Image reconstruction of electrical capacitance tomography based on optimal simulated annealing algorithm using orthogonal test method

Electrical capacitance tomography (ECT) is a visualization measurement method for two-phase flow. Imaging permittivity distributions using electrical capacitance tomography has always been one of the most significant issues studied by scholars, and the algorithm will have a great impact on the accuracy of image reconstruction result. This paper applies simulated annealing (SA) algorithm to image reconstruction in ECT. However, some parameters of SA algorithm need to be optimized in order to obtain better reconstructed images in ECT. The influence of different parameter values in SA algorithm for image reconstruction in ECT is studied, and a set of optimal parameters of the SA algorithm is obtained based on the orthogonal experimental design method in this paper. At the same time, simulation and static experiments are conducted. Reconstructed images by SA algorithm with optimized parameter are compared with the linear back projection (LBP) and Landweber iterative algorithms. The results show that better images can be obtained for typical oil-gas two-phase flow using SA algorithm. The quality and shape fidelity of reconstructed image for the central object are obviously improved.     

Preconditioned Landweber iteration algorithm for electrical capacitance tomography

Electrical capacitance tomography (ECT) has been used to obtain the cross-section images of processes with different dielectric materials inside. Image reconstruction with ECT is to retrieve the permittivity distribution of materials inside the sensor from the capacitance measurements. Algorithms for ECT image reconstruction should be both precise and fast in order to satisfy the requirements of real-time monitoring of the dynamic behavior of processes. Several algorithms have been developed for ECT image reconstruction. The Landweber iteration is the most precise one. However, the low convergence rate of the Landweber iteration limits its application for on-line imaging.This paper introduces an iterative algorithm based on the Landweber method with preconditioning for ECT image reconstruction. A preconditioner, which is equivalent to a filter, is applied to the Landweber iteration. The convergence of this algorithm is analyzed. Its performance is evaluated by using simulated and experimental data corresponding to certain typical permittivity distributions. Preliminary numerical and experimental results show that this algorithm converges more rapidly than the Landweber iteration without preconditioning. Therefore, image reconstruction iteration can be accelerated, which makes on-line quantitative image reconstruction possible.     

基于改进正则法的ECT图像重建算法

电容层析成像图像重建是一个典型的病态问题,其解是不稳定的。为获得良好的重建效果,需要采用既保证解的稳定性且又能提高重建图像质量的算法。本文提出了一种新的图像重建算法。在分析标准Tikhonov正则法的基础上,针对ECT逆问题的病态性进行改进,并推导出两步图像重建算法：第一步利用标准Tikhonov正则法的计算值获得权矩阵的估计;第二步采用本文所推导的改进Tikhonov正则法获得最终的重建图像。数值实验表明,该算法所获得的图像重建质量得到了明显的提高,且该算法无需迭代,保证了算法实时性。     

一个基于Quantile估计的电容层析成像图像重建算法

电容层析成像图像重建是一个典型的病态问题,它的解是不稳定的。为了获得有意义的重建结果,能够保证解的稳定性而又能提高重建图像质量的方法应该被采用。本文提出了一个新的电容层析成像图像重建算法。在分析标准Tikhonov正则法的基础上,针对ECT逆问题的病态特点利用Quantile估计和加权l_p范数构建扩展的目标泛函,将图像重建问题转化为一个最优化问题;在此基础上用Newton法求解该泛函。数值实验表明该算法是可行的,能够有效克服ECT图像重建的数值不稳定性。就本文所考察的重建对象而言,该法所重建图像的空间分辨率得到了提高。而且该算法计算直接、无需任何复杂的技巧,从而为ECT图像重建提供了一种有效的方法。     

粒子滤波算法在ECT图像重建中的应用

针对电容层析成像技术(ECT)的图像重建质量精度较低的问题,提出了一种基于粒子滤波的ECT图像重建方法。首先,分析了ECT图像重建基本原理,以系统状态估计的方式描述了ECT图像重建最优解的搜索过程,并建立了状态空间模型。然后,以线性反投影(LBP)算法的图像重建结果作为初始状态,利用测量信息对从状态空间中获取的随机样本进行最优加权,以获得重建图像的最小方差估计。最后,对5种不同的流型进行了仿真实验。实验结果表明,利用本文方法获得的重建图像误差平均值为42.93%,相关系数平均值为0.813 9,比LBP算法、Landweber迭代算法和IMN-SNOF算法得到的相应指标要好。本文方法是一种有效、精度较高的ECT图像重建方法,为ECT图像重建技术提供了新的途径和手段。     

