基于 Tikhonov 和 TV 混合正则化的接地 网电阻抗成像算法研究

电阻抗成像技术(EIT)是解决接地网腐蚀定位问题的方法之一,为了改善接地网 EIT 逆问题的病态性,提高求解稳定 性以及重建图像清晰度,提出了经典吉洪诺夫正则化(Tikhonov)和全变差正则化(TV)相结合的混合正则化(Tikhonov-TV)接地 网成像算法。 首先,在循环测量原理的基础上,创新地借助 COMSOL 与 MATLAB 联合仿真求取接地网 EIT 正问题模型电压数 据;其次,在理论分析基础上,通过 Tikhonov-TV 正则化的 EIT 算法分别求解基于先验拓扑信息和未知拓扑信息的两种接地网逆 问题模型的场域电阻率分布;最后仿真和实验对比了 Tikhonov、TV 以及 Tikhonov-TV 3 种正则化算法的接地网 EIT 重建图像,并 采用电阻率均方误差(Resistivity MSE)和截线电阻率曲线图来衡量图像质量,实验得出基于先验拓扑信息的 1 处和 2 处腐蚀情 况下 Resistivity MSE 分别达到 1. 27×10 -15 和 1. 59×10 -15 ,电阻率均方误差最小。 结果表明,提出的 Tikhonov-TV 正则化算法有效 地改善了 EIT 逆问题的病态性,收敛性能最优,重建图像效果优于 Tikhonov 和 TV 正则化算法。     

基于 V-ResNet 的电阻抗层析成像方法

电阻抗层析成像技术(EIT)因其非侵入和可视化等特性为人体肺部空间特性的监测提供了一种有效的方法。但是EIT的逆问题具有严重的非线性、病态性和欠定性,使得图像重建结果含有严重的伪影。针对上述问题,提出了一种由预映射、特征提取、深度重建以及残差去噪四个模块构成的V-ResNet的深度网络成像算法,实现对场域空间位置和电导率参数分布的重建。该算法有效地增加了前馈信息的多重传递并解决了深度网络的梯度消失问题,同时残差去噪模块有效地平滑了图像边界。采用相对误差(RE)和结构相似度(SSIM)来衡量成像质量,实验得出RE的平均值为0.14,SSIM平均值为0.96。仿真与实验结果表明,基于V-ResNet的成像算法与传统的成像算法相比,图像重建结果边界清晰,空间分辨率高。     

Maximum entropy regularization method for electrical impedance tomography combined with a normalized sensitivity map

Electrical impedance tomography (EIT) aims to estimate the electrical properties at the interior of an object from current–voltage measurements on its boundary. To overcome ill-posedness, regularization techniques such as Tikhonov regularization as well as some iterative methods were developed. In difference imaging between two different conductivity distributions, a conductivity change can be seen relatively non-negative to the medium with lower conductivity through some safeguard techniques. Therefore, the concept of maximum entropy from information theory and statistic mechanics can be used for this purpose. Furthermore, because the sensing field is “soft-field” and non-uniform, the same anomaly may produce different reconstruction signatures depending on its location within the image plane. Therefore, in this paper, maximum entropy based on general Tikhonov regularization, combined with normalized sensitivity map, is proposed to solve the inverse problem of EIT. Image reconstruction was carried out by maximum entropy regularization (MER) with a normalized sensitivity map and compared with the results from conjugate gradient method (CG), Tikhonov regularization, and CG with a normalized sensitivity map accordingly. Simulation and experiment results indicate that reconstructed images with higher quality can be obtained by MER with a normalized sensitivity map.     

Projection Error Propagation-based Regularization (PEPR) method for resistivity reconstruction in Electrical Impedance Tomography (EIT)

A novel Projection Error Propagation-based Regularization (PEPR) method is proposed to improve the image quality in Electrical Impedance Tomography (EIT). PEPR method defines the regularization parameter as a function of the projection error developed by difference between experimental measurements and calculated data. The regularization parameter in the reconstruction algorithm gets modified automatically according to the noise level in measured data and ill-posedness of the Hessian matrix. Resistivity imaging of practical phantoms in a Model Based Iterative Image Reconstruction (MoBIIR) algorithm as well as with Electrical Impedance Diffuse Optical Reconstruction Software (EIDORS) with PEPR. The effect of PEPR method is also studied with phantoms with different configurations and with different current injection methods. All the resistivity images reconstructed with PEPR method are compared with the single step regularization (STR) and Modified Levenberg Regularization (LMR) techniques. The results show that, the PEPR technique reduces the projection error and solution error in each iterations both for simulated and experimental data in both the algorithms and improves the reconstructed images with better contrast to noise ratio (CNR), percentage of contrast recovery (PCR), coefficient of contrast (COC) and diametric resistivity profile (DRP).     

