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).     

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.     

Noise Reduction of Electrical Impedance Tomography via Movable Electrodes

Abstract

In this paper, a movable electrical impedance tomography (MEIT) system is introduced to reduce the noise of electrical impedance tomography. This moving scheme could yield more independent measurements and reconstruct improved impedance images. After averaging the entire reconstructed image, we could improve the image quality substantially. The experiment result shows a quality improvement compared with the measuring systems without moving scheme. This preliminary work provides a feasibility to reduce the noise of electrical impedance tomography by a moving electrode scheme.     

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。     

Evaluation of fringe effect of electrical resistance tomography sensor

A conventional electrical resistance tomography (ERT) sensor uses pin electrodes for current injection, and the electric field spreads far beyond the electrode plane, as a result of “soft field” nature. This phenomenon is referred to as “fringe effect” and would cause measurement errors and image distortion. The impact of fringe effect on measurement and reconstructed images depends on the object distributions, the conductivity contrast and others. It is not trivial to evaluate the fringe effect of an ERT sensor and its impact on the measurement and the reconstructed images. In this paper the fringe effect of an ERT sensor is evaluated for central core and off-central core distributions at different axial positions and with different axial dimensions and conductivity contrasts. Then, how to compensate for the fringe effect of the ERT sensor is discussed and a method proposed for improving the measurement accuracy and image reconstruction. Finally, the findings and methodology is verified by experiment.     

An adaptive non-convex hybrid total variation regularization method for image reconstruction in electrical impedance tomography

The image reconstruction of conductivity distribution in electrical impedance tomography (EIT) is a seriously ill-posed inverse problem. To cope with the problem, it is recognized that the regularization method is an effective approach. In this paper, an adaptive non-convex hybrid total variation (ANHTV) regularization method is proposed to reconstruct the conductivity distribution in EIT. The iterative reweighted least squares algorithm and the iterative alternating direction method of multipliers algorithm are developed to solve the ANHTV-based inverse model in the image reconstruction. Besides, all the parameters utilized in the inverse model are adaptively selected. To validate the advantage of the proposed method, extensive numerical simulation and experimental work have been carried out. Also, qualitative and quantitative comparisons with two convex TV-based regularization methods are conducted. The results show that the proposed method is more advantageous in terms of staircase effect suppression, edge information preservation and noise resisting in the image reconstruction.     

基于数据融合的ECT图像重建算法

针对固定电极的ECT成像独立测量值较少和因电极位置的影响而导致重建图像失真等问题,提出了基于旋转电极ECT系统模型和数据融合方法来提高重建图像质量。本模型对16电极的ECT模型进行5次旋转,得到的数据采用两种方式进行处理:一是5组数据分别采用线性反投影(LBP)和修正共轭梯度法(MCG)进行重建,再对重建数据进行主分量分析(PCA)的数据融合;二是直接用PCA数据融合再分别进行LBP和MCG图像重建。实验证明:通过增加测量电容数,结合两种数据处理方式可明显提高重构图像质量,降低成像误差。     

结合压缩感知和曲波的天文图像去噪

在天文图像去噪中,为了提高迭代曲波阈值算法的去噪重建性能,提出了基于循环平移和曲波维纳滤波的压缩感知迭代重构算法。首先,使用基于曲波阈值的循环平移方法对重构图像进行调整以抑制重构图像中的伪吉布斯效应;接着,用提出的曲波维纳滤波算子替代小波阈值在迭代过程中对图像曲波系数进行筛选以进一步提高重构图像的质量。通过对添加高斯白噪声的Lena图像和月球图像进行重构实验,分析本文算法和当前主流算法的性能。实验结果表明,与传统的压缩感知迭代曲波阈值算法相比,本文算法能够获得较优的去噪性能,有效地保护天文图像的细节信息,峰值信噪比大约提高了2.6~3.2dB。     

Reconstruction of electrical impedance tomography (EIT) images based on the expectation maximum (EM) method

