Analytical inversion formula for uniformly attenuated fan-beamprojections

A convolution backprojection algorithm was derived by Tretiak and Metz (198) to reconstruct two-dimensional (2-D) transaxial slices from uniformly attenuated parallel-beam projections. Using transformation of coordinates, this algorithm can be modified to obtain a formulation useful to reconstruct uniformly attenuated fan-beam projections. Unlike that for parallel-beam projections, this formulation does not produce a filtered backprojection reconstruction algorithm but instead has a formulation that is an inverse integral operator with a spatially varying kernel. This algorithm thus requires more computation time than does the filtered backprojection reconstruction algorithm for the uniformly attenuated parallel-beam case. However, the fan-beam reconstructions demonstrate the same image quality as that of parallel-beam reconstructions     

Short-Scan Fan-Beam Algorithms for Cr

Several short-scan reconstruction algorithms of the convolution type for fan-beam projections are presented and discussed. Their derivation fran new, exact integral representation formulas is outlined, and the performance of same of these algorithms is demonstrated with the aid of simulation results.     

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.     

扇形束投影域重建—再投影迭代法

本文所提出的投影域重建——再投影迭代算法可以恢复不完整的扇形束投影数据,从而实现从有限的投影数据重建图象。这种算法把滤波——反投影图象重建过程和再投影的过程纳入一个公式,仅在投影域上估算未知的投影数据,因此避免了重建过程和反投影过程中的插值运算,改善了收敛性,提高了计算精度,缩短了运算时间。模拟实验表明:即使有70％的投影数据丢失,经过两次迭代就能以令人满意的精度恢复丢失的投影数据。     

基于FDK算法的锥束CT重建近似算法性能比较

相比通常的扇束和平行束CT重建,锥束CT有诸多优点(如空间分辨率高,扫描速度快等)。近似锥束重建算法理论结构简单,重建速度快,易于实际应用。对新出现的几种近似锥束重建算法作了简单介绍,并利用这些算法对3D Shepp-logan模型的仿真模拟对这些算法的特点作了比较和讨论。     

Iterative reconstruction with attenuation compensation fromcone-beam projections acquired via nonplanar orbits

Single photon emission computed tomography (SPECT) imaging with cone-beam collimators provides improved sensitivity and spatial resolution for imaging small objects with large field-of-view detectors. It is known that Tuy's cone-beam data sufficiency condition must be met to obtain artifact-free reconstructions. Even though Tuy's condition was derived for an attenuation-free situation, the authors hypothesize that an artifact-free reconstruction can be obtained even if the cone-beam data are attenuated, provided the imaging orbit satisfies Tuy's condition and the exact attenuation map is known. In the authors' studies, emission data are acquired using nonplanar circle-and-line orbits to acquire cone-beam data for tomographic reconstructions. An extended iterative ML-EM (maximum likelihood-expectation maximization) reconstruction algorithm is derived and used to reconstruct projection data with either a pre-acquired or assumed attenuation map. Quantitative accuracy of the attenuation corrected emission reconstruction is significantly improved     

巨大长型物体的双直线扫描断层成像

本文从实际应用背景出发，对直线源轨迹的扇束重建公式进行了简单推导，给出了相应的计算机模拟结果，同时根据实际情况提出了双直线轨迹的图像重建公式，最后将此算法推广到三维锥束图像重建，克服了传统三维图像重建中在锥角处误差很大的缺点。     

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 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.     

基于SART算法的CL硬化伪影校正方法研究

X射线薄板层析成像(CL)系统是一种针对板状构件的新型断层成像系统,该系统中存在射束硬化现象。本工作研究了一种基于SART算法的硬化伪影校正算法（SART-BHC算法）,通过对该算法的研究及对CL系统矩阵的计算,使该方法能应用于CL中。通过模拟与实验相结合的方式,利用蒙特卡罗方法获得CL投影的模拟数据,在实际CL中获得实验数据,然后利用SART-BHC与FPB算法对两种数据分别重建。结果表明,SART-BHC算法可应用于CL中,不需要任何先验知识,能很好地校正硬化伪影,并对层间混叠有抑制作用。     

Algorithmic techniques for quantitative Compton tomography

Compton tomography is a non-destructive technique that allows one to reconstruct the spatial distribution of the electronic density of the sample analyzed. This information is complementary to the absorption coefficient distribution at a given energy, which can be obtained by a more conventional transmission tomography. However, the reconstruction algorithms used in Compton tomography are different and more complex than those used in transmission tomography. This is mainly due to the absorption of the X-ray photons along the path from the source to the interaction point and from the interaction point to the detector. Only a few of the reconstruction algorithms reported in the literature take absorption corrections into account, and the problems of a quantitative reconstruction have seldom been discussed. In this paper a new kind of reconstruction algorithm is described and the first results are reported and discussed.     