Electrical capacitance tomography using an accelerated proximal gradient algorithm

Image reconstruction in electrical capacitance tomography requires a solution of an ill-posed inverse problem. This paper applies an accelerated proximal gradient (APG) singular value thresholding algorithm, which is originally proposed for the matrix completion problem, to image two-phase flow. Aiming to improve the image quality, a nuclear norm-based regularization technique is adopted to treat the ill-posedness of the inverse problem, and a simple updating technique is used to update the sensitivity matrix. Both typical and complicated distributions (e.g., "sun-rise" and cross-shape), have been examined based on a 16-electrode configuration. The results showed that the APG algorithm with updated sensitivity matrix could produce higher quality images when compared to the algorithm based on the typical sensitivity matrix. Both simulation and experiment results indicate that the algorithm developed has been able to achieve good quality reconstructed images with relativity fast computation speed for the cases tested in this paper.     

Fast reconstruction of computerized tomography images based on the cross-entropy method

Computerized tomography (CT) has been applied to multi-phase flow measurement in recent years. Image reconstruction of CT often involves repeatedly solving large-dimensional matrix equations, which are computationally expensive, especially for the case of on-line flow regime identification. In this paper, a minimum cross-entropy (MCE) reconstruction based on wavelet multi-resolution processing, i.e., an MRMCE method, is proposed for fast reconstruction of CT images. Each row of the system’s matrix is transformed by 1-D wavelet decomposition. A regularized MCE solution is obtained using the simultaneous multiplicative algebraic reconstruction technique (SMART) at a coarse resolution level, where important information of the reconstructed image is contained. Then the solution in the finest resolution is obtained by inverse fast wavelet transformation (IFWT). Both computer simulation and experimental work were carried out for oil-gas two-phase flow regimes. Results obtained indicate that the MRMCE method improves the resolution of the reconstructed images and dramatically reduces the computation time compared with the traditional linear back-projection (LBP), MCE and algebraic reconstruction technique (ART) methods. Furthermore, the new method can also be used to accurately estimate the local time-averaged void fraction of dynamic two-phase flow. It is suitable for on-line multi-phase flow measurement.     

A modified conjugate gradient method based on the Tikhonov system for computerized tomography (CT)

During the past few decades, computerized tomography (CT) was widely used for non-destructive testing (NDT) and non-destructive examination (NDE) in the industrial area because of its characteristics of non-invasiveness and visibility. Recently, CT technology has been applied to multi-phase flow measurement. Using the principle of radiation attenuation measurements along different directions through the investigated object with a special reconstruction algorithm, cross-sectional information of the scanned object can be worked out. It is a typical inverse problem and has always been a challenge for its nonlinearity and ill-conditions. The Tikhonov regulation method is widely used for similar ill-posed problems. However, the conventional Tikhonov method does not provide reconstructions with qualities good enough, the relative errors between the reconstructed images and the real distribution should be further reduced. In this paper, a modified conjugate gradient (CG) method is applied to a Tikhonov system (MCGT method) for reconstructing CT images. The computational load is dominated by the number of independent measurements m, and a preconditioner is imported to lower the condition number of the Tikhonov system. Both simulation and experiment results indicate that the proposed method can reduce the computational time and improve the quality of image reconstruction.     