Electrical impedance tomography (EIT) calculates the internal conductivity distribution within a body using electrical contact measurements. The image reconstruction for EIT is an inverse problem, which is both non-linear and ill-posed. The traditional regularization method cannot avoid introducing negative values in the solution. The negativity of the solution produces artifacts in reconstructed images in presence of noise. A statistical method, namely, the expectation maximization (EM) method, is used to solve the inverse problem for EIT in this paper. The mathematical model of EIT is transformed to the non-negatively constrained likelihood minimization problem. The solution is obtained by the gradient projection-reduced Newton (GPRN) iteration method. This paper also discusses the strategies of choosing parameters. Simulation and experimental results indicate that the reconstructed images with higher quality can be obtained by the EM method, compared with the traditional Tikhonov and conjugate gradient (CG) methods, even with non-negative processing.     

Data fusion in dual-mode tomography for imaging oil–gas two-phase flow

Process tomography (PT) techniques have been developed rapidly for visualizing the internal behavior of industrial processes, e.g. multi-phase flow measurement. Most of tomography systems employ a single measurement technique, such as computerized tomography (CT), optical tomography (OT), electrical resistance tomography (ERT) or electrical capacitance tomography (ECT). It is now possible to fit two or more tomographic systems to an industrial process. Detailed information from different modalities can be gained by inspection of separate tomographs, and the advantage of the strongest features provided by each unit can be taken. A combined tomogram can be produced of superior quality to any of the separate tomograms. To maximize the information available from the combined tomographic system, data fusion is the better option. In this paper, a dual-mode tomography system based on capacitance sensor and gamma sensor was developed to capture oil–gas two-phase flow. The two modalities can work at the same time. Two fusion methods, namely image fusion method and data fusion method, are proposed. Both simulation and static experiments for oil–gas two-phase flow were conducted. The reconstruction results of different fusion methods and modalities were compared and discussed.     

Studies on thin film based flexible gold electrode arrays for resistivity imaging in electrical impedance tomography

Practical phantoms are essential to assess the electrical impedance tomography (EIT) systems for their validation, calibration and comparison purposes. Metal surface electrodes are generally used in practical phantoms which reduce the SNR of the boundary data due to their design and development errors. Novel flexible and biocompatible gold electrode arrays of high geometric precision are proposed to improve the boundary data quality in EIT. The flexible gold electrode arrays are developed on flexible FR4 sheets using thin film technology and practical gold electrode phantoms are developed with different configurations. Injecting a constant current to the phantom boundary the surface potentials are measured by a LabVIEW based data acquisition system and the resistivity images are reconstructed in EIDORS. Boundary data profile and the resistivity images obtained from the gold electrode phantoms are compared with identical phantoms developed with stainless steel electrodes. Surface profilometry, microscopy and the impedance spectroscopy show that the gold electrode arrays are smooth, geometrically precised and less resistive. Results show that the boundary data accuracy and image quality are improved with gold electrode arrays. Results show that the diametric resistivity plot (DRP), contrast to noise ratio (CNR), percentage of contrast recovery (PCR) and coefficient of contrast (COC) of reconstructed images are improved in gold electrode phantoms.     

ECT图像重建正则化参数选取新方法

电容层析成像图像重建是一不适定反问题。此种情况下，仅使用最小二乘法不能保证获得满意的介质分布图像重建结果，因此广泛使用TIkhonov正则化算法来产生适当的解。正则化参数的合适选取对图像重建至关重要，其对重建质量和计算时间都有影响。本文提出了一种基于最平坦斜率的Tikhonov正则化参数选择方法，并针对2种典型介质分布，将基于此方法计算的正则化参数同L-曲线法在电容测量数据无噪声和施加噪声情况下的图像重建结果进行了比较。     

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。     

A hybrid regularization method combining Tikhonov with total variation for electrical resistance tomography

