Image reconstruction algorithm for capacitively coupled electrical resistance tomography

Capacitively Coupled Electrical Resistance Tomography (CCERT), which is on the basis of Capacitively Coupled Contactless Conductivity Detection (C⁴D), is a novel electrical tomography technique. As a developing technique, more research work should be undertaken. This work focuses on the study of image reconstruction algorithm of CCERT. Combining Tikhonov regularization principle and Simultaneous Iterative Reconstruction Technique (SIRT), a new hybrid image reconstruction algorithm is proposed. Tikhonov regularization is introduced to obtain the initial reconstructed image. SIRT is used to obtain the final reconstructed image. With a 12-electrode CCERT prototype, image reconstruction experiments are carried out. Experimental results show that the images reconstructed by the proposed image reconstruction algorithm are satisfactory and are in accord with the actual distributions of two-phase flows. The research work also indicates that the proposed image reconstruction algorithm is more suitable for image reconstruction of CCERT, comparing with the conventional image reconstruction algorithms of Electrical Capacitance Tomography (ECT) and Electrical Resistance Tomography (ERT).     

基于预优化变换的电容层析成像图像重建算法

本文提出了一种新型快速电容层析成像的图像重建算法。该方法首先将图像重建的病态问题转化为泛函极小化问题，然后采用Fletcher-Reeves算法（FR）有效地求解该泛函，并在求解的过程中引入物理意义上的约束使获得的解更符合实际情况。数值实验表明该算法的图像重建效果优于线性反投影法、Tikhonov正则法和Landweber迭代法，而且该算法具有较强的抗噪声能力。     

Split Bregman iteration based image reconstruction algorithm for electrical capacitance tomography

Practical applications of the electrical capacitance tomography (ECT) rely mainly on the effectiveness of reconstruction algorithms. In this paper the solution of the inverse problem with the focus on the ECT imaging is reformulated to be an optimization problem by introducing a new loss function with regularizes encoding multiple features of solution. An iterative scheme that decomposes a complex optimization problem into several simpler sub-problems is developed to solve the proposed loss function, in which the linearization approximation and the acceleration strategy are introduced to improve numerical performances. Numerical experiments validate the effectiveness of the proposed imaging method in tackling the ECT inverse problem.     

基于自适应模拟退火及LM联合反演算法的ECT图像重建

为解决电容层析成像技术(ECT)中图像重建的非线性和病态性问题,提出了一种自适应模拟退火-Levenberg Marquardt(ASA-LM)联合反演算法.改进了标准模拟退火(SA)算法的新解生成策略、能量函数的定义及退火策略,并结合LM的直接局部搜索方法联合反演ECT图像重建问题.同时,利用Savitzky-Gol...     

Regularization parameter optimization based on the constraint of Landweber algorithm for electrical capacitance tomography

Image reconstruction algorithms play an important role in practical applications of electrical capacitance tomography. In the present paper, a combined image reconstruction method is proposed, which takes the results of Landweber algorithm as the constraint condition of Tikhonov algorithm's regularization parameter, calculates the regular parameter, inverts the inverse matrix of sensitivity matrix, and finally obtains the dielectric constant distribution; thus, reconstructed images with improved clarity were obtained. Simulation test are carried out to evaluate and analyze the proposed method from image error, correlation coefficient, image reconstruction time, and anti-noise ability. The results revealed that the Tikhonov regularization algorithm had excellent anti-noise ability; thus, it significantly improved the clarity of reconstructed images and clearly distinguished the multi-phase flow pattern and distribution.     

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.     

Nonlinear image reconstruction using a GA-ECT technique in electrical capacitance tomography

Electrical capacitance tomography (ECT) is a non-invasive measurement technique that estimates the dielectric permittivity distribution of an inhomogeneous object from the boundary potentials at floating electrodes or mutual capacitances. In this paper, a stochastic inverse technique based on genetic algorithm (GA-ECT) is developed, which is adapted to the two different methods, i.e. potential measurement and capacitance measurement. Numerical simulation results are presented to evaluate the inverse technique both for noise free and noisy data and the results show that quantitative image can be reconstructed not only with the low permittivity contrast but also with the high contrast. Furthermore, the influence of a priori knowledge to image reconstruction is discussed.     

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。     

基于加权奇异值分解截断共轭梯度的电容层析图像重建

针对电容层析成像技术(ECT)中的软场效应和病态问题,提出了一种基于加权奇异值分解(SVD)截断共轭梯度的电容层析(ECT)图像重建算法。阐述了电容层析成像工作原理,提出了12电极ECT系统的测量方法。在分析灵敏度矩阵的奇异值分解理论的基础上,推导出了加权SVD截断共轭梯度的数学模型,并利用Tikhonov方法进行正则化加权处理。最后,分析了算法的收敛性,并将其应用于电容层析成像系统的图像重建中。实验结果表明,对于层流,截断共轭梯度算法的平均误差能达到27.54%,全部流型平均迭代步数达到13步,与LBP、Landweber和CG算法比较,该算法具有成像效果好,成像速度快,易于实现等特点。     

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。     

A new hierarchical reconstruction algorithm for electrical capacitance tomography using a relaxation region-based approach

This paper presents a new two-dimensional tomography algorithm to reconstruct the internal image of a multiphase fluid passing through a section of a pipe. The embedded sensing module consists of an array of electrodes placed around the pipe to measure all possible combinations of capacitances between these electrodes. The algorithm is hierarchical and consists to confine progressively the regions of interest which hold the inhomogeneous phase by refining the finite element mesh size around their boundaries. Experimental results done on various images clearly indicate that the proposed algorithm improves the quality of the reconstructed images while keeping the computation time significantly lower than other traditional methods.     