A nonlinear fuzzy assisted image reconstruction algorithm for electrical capacitance tomography

A nonlinear method based on a Fuzzy Inference System (FIS) to improve the images obtained from Electrical Capacitance Tomography (ECT) is proposed. Estimation of the molten metal characteristic in the Lost Foam Casting (LFC) process is a novel application in the area of the tomography process. The convergence rate of iterative image reconstruction techniques is dependent on the accuracy of the first image. The possibility of the existence of metal in the first image is computed by the proposed fuzzy system. This first image is passed to an iterative image reconstruction technique to get more precise images and to speed up the convergence rate. The proposed technique is able to detect the position of the metal on the periphery of the imaging area by using just eight capacitive sensors. The final results demonstrate the advantage of using the FIS compared to the performance of the iterative back projection image reconstruction technique.     

3D ECT reconstruction by an improved Landweber iteration algorithm

Electrical capacitance tomography (ECT) is a relatively mature non-invasive imaging technique that attempts to map dielectric permittivity of materials. Recently, 3D ECT has gained interest because of its potential to generate volumetric images. The study of a fast and accurate image reconstruction algorithm is a challenge task, especially for 3D reconstruction. In this paper, we propose an improved Landweber iteration algorithm. We incorporate an additional acceleration term into the cost function and apply an adaptive threshold operation to the image obtained in each iteration for reducing artefacts. The algorithm proposed is tested by the noise-free and noise-contaminated capacitance data. Sensitivity matrixes and capacitance data of a 3D ECT sensor are obtained by using the finite element (FE) method. Extensive simulations in 3D reconstruction are carried out. The results verify the effectiveness of these improvements. Both the reconstruction time and the artefacts in the reconstructed image are reduced obviously. The experimental results of 3D reconstruction of objects in the shape of letters U and L confirm the effectiveness of the proposed algorithm further.     

基于MCMC方法的电容成像图像重构算法

研究基于概率统计的电容成像图像重构算法,以马尔科夫随机场的方式给出介电常数分布的先验概率,利用电容成像(electrical capacitance tomography,ECT)线性模型得到似然函数,通过马尔科夫链蒙特卡罗(Markov chain Monte Carlo,MCMC)方法对介电常数分布的后验概率密度进行采样,马尔科夫链的转移核利用Metropolis-Hastings方法得到,结合嵌套迭代提高计算效率。仿真结果表明,嵌套迭代-MCMC方法在正则化参数设置合适的条件下,可以得到较好的图像质量,基于MCMC方法图像重构算法为解决ECT图像重构问题提供一种新思路。     

Window function-based regularization for electrical capacitance tomography image reconstruction

Image reconstruction for electrical capacitance tomography (ECT) is to retrieve the permittivity distribution of materials inside the sensor from the capacitance measurements outside. It is a typical inverse problem and has long been a challenge for its nonlinearity and ill-posedness. This paper discusses the application of Tikhonov regularization, widely used for ill-posed problems, to the image reconstruction for electrical capacitance tomography. Two methods using different regularizations are investigated, which are the standard Tikhonov regularization and the Tikhonov regularization based on the second order derivative operator. Particularly, a combined method using the linear back projection (LBP) result as the prior constraint for the Tikhonov regularization with the second order derivative operator is suggested. Simulation and experiment results show that this combined method takes advantages from both the linear back projection and the Tikhonov regularization and provides reconstructions better than those from the LBP and the Tikhonov regularization. In addition, considering the essence that the Tikhonov regularization can be described as a spectral filter characterized by its corresponding window function, we propose the possibility of applying other window functions to the ECT image reconstruction, which include the Gauss window, the Hanning window, the Blackman window, and the cosine window. Results also show the feasibility of using window functions as regularization, which presents a new strategy for the regularization of ECT image reconstruction.     

