT is based on an optimization Siddon’s algorithm to calculate the SRM,generating line-of-response(LOR) which is approximately Gaussian-shaped,achieving better modeling of detector response function(DRF).The results demonstrate that image resolution recovery achieves the inherent properties of the scanner and that on-the-fly ray-tracer for real-time calculation of system response matrix is feasible for dynamic reconstruction.Meanwhile,the optimal parameters for calculating SRM are found by experiments.     

基于DSP技术的工业CT重建软件设计

提出了基于现代数字信号处理器(DSP)技术进行CT重建软件设计.在实际的CT软件设计过程中,利用TI的C6701 DSP芯片的硬件处理系统,建立了基于DSP硬件系统的CT算法重建软件,该软件全部使用与DSP硬件系统相关的DSP汇编语言进行编程.并利用TI的C6701 EVM开发板,通过输入CT数据进行计算,得出的CT图像满足实际要求.     

The EM imaging reconstruction method in γ-ray astronomy

The simpler imaging reconstruction methods used for γ-ray coded mask telescopes are based on correlation methods, very fast and simple-to-use but with limitations in the reconstructed image. To improve these results, other reconstruction methods have been developed, such as the maximum entropy methods or the Iterative Removal Of Sources (IROS). However, such kind of methods are slower and can be impracticable for very complex telescopes.In this paper we present an alternative image reconstruction method, based on an iterative maximum likelihood algorithm called the EM algorithm, easy to implement and that can be successfully used for not very complex coded mask systems, as is the case of the LEGRI telescope. This is the first time this algorithm has been applied in γ-ray astronomy.     

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     

Range Condition and ML-EM Checkerboard Artifacts

The expectation maximization (EM) algorithm for the maximum likelihood (ML) image reconstruction criterion generates severe checkerboard artifacts in the presence of noise. A classical remedy is to impose an a priori constraint for a penalized ML or maximum a posteriori probability solution. The penalty reduces the checkerboard artifacts and also introduces uncertainty because a priori information is usually unknown in clinic. Recent theoretical investigation reveals that the noise can be divided into two components: one is called null-space noise and the other is range-space noise. The null-space noise can be numerically estimated using filtered backprojection (FBP) algorithm. By the FBP algorithm, the null-space noise annihilates in the reconstruction while the range-space noise propagates into the reconstructed image. The aim of this work is to investigate the relation between the null-space noise and the checkerboard artifacts in the ML-EM reconstruction from noisy projection data. Our study suggests that removing the null-space noise from the projection data could improve the signal-to-noise ratio of the projection data and, therefore, reduce the checkerboard artifacts in the ML-EM reconstructed images. This study reveals an in-depth understanding of the different noise propagations in analytical and iterative image reconstructions, which may be useful to single photon emission computed tomography, where the noise has been a major factor for image degradation. The reduction of the ML-EM checkerboard artifacts by removing the null-space noise avoids the uncertainty of using a priori penalty.     

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.     

基于Chambolle-Pock算法的TV重建方法研究

为实现CT稀疏视角下的投影图像重建,Sidky等设计了基于Chambolle-Pock(CP)算法,论文在此基础上实现了CP算法。仿真实验表明,与传统的滤波反投影算法相比,CP算法不存在伪影,在含噪情况下,CP算法具有较好的性能,可以实现稀疏角度下的高精度图像重建。同时,探讨了平衡因子的选取对重建精度的影响。     

MC法模拟多路平行束准直器对比度

采用MC法模拟设计了用于SPECT成像的多路平行束(MPB)准直器,将MPB系统重建的模具图像与平行束(PB)系统重建图像进行对比。用OS-EM迭代算法重建图像并计算对比度、信噪比、归一化标准偏差三个指标用于评价图像质量。结果表明:随着迭代次数增加,MPB系统重建图像中热源的对比度高于PB系统,对于小半径热源这个差值更明显,但是冷源的对比度低于PB系统;两个系统有可比较的重建图像收敛速度,随着迭代次数增加,MPB系统的噪声特性略差于PB系统。     

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.     

静态CT行包安检系统关键技术研究

本文介绍了安检用静态CT技术的基本原理,对基于超顺排碳纳米管技术的冷阴极X射线源、基于光子计数技术的多能谱X射线成像技术和安检用静态CT系统图像重建算法等进行了研究。冷阴极X射线源由基于超顺排碳纳米管技术的冷阴极X射线管、两套高压系统和1个控制系统组成,在130 kV以下可稳定工作。研制并测试了一款具有三能谱成像功能的光子计数型X射线探测器系统。对安检用静态CT系统图像重建算法进行了讨论,提出了一种解决方法。安检用静态CT系统关键技术的研究为安检用静态CT系统的研制提供了技术基础。     

基于改进的二维Otsu分割算法及其应用研究

传统的二维Otsu方法考虑了图像的灰度信息和像素间的空间邻域信息,是一种有效的图像分割方法。针对传统二维阈值分割算法处理图像计算时间长、噪声干扰严重等缺点,提出了一种改进的二维快速Otsu阈值自动分割算法。该算法通过改变二维直方图判别域的划分,将阈值搜索空间由二维降为一维,并运用迭代运算提高运算速度。实验结果证明,所用的改进方法更为准确地划分了目标和背景区域,增强了图像的分割效果,运用迭代运算和传统方法相比减少了处理时间。     