Studying the resistivity imaging of chicken tissue phantoms with different current patterns in Electrical Impedance Tomography (EIT)

A current injection pattern in Electrical Impedance Tomography (EIT) has its own current distribution profile within the domain under test. Hence, different current patterns have different sensitivity, spatial resolution and distinguishability. Image reconstruction studies with practical phantoms are essential to assess the performance of EIT systems for their validation, calibration and comparison purposes. Impedance imaging of real tissue phantoms with different current injection methods is also essential for better assessment of the biomedical EIT systems. Chicken tissue paste phantoms and chicken tissue block phantoms are developed and the resistivity image reconstruction is studied with different current injection methods. A 16-electrode array is placed inside the phantom tank and the tank is filled with chicken muscle tissue paste or chicken tissue blocks as the background mediums. Chicken fat tissue, chicken bone, air hole and nylon cylinders are used as the inhomogeneity to obtained different phantom configurations. A low magnitude low frequency constant sinusoidal current is injected at the phantom boundary with opposite and neighboring current patterns and the boundary potentials are measured. Resistivity images are reconstructed from the boundary data using EIDORS and the reconstructed images are analyzed with the contrast parameters calculated from their elemental resistivity profiles. Results show that the resistivity profiles of all the phantom domains are successfully reconstructed with a proper background resistivity and high inhomogeneity resistivity for both the current injection methods. Reconstructed images show that, for all the chicken tissue phantoms, the inhomogeneities are suitably reconstructed with both the current injection protocols though the chicken tissue block phantom and opposite method are found more suitable. It is observed that the boundary potentials of the chicken tissue block phantoms are higher than the chicken tissue paste phantom. SNR of the chicken tissue block phantoms are found comparatively more and hence the chicken tissue block phantom is found more suitable for its lower noise performance. The background noise is found less in opposite method for all the phantom configurations which yields the better resistivity images with high PCR and COC and proper IR_Mean and IR_Max neighboring method showed higher noise level for both the chicken tissue paste phantoms and chicken tissue block phantoms with all the inhomogeneities. Opposite method is found more suitable for both the chicken tissue phantoms, and also, chicken tissue block phantoms are found more suitable compared to the chicken tissue paste phantom.     

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。     

A Chicken Tissue Phantom for Studying an Electrical Impedance Tomography (EIT) System Suitable for Clinical Imaging

The study of practical phantoms is essential for assessing the reconstruction algorithms and instrumentation used in Electrical Impedance Tomography (EIT). Responses of saline phantoms with insulator inhomogeneities differ from the real tissue phantoms in several aspects. Also, it is difficult to reconstruct the actual resistivity of the insulator inhomogeneity in a saline background because of their large resistivity difference. A practical biological phantom consisting of two different materials with low resistivity difference is more suitable for impedance imaging studies. In order to demonstrate this, a chicken tissue phantom was developed to study the resistivity imaging in EIT. A 16-electrode array was placed inside the phantom tank filled with chicken muscle tissue paste and chicken tissue. A 1 mA, 50 kHz sinusoidal current was injected at the phantom boundary and the boundary potentials are measured using opposite current injection protocol. Resistivity images were reconstructed from the boundary data using Electrical Impedance and Diffuse Optical Reconstruction Software (EIDORS) and the reconstruction was evaluated by calculating the contrast parameters of the images. Results show that the resistivity of the chicken fat is successfully reconstructed with a proper background resistivity. Impedance spectroscopic studies show that the chicken tissue phantom can be suitably used to evaluate a multifrequency EIT system.     

Enhancing the reconstruction of acoustic source field using wavelet transformation

This paper shows the use of wavelet transformation combined with inverse acoustics to reconstruct the surface velocity of a noise source. This approach uses the boundary element analysis based on the measured sound pressure at a set of field points, the Helmholtz integral equations and wavelet transformation for reconstructing the normal surface velocity field. The reconstructed field can be diverged due to the small measurement errors in the case of nearfield acoustic holography (NAH) using an inverse boundary element method. In order to avoid this instability in the inverse problem, the reconstruction process should include some form of regularization for enhancing the resolution of source images. The usual method of regularization has been the truncation of wave vectors associated with small singular values, although the order of an optimal truncation is difficult to determine. In this paper, a wavelet transformation is applied to reduce the computation time for inverse acoustics and to enhance the reconstructed vibration field. The computational speed-up is achieved, with solution time being reduced to 14.5%.     

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RBF神经网络的电阻层析成像算法的研究

本文提出了一种基于RBF神经网络的ERT图像重建算法,并用作者开发的ERT仿真软件得到了数据进行图像重建,与其它传统的成像算法作了对比。研究表明,RBF神经网络适合解决ERT图像重建的非线性问题,该算法具有速度快、精度高的优越性。     

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.     