Electrical resistance tomography (ERT) is a promising measurement technique in industrial process imaging. However, image reconstruction in ERT is an ill-posed inverse problem. Regularization methods have been developed to solve the ill-posed inverse problem. Since the penalty term is a form of L2-norm, Tikhonov regularization method guarantees the stability of the solution, but it always makes the image edge oversmoothed. Total variation (TV) regularization method has good ability of preserving image edges. A hybrid regularization method, which combines Tikhonov with TV regularization method, is proposed to get better reconstructed images. The choice of the adaptive weighted parameter between TV and Tikhonov penalty term has been discussed in detail. In the proposed hybrid regularization method, the function of conductivity gradients is used as the adaptive weighted parameter to control automatically the weighting between the penalty terms from TV and Tikhonov regularization. For the model with sharp edges, the proportion of the penalty term from TV regularization is increased to preserve the edges, while for the model with smooth edges, the proportion of penalty term from Tikhonov regularization is increased to make the solution stable and robust to noise. Both simulation and experimental results of Tikhonov, TV and hybrid regularization method are shown respectively, which indicates that the hybrid regularization method can improve the reconstruction quality with sharp edges and is more robust to noise, and it is applicable for models with different edge characteristic.     

基于栈式自编码器的磁探测电阻抗成像算法研究

针对目前磁探测电阻抗成像算法图像重建分辨率不高、精确度低的问题,提出了一种基于栈式自编码(SAE)神经网络的磁探测电阻抗成像算法。使用方形成像体进行仿真实验,通过训练样本建立SAE神经网络模型,确定神经元权重和偏置值。利用该网络模型重建成像体内部的电导率分布;并在异质体中心位置、算法的抗噪性能等方面将重建结果与基于Levenberg-Marquardt算法的反向传播神经网络的重建结果进行对比。结果表明栈式自编码神经网络算法显著提高了磁探测电阻抗成像的重建精度、抗噪性能。最后,通过仿体实验验证了SAE算法的可行性。根据实际测得的磁场,使用神经网络算法重建电导率,准确定位异质体位置。SAE神经网络算法的提出对于磁探测电阻抗成像技术的广泛应用具有重要意义。     

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.     

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.     

The application of the maximum entropy method to electron microscopic tomography

The maximum entropy method has been applied to single axis tilt electron microscopic tomography. Its application requires that the problem be correctly formulated and that the model for the noise in electron micrographs be developed. A suitable noise model was determined empirically. The maximum entropy method was applied to a reconstruction of a test object from projections to which noise had been added. These reconstructions were superior to those obtained by reciprocal space weighted back protection. The method was also robust towards the incorrect specification of the noise, the penalty being an increase in the time required for convergence rather than degradation of the quality of the reconstructed image. In the reconstruction of negatively stained chromatin fibres it was possible to obtain satisfactory images utilizing all the information in the projections, in contrast to conventional methods in which high resolution data are removed by the application of Fourier space filters.     

基于遗传算法的组合ERT图像重建算法研究

针对目前电阻层析成像图像重建算法存在成像精度较低的问题,以及为了满足应用于多相流领域的精度要求,提出一种基于遗传算法的组合算法,将线性反投影算法、修正的牛顿-拉夫逊类算法与区间剖分引入遗传算法种群初始化操作中,同时为了改善单纯遗传算法局部搜索能力差与未成熟收敛的问题,将粒子群算法引入遗传算法变异操作中。实验结果表明组合算法效果明显优于线性反投影算法,修正的牛顿-拉夫逊类算法,有效克服了遗传算法早熟收敛现象,提高了成像精度。     

ITS Reconstruction Tool-Suite: An inverse algorithm package for industrial process tomography

Electrical resistance tomography (ERT) and electrical capacitance tomography (ECT) are two established process tomography techniques that can be applied into various indsutries. ERT can monitor the electrical conductivity changes in the process whereas ECT can detect the electrical dielectric materials. Due to their high-speed and low cost features, they are particularly attractive to industrial applications which require real time conditional monitoring. For the past decades, 2D linear back projection (LBP) has been the standard technique for both commercialised ERT and ECT systems because of its simplicity and fast reconstruction speed. In this paper, ITS Plc has released a 'Reconstruction Tool-Suite' software that allows industrial users to utilise different reconstruction algorithms to further understand their processes. Different algorithms are integrated into this software package including the single step Tikhonov method and the iterative Landweber method. In the latest version of the software, the full-field 3D tomography reconstruction scheme is also included, which allows the users to perform 3D reconstruction for their processes. A series of experiments are conducted to validate the pros and cons of different methods.