由相叠的低分辨扇形束投影数据重建高分辨CT图像

在研究扇形束插值代数重建法基础上，提出了由相叠的低分辨扇形束投影数据重建高分辨CT图像的两个新算法，即扇形束的虚拟探测器法和扇形束的直接重建法，并给出和分析了数值模拟结果。     

数字图象重建的一种综合快速算法

本文提出一种综合快速算法,可直接快速地计算重建图象平面上任何一点的检测角,并采用三次B样条函数对滤波的投影数据进行内插,来代替反投影时的内插。实验表明,在保证同样的主客观保真度下,此算法的内插计算量约为原来算法的1/12;当象素数N增大时,计算量的减少更为显著。对端点条件的影响进行了分析,证明用此法插值所造成的误差以相当高的速率由边缘向中心衰减,大约每向中心移动两个象素其误差减少一个数量级。     

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.     

双正则化参数法超分辨率重建核磁共振图像

针对基于稀疏编码的超分辨率算法噪点、伪影较多的问题,提出一种双正则化参数核磁共振图像超分算法。该算法引入在线字典学习方法,以训练正则化参数λt分开训练生成精确的超完备字典对,并调整重建正则化参数λr,得到最佳的稀疏系数用于恢复目标高分图像。实验结果表明:改进算法比双字典学习超分法的目标图像峰值信噪比和结构相似性平均值分别提高了1.30 d B和0.023,有效地抑制了噪点和边缘伪影,较大幅度地提升了核磁共振图像的超分效果。     

Hybrid reconstruction algorithm for computed tomography based on diagonal total variation

Inspired by total variation(TV), this paper represents a new iterative algorithm based on diagonal total variation(DTV) to address the computed tomography image reconstruction problem. To improve the quality of a reconstructed image, we used DTV to sparsely represent images when iterative convergence of the reconstructed algorithm with TV-constraint had no effect during the reconstruction process. To investigate our proposed algorithm, the numerical and experimental studies were performed, and rootmean-square error(RMSE) and structure similarity(SSIM)were used to evaluate the reconstructed image quality. The results demonstrated that the proposed method could effectively reduce noise, suppress artifacts, and reconstruct highquality image from incomplete projection data.     

A New Approach to the Fan Beam Geometry Image Reconstruction for a CT Scanner

A new derivation of the fan beam geometry image reconstruction formula for CT scanners has been made in this paper. Moreover there are two points discussed here in order to develop fast algorithms based upon this formula. First is to establish a principle of filterered back-projection algorithm for fan beam geometry which enables us to use FFT algorithm. Second is to develop a fast algorithm for fan back-projection process. With these algorithms, the fan beam image reconstruction time to compute can be made comparable with the filtered back-projection algorithm for the parallel beam geometry image reconstruction.     

高分辨针孔SPECT三维图像重建的实现

采用一种新颖的查找表法来实施有序子集期望值最大化（OSEM）的针孔SPECT图像重建算法,有效地将针孔响应修正包含在查找表中,进而实现高分辨针孔SPECT的三维图像重建。标准Jaszczak模具的成像实验结果表明：该方法不但能显著减少图像重建过程的计算时间和内存占用,且能显著改善重建图像的分辨率。因此,查找表法是能够快速实现针孔SPECTOSEM图像重建算法,并能将针孔响应修正包含在查找表中以获取高分辨断层图像的有效方法。     

The 3081/E Processor and Its on-Line Use

The 3081/E is a second generation emulator of a mainframe IBM. One of it's applications will be to form part of the data acquisition system of the upgraded Mark II detector for data taking at the SLAC linear collider. Since the processor does not have direct connections to I/O devices a FASTBUS interface will be provided to allow communication with both SLAC Scanner Processors (which are responsible for the accumulation of data at a crate level) and the experiment's VAX 8600 mainframe. The 3081/E's will supply a significant amount of on-line computing power to the experiment (a single 3081/E is equivalent to 4-5 VAX 11/780'S). A major advantage of the 3081/E is that program development can be done on an IBM mainframe (such as the one used for off-line analysis) which gives the programmer access to a full range of debugging tools. The processor's performance can be continually monitored by comparison of the results obtained using it to those given when the same program is run on an IBM computer.     

Development of a real-time magnetic island reconstruction system based on PCIe platform for HL-2A tokamak

A real-time magnetic island reconstruction(MIR) system based on PCI express platform for HL-2 A tokamak is introduced. The front-end analog circuit and high performance analog-to-digital converters complete high-precision synchronous sampling of 18 channel Mirnov signals, and the application of PCIe platform and direct memory access technology enables high speed data transmission between graphics processing unit and field programmable gate array(FPGA).FPGA, as a mainstream high speed parallelizable computing tool, was used to implement the MIR algorithm, while a parameter table is established in an external double data rate SDRAM to improve the computational efficiency. The software of the MIR system is developed with Compute Unified Device Architecture 8.0 in Centos 6 system, which mainly realizes driver development, data transmission, network communication, parameter calculation and system control. This system has been tested in HL-2 A plasma discharge experiment, and the reconstructed magnetic island structure can achieve a spatial resolution of 1.02 cm while the time resolution can reach 2 ms.