Impedance imaging of two-phase flow field with mesh grouping method

There have been many attempts to measure the bubble distribution in two-phase flow fields and various techniques have been devised. However, the existing techniques require much improvement for imaging two-phase flow fields. In this study, the EIT (Electrical Impedance Tomography) technique is introduced for two-phase flow visualization. In the EIT, a static image reconstruction algorithm providing a higher spatial resolution is required. Using the conventional iterative static image reconstruction algorithms, however, the processing time increases rapidly with poor convergence characteristics as we try to obtain a higher spatial resolution. In order to overcome this problem, we propose an adaptive mesh grouping method utilizing the genetic algorithm and the fuzzy set theory. Computer simulations using the improved Newton–Raphson method with the proposed method show promising results indicating that we can significantly reduce the image reconstruction time without sacrificing spatial resolution.     

A study of the effect of inelastic absorption on the validity of trajectory simulation of elastic scattering

The effect of inelastic events on the elastic scattering of particles in a scattering medium may be described in terms of inelastic absorption (depletion of the elastic scattering channel), which may be implemented either by means of a complex phaseshift or by means of an optical potential. Using both methods, inelastic absorption is introduced in the exact quantum calculation of multiple elastic s-wave scattering of a particle in a cluster of point scatterers. The average solution of the quantum calculation for a large number of simulated clusters with identical boundaries but with scatterers in randomly varying positions is compared with the result of a corresponding trajectory simulation, where an inelastic mean free path has been introduced. In the trajectory simulation an inelastic event results in the absorption of the particle, i.e. termination of the trajectory. It has previously been shown that trajectory simulation of purely elastic scattering is a valid approximation of the average quantum solution if the incident particle wavelength is at most about equal to the average distance between neighbour scatterers. It is found that this condition still holds in the presence of inelastic absorption, although quantum and trajectory calculations of the scattering event distribution inside the cluster give increasingly similar results for decreasing inelastic mean free path.     

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.     

宇宙射线μ子探测裂变核材料的成像算法

宇宙射线μ子探测作为一种清洁源、深穿透、真正识别裂变核材料的新方法正在世界范围内日益受到重视,我国也在反恐领域开展此项研究,论文介绍了研究工作中图像重建算法(PoCA算法、期望最大化算法)以及算法模拟实验结果和分析,模拟结果初步证明了宇宙线μ子进行特殊核材料检测的可行性以及图像重建算法的有效性.     

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.     

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。     

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.     

Slice-wise reconstruction for low-dose cone-beam CT using a deep residual convolutional neural network

Because of the growing concern over the radiation dose delivered to patients, X-ray cone-beam CT(CBCT) imaging of low dose is of great interest. It is difficult for traditional reconstruction methods such as Feldkamp to reduce noise and keep resolution at low doses. A typical method to solve this problem is using optimizationbased methods with careful modeling of physics and additional constraints. However, it is computationally expensive and very time-consuming to reach an optimal solution. Recently, some pioneering work applying deep neural networks had some success in characterizing and removing artifacts from a low-dose data set. In this study,we incorporate imaging physics for a cone-beam CT into a residual convolutional neural network and propose a new end-to-end deep learning-based method for slice-wise reconstruction. By transferring 3D projection to a 2D problem with a noise reduction property, we can not only obtain reconstructions of high image quality, but also lower the computational complexity. The proposed network is composed of three serially connected sub-networks: a cone-to-fan transformation sub-network, a 2D analytical inversion sub-network, and an image refinement sub-network. This provides a comprehensive solution for end-to-end reconstruction for CBCT. The advantages of our method are that the network can simplify a 3D reconstruction problem to a 2D slice-wise reconstruction problem and can complete reconstruction in an end-to-end manner with the system matrix integrated into the network design. Furthermore, reconstruction can be less computationally expensive and easily parallelizable compared with iterative reconstruction methods.     

量子粒子群融合算法在放射源探测标定中的应用

为有效进行辐射剂量探测,设计了有源在线监控模块。针对监控模块辐射测量值标定这一难题,提出了基于量子粒子群的融合算法实现对测量值与剂量值之间的高精度逼近。使用聚类和数据融合算法实现了拟合数据的自主最佳分段,避免了分段选择的主观性。仿真结果表明,融合算法能有效减少计数率较小时拟合函数的误差,提高各数据段测量值与剂量率之间的拟合精度,与整体拟合函数相比,进一步提高了拟合的精度。