基于极限学习机求解正问题的 ECT 图像重建

在电容层析成像(ECT)图像重建迭代类算法中,通常采用线性正问题求解,以加快重建速度,由此产生重建误差。针对这一问题,提出了基于极限学习机(ELM)的非线性ECT正问题求解方法,ELM网络输入为介电常数分布,其输出为预测的电容测量值。将该方法与传统的Landweber迭代算法相结合构成ELM-Landweber迭代算法进行图像重建。为使样本具有较好的代表性,物体分布位置及大小均随机生成,并计算相应的归一化电容值作为ELM网络训练及测试样本,对ELM-Landweber迭代算法进行了仿真与静态实验,并与传统Landweber迭代算法进行比较。实验结果表明,相较于传统Landweber迭代算法,采用ELM-Landweber迭代算法,其算法收敛速度显著提高,重建图像质量得到明显改善。训练样本的平均图像相对误差由0.728减小至0.504,测试样本的平均图像相对误差由0.596减小至0.475。     

油气润滑ECT系统图像重建中病态问题分析

建立油气润滑ECT系统图像重建的数学模型,分析油气润滑ECT系统图像重建中产生病态性的主要原因和影响因素。采用条件指标-方差分解比(CIVDP)方法,对油气润滑ECT系统图像重建中灵敏度矩阵的病态进行诊断分析。分析表明:油气润滑ECT系统图像敏感场的灵敏度矩阵列向量间存在很强的复共线性关系,即存在很强甚至严重的病态性;油膜厚度和极板数目影响图像重建的病态性,通过对灵敏度数据列的回归分析与残差处理,可有效削弱病态程度。     

动态电容层析成像图像重建算法

提出了融合ECT测量信息和被测对象动态演化信息的新型图像重建模型;基于Tikhonov正则化方法,建立一个同时考虑了ECT测量信息、被测对象动态演化信息、时间与空间约束的新型图像重建目标泛涵,将图像重建问题转化为最优化问题;提出了集成分裂Bregman迭代法优势的新型算法求解该目标泛涵。数值仿真结果表明,所提出的图像重建算法其图像重建质量均优于OIOR算法、STR算法及PLI算法;同时由于所提出的图像重建算法同时考虑了测量数据和重建模型的不精确性,其抵抗测量噪声的能力得以提高。     

An extreme learning machine combined with Landweber iteration algorithm for the inverse problem of electrical capacitance tomography

The image reconstruction of the electrical capacitance tomography (ECT) is an ill-posed and sparse problem. In order to increase the accuracy and speed of the image reconstruction, this paper proposes a new reconstruction algorithm which is based on the extreme learning machine (ELM) with the Landweber iteration method. Firstly, a nonlinear mapping model is established between the pixel gray-scale values and the interelectrode capacitances by using the ELM which has a good learning ability and high speed. Secondly, the Landweber iteration method, which has a good performance in convergence and stability, is applied to calculate the output weight matrix of ELM. Finally, a convergence and stable mapping model of ELM with the Landweber iteration algorithm (L-ELM) for ECT image reconstruction is trained on Matlab platform. Both simulation and measurement tests are carried out to evaluate and analyze the proposed method. Experimental results indicate that the proposed algorithm has good generalization ability and high image reconstruction quality which are better than those of conventional ELM algorithm.     

双臂对称性对压缩传感用于关联成像重构的影响

根据压缩传感理论和关联成像模型,将压缩传感理论应用于关联成像中,实现了传统的双臂关联成像的压缩传感重构。通过仿真实验验证了压缩传感用于关联成像的可行性,以峰值信噪比（PSNR）为衡量指标,分别对压缩传感和传统关联算法的重构图像质量进行了量化。仿真实验表明,压缩传感和关联算法的重构效果均随测量次数的增加而变优,在相同的测量次数下,压缩传感在关联成像中的重构图像的PSNR比传统的关联重构图像高20 dB以上。将压缩传感用于实际双臂关联成像的实验结果表明,压缩传感可以实现双臂关联成像装置的图像重构,但其重构质量很难优于传统关联算法的重构。针对这一实际实验与仿真实验似乎相矛盾的特殊现象,从双臂对称性的角度进行了合理解释,并利用实验中实际的散斑场对该现象进行了验证,最后提出了解决方案。     

介电常数分布对电容层析成像传感器灵敏度的影响

电容层析成像技术（ECT）近年来发展迅速。ECT传感器属“软场”传感器，其灵敏度分布受被成像介电常数分布的影响。由于“软场”特性的复杂性，图像重建时常忽略其影响，其结果是重建图像中有较大的“软场”误差。为获得高质量的图像重建，必须研究ECT传感器的软场特性。本文通过典型介电常数分布下灵敏度分布的计算与比较，分析了ECT传感器的“软场”特性，给出了介电常数分布对灵敏度分布影响的主要规律。     

钢丝绳缺陷涡流热成像在线检测方法研究

为保证钢丝绳的安全运行,提出钢丝绳缺陷涡流热成像在线检测方法.首先,提出基于等时加热的图像重构算法,建立钢丝绳全长均经历相同加热过程的重构图像;进一步,提出列最大值归一化算法,消除发射率不一致造成的温度采集误差;最后,建立涡流热成像在线检测系统,对不同数目断丝和磨损缺陷进行在线检测实验.实验结果证明,该方法可以实现钢丝...     