An element-free Galerkin forward solver for the complete-electrode model in electrical impedance tomography

An element-free Galerkin method (EFGM) is used for solving forward problem based on the complete electrode model (CEM) in electrical impedance tomography (EIT). The EFGM requires only nodal data and has the ability of providing mesh-independent solutions because no element connectivity is needed to be used in this method. However, direct imposition of Dirichlet boundary conditions for the EFGM is difficult because the shape functions employed in this method do not have the property of Dirac delta function. Solving the EIT forward problem based on the CEM by the EFGM, the effects of electrodes and contact impedances are taken into account and the complete solution of equations is provided without imposing Dirichlet boundary conditions. The numerical results are validated with experimental results obtained from a 2D circular homogeneous phantom, and the performance of the EFGM compared with the finite element method is also illustrated. Moreover, results obtained from the EFGM are presented for an inhomogeneous numerical phantom.     

基于L0正则化模糊核估计的遥感图像复原

基于模糊图像的退化过程、卷积模糊模型和模糊图像生成的机理,提出一种基于L₀范数的正则化模糊核估计方法,解决了遥感图像重建问题中0范数难求解的难题。该方法以模糊核稀疏性为先验知识,采用对应梯度的L₀范数为正则项,有效避免了细小边缘对模糊核估计的影响,使得模糊核的估计更加准确。进一步采用超拉普拉斯分布来近似图像梯度的重尾分布,利用L_0.5范数正则化对模糊图像做反卷积,从而恢复出原始图像。与传统方法相比,本文方法可以准确地估计出图像的模糊核,很好地抑制恢复图像的振铃现象,有效地提升遥感图像的质量。模糊图像以及各方法重构图像在同一刀刃下的调制传递函数（MTF）曲线显示,本文方法的MTF曲线得到了较好的提升。     

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.     

Exact solution of one problem of magnetostatics in bipolar coordinates (continued)

An exact solution for a linear problem of magnetostatics about an infinite cylinder with an infinite noncoaxial cylindrical flaw has been derived in the system of plane bipolar coordinates under the condition that external magnetizing field remains unchanged along the length axis of this model body. The solution has been tested for theoretical veracity and compared with the solution of a similar problem that was obtained by one semianalytic method [2]. For a particular problem about a halfspace with an infinite cylindrical flaw, an exact solution has been obtained and compared with results that were achieved by other methods. The mismatch between the solution of the problem about a halfspace and the solution of the problem with passage to the limit of a half-space has been considered. An algorithm is described for solving the inverse problem of separate determination of flaw depth and dimensions.     

梯度引导电学成像自适应网格生成方法

电学层析成像是一种观测场域内电导率分布的无损检测技术。有限元法是求解电学层析成像问题的常用方法。其作为线性化的近似方法,剖分单元的大小会影响有限元法求解的精度。更密的尺寸可以提高重建图像的空间分辨率,但会增加计算成本,同时未知量个数的增加会加剧逆问题的欠定性。针对上述问题,提出一种基于图像梯度的自适应网格生成方法。根据初始重建图像的梯度,自适应地提高内含物区域的网格密度,降低其他区域的网格密度,并对场域边界进行精确拟合来优化被测场域的网格剖分。通过仿真与实验研究对比分析了所提方法与常用网格剖分方法。结果表明,所提方法的重建结果图像误差平均降低15%,相关系数平均提高7%,因此所提方法在不显著增加或减少网格数的情况下,可以有效提高内含物的重建精度和图像重建质量。     

基于自适应PCNN和小波变换的多聚焦图像融合算法

提出了一种基于自适应PCNN和小波变换的新型多聚焦图像融合算法。首先,对待融合的两幅图像进行小波分解得到两组多尺度图像,然后在小波域充分利用PCNN的同步激发特性,进行基于PCNN的融合策略设计。使用不同频率下小波系数的局域熵作为PCNN对应神经元的链接强度,经过PCNN点火获得参与融合图像在小波域中的点火映射图,根据点火时间计算点火映射梯度图,再通过判决选择算子,判定并选择点火时间梯度最大的小波系数作为融合系数。最后对融合后的小波系数进行重构生成融合图像。该方法中,根据设置的迭代次数来确定阈值调整时间常量 ,从而在迭代结束时,所有小波系数均得到激发,充分反映了点火时间的先后次序。实验结果以及与其他融合算法的比较分析表明,所提出的算法能有效地突出边缘细节、更好地保持图像的空间分辨力。