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。     

Robust dynamic inversion algorithm for the visualization in electrical capacitance tomography

Electrical capacitance tomography (ECT) is considered as a promising visualization measurement technique, in which reconstructing high-quality images is crucial for real applications. In this paper, a robust dynamic reconstruction model, which incorporates the ECT measurement information and the dynamic evolution information of a dynamic object, is presented. Under the considerations of the low rank property of an ECT image and the inaccuracies on the sensitivity matrix, the reconstruction model and the measurement data, an objective functional that fuses the ECT measurement information, the dynamic evolution information of a dynamic object, the spatial constraint, the temporal constraint and the low rank constraint is proposed. An iteration scheme that integrates the advantages of the fast composite splitting (FCS) algorithm is developed for solving the proposed objective functional. Numerical simulations are implemented to validate the feasibility of the proposed algorithm.     

电容层析成像图像重建的总变差正则化算法

针对电容层析成像（ECT）逆问题解的不适定性,本文提出一种基于总变差（total variation,TV）正则化的图像重建算法。同传统的2范数Tikhonov正则化方法相比,该算法（基于1范数正则化）不仅保证了逆问题求解的稳定性,而且提高了对介质非连续分布的区域成像的分辨能力,具有良好的保边缘性。仿真及实验结果表明,该算法在重建图像质量和重建速度两方面均具有优势。     

Sparsity-inspired image reconstruction for electrical capacitance tomography

We present a new image reconstruction method for Electrical Capacitance Tomography (ECT). ECT image reconstruction is generally ill-posed because the number of measurements is small whereas the image dimensions are large. Here, we present a sparsity-inspired approach to achieve better ECT image reconstruction from the small number of measurements. Our approach for ECT image reconstruction is based on Total Variation (TV) regularization. We apply an efficient Split-Bregman Iteration (SBI) approach to solve the problem. We also propose three metrics to evaluate image reconstruction performance, i.e., a joint metric of positive reconstruction rate (PRR) and false reconstruction rate (FRR), correlation coefficient, and a shape and location metric. The results on both synthetic and real data show that the proposed TV-SBI method can better preserve the edges of images and better resolve different objects within reconstructed images, as compared to a representative state-of-the-art ECT image reconstruction algorithm, Projected Landweber Iteration with Linear Back Projection initialization (LBP-PLI).     

A novel method of plotting sensor sensitivity field and image reconstruction algorithm for electrical capacitance tomography system

Sensor sensitivity field in electrical capacitance tomography is affected by the distribution of multiphase medium, which is the peculiarity of soft field. This brings great difficulty for image reconstruction. To improve the quality of image reconstruction, it is important to analyze the distribution of the sensitivity field. In this article, using the finite element method, we expound a kind of novel plotting pattern to field, which is the distribution of sensitivity field through computer simulation. From experiments and results of sensitivity field analysis, a novel method of image reconstruction based on genetic algorithms is presented. The finite element model is correct and simulation result is fine by adopting unequal interval plotting patterns. At the same time, the result of image reconstruction has high precision. __________ Translated from Chinese Journal of Scientific Instrument, 2005, 26(3) (in Chinese)     

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。     

A non-convex regularization method combined with Landweber method for image reconstruction in electrical resistance tomography

Electrical resistance tomography (ERT) is a promising technique with which the conductivity distribution in the detected region can be visualized. Mathematically, the reconstruction of conductivity distribution is a seriously ill-posed inverse problem which poses a great challenge for the ERT sensing technique. The regularization method has been found to be an effective approach in coping with the inverse problem. In this work, a novel reconstruction strategy which combines the non-convex regularization method with Landweber method is proposed for the image reconstruction in ERT. At each iteration, the non-convex regularization is used to constrain the conductivity calculated with the Landweber method. A simple and efficient generalized iterated shrinkage algorithm is developed to solve the proposed method. To validate the performance of the proposed method, a series of numerical simulation is conducted and comparative analysis with other methods is performed. From the results, it can be observed that images with high quality are obtained when reconstructing with the proposed method. The impact of noise on the reconstruction is also investigated which shows that the images reconstructed by the proposed method are the least sensitive to the noise. The performance of the proposed method in the image reconstruction is also verified by experimental data. The results demonstrate that the inclusion is accurately reconstructed and the background is clear when the proposed method is adopted for the image reconstruction.     

电容层析成像系统传感器设计新方法

在电容层析成像系统中,为了提高重建图像的精度,常用的方法是提高成像传感器的极板数目,以获得较多的图像重建所需的独立电容测量值数目,但这种方法是以牺牲检测场的灵敏度为代价的。该文提出了一种在有限极板数条件下通过改变极板的组合方式成倍提高成像系统的独立电容测量值数目的方法。仿真结果表明该方法在不降低检测场灵敏度的前提下提高了电容测量值数目,从而提高了图像重建质量。