Dynamic imaging method using the low n-rank tensor for electrical capacitance tomography

Imaging objects in electrical capacitance tomography (ECT) measurement are often in a dynamic evolution process, and exploiting the spatial–temporal properties of the dynamic reconstruction objects is crucial for the improvement of the reconstruction quality. Based on the multiple measurement vectors, in this paper a robust dynamic reconstruction model that incorporates the ECT measurement information and the dynamic evolution information of a dynamic object, in which a series of dynamic images is cast as a third-order tensor that the first two dimensions are space and the third is time, is proposed. Under the considerations of the two-dimensional spatial structure property of a difference image and the spatial–temporal property of a third-order image tensor, a new objective functional that fuses the ECT measurement information, the dynamic evolution information, the temporal constraint, the spatial constraint, the low rank constraint of a difference image and the low n-rank constraint of a third-order tensor is proposed, where the images are reconstructed by a batching pattern. The split Bregman iteration (SBI) algorithm is developed for solving the proposed objective functional. Numerical simulations are implemented to demonstrate the advantages of the proposed algorithm on improving the reconstruction quality and the robustness.     

Effectiveness of rotatable sensor to improve image accuracy of ECT system

This paper presents a new design of rotatable sensor for ECT systems that can be mounted on a multi-phase flow installation. In order to attest how the performance of the sensor is affected by the rotatable frame, the effectiveness of the rotatable sensor is analyzed in terms of SNR (Signal-to-Noise Ratio) and image accuracy, which is dependent on the number of independent measurements, the image reconstruction strategy and the size of the mesh. The results confirm that with a sensor equipped with 16 electrodes, the optimum number of rotation steps is 3 in order to get the best compromise in terms of image accuracy and image reconstruction time. Results also show that this configuration achieves results similar to a classical sensor equipped with 32 electrodes.     

Generalized multi-scale dynamic inversion algorithm for electrical capacitance tomography

Owing to distinct advantages such as the easy implementation, low cost, high safety and non-intrusive sensing, the electrical capacitance tomography (ECT) is considered as a promising visualization measurement technique, in which reconstructing high quality images is highly desirable for real applications. In this paper, a multi-scale dynamic reconstruction model, which simultaneously utilizes the ECT measurement information and the dynamic evolution information of a dynamic object, is presented. The original dynamic image reconstruction problem is decomposed into a sequence of inverse problems, which are solved successively from the largest scale to the original scale. A generalized objective functional that considers the ECT measurement information, the dynamic evolution information of a dynamic object, the temporal constraint and the spatial constraint is proposed. An iterative algorithm, which integrates the beneficial advantages of the evolutionary strategy (ES) algorithm and the homotopy method, is designed for solving the proposed objective functional. Numerical simulations are implemented to evaluate the feasibility of the proposed algorithm. For the cases simulated in this paper, the quality of the images reconstructed by the proposed algorithm is improved, which indicates that the proposed algorithm is successful in solving ECT inverse problems.     

基于U曲线法的油气润滑ECT系统图像重建病态优化

采用U曲线法确定油气润滑ECT系统图像重建中的正则化参数,分析正则化处理后灵敏度矩阵的病态性;通过LBP算法和Tikhonov正则化算法分别对油气润滑ECT系统管道截面进行第一次图像重建;对第一次重建图像的灰度分布矩阵进行门限滤波阈值的优化,并对管道截面进行二次图像重建。结果表明:相较于L曲线法,U曲线法选取的正则化参数在削弱灵敏度矩阵病态程度方面的作用显著;第一次图像重建中,图像重建质量有较大改善;门限滤波阈值优化后的二次图像重建中,图像重建质量进一步提高。研究表明U曲线法确定的正则化参数和门限滤波阈值优化有助于提高油气润滑ECT系统的图像重建质量。