The nonlinear variation regularization algorithm for the magnetic resonance electrical impedance tomography

The nonlinear variation regularization algorithm (NVRA) is an effective method to enhance the contrast and robustness of the reconstruction in medical imaging. In order to improve the reconstruction quality the variation regularization is introduced to the nonlinear algorithm based on one component of the magnetic flux density by injecting one current. Firstly, we propose a novel algorithm for magnetic resonance electrical impedance tomography (MREIT) using NVRA, and clarify the implementation of this algorithm. Secondly, we analyze the performance of the proposed nonlinear algorithm and the linear sensitivity method with noisy data in the phantom models. Finally, in the case of 0.36 T low field intensity magnetic resonance scanner, we present the method for reducing the electrode model error, and evaluate the performance of two reconstruction algorithms in the agar gel model. The results indicate that the NVRA is able to improve the reconstruction quality with sharp contrast and more robust to noise in comparison to the sensitivity method. In addition, this study shows that with just one current injection and one component of the magnetic flux density we can obtain a high quality imaging, which promotes the MREIT in clinical application. © 2015 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 25, 68–76, 2015     

基于非线性最小二乘的电容层析成像图像重建算法

针对电容层析成像技术中的软场效应和病态问题,提出了基于非线性最小二乘算法的新电容层析成像(ECT)算法。在分析非线性最小二乘问题残量原理的基础上,给出了目标函数中二阶信息项的割线近似的校正公式,并利用Lipschitz空间连续的性质对非线性最小二乘算法的收敛性进行了证明,在此基础上探讨了ECT应用该算法的可行性。该算法满足收敛条件且重建图像误差小。仿真和实验结果表明,与LBP、Landweber和共轭梯度算法相比,对于简单流型该算法兼备成像质量高、边界均匀稳定等优点,该算法的提出为ECT图像重建算法的研究提供了一个新的思路。     

Inclusion boundary reconstruction and sensitivity analysis in electrical impedance tomography

Reconstruction of conductive inclusions in a homogeneous background medium is commonly seen in electrical impedance tomography (EIT). One of the methods to deal with the inclusion reconstruction problems is the shape-based method. With prior knowledge of conductivity of target inclusions, the boundary of inclusions is parameterized by several shape coefficients and recovered from EIT measurements. This paper presents a shape-based inclusion reconstruction method and its numerical implementation with boundary element method (BEM). A shape perturbation method (SPM) is proposed to calculate the shape sensitivity in EIT. To evaluate the accuracy of the presented method, a series of numerical tests are conducted. The characteristics of EIT shape sensitivity are analysed. Some factors influencing the reconstruction performance are discussed.     

Constrained image reconstruction for magnetic detection electrical impedance tomography

Magnetic detection electrical impedance tomography (MD‐EIT) produces images of conductivity from magnetic field measurements taken around the body. The ill‐conditioned nature of the MD‐EIT inverse problem is improved by limiting the number of unknowns to be solved. In this article, a method of iterative grid refinement for MD‐EIT, which produces images significantly better than unconstrained solutions, is described. © 2008 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 17, 379–382, 2007     

Boundary element method and internal electrodes in electrical impedance tomography

Traditionally in electrical impedance tomography an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the object. However, in certain applications it is also possible to use internal current sources and voltage measurements. In this paper we propose a boundary element‐based method which utilizes data also from internal electrodes in the image reconstruction. The proposed approach assumes that the internal geometry is known a priori and only the conductivities of the predetermined regions are estimated. Two‐dimensional simulations with four additional sources/measurement locations show clear improvement in the reconstructed images when the results are compared to those based only on boundary data. Copyright © 2001 John Wiley & Sons, Ltd.     

面向CFRP损伤检测的改进L1正则化EIT方法

由于碳纤维复合材料(carbon fiber reinforced polymer, CFRP)具有导电特性,因此可利用电阻抗层析成像(electrical impedance tomography, EIT)技术实现结构损伤检测。考虑EIT电极位置、数量有限以及电场软场特性的影响,其灵敏度矩阵呈现非均匀分布特征,导致场域内不同位置成像效果差别较大。该研究基于传统L1正则化的边缘锐化特性,提出了一种改进L1正则化方法。该方法通过分析损伤重建电导率分布规律,发现其在各邻域梯度分布的特征,并利用此特征保留L1正则化可能滤除的有效数据,在保证重建图像锐利边缘的同时,改善了不均匀灵敏度分布导致的区域成像精度差别。为验证所提出方法的有效性,仿真中设计了不同类型、不同相对位置的损伤模型,并且通过搭建的16电极EIT测试系统对损伤CFRP样品进行测试。仿真和试验结果表明,改进后的L1正则化方法不仅能重建更多位置上的损伤图像,而且不同程度地提高了各类损伤重建图像的精度。     

Experimental evaluation of 3D electrical impedance tomography with total variation prior

In electrical impedance tomography (EIT), two- or three-dimensional (2D or 3D) distribution of the electrical conductivity is reconstructed based on potential measurements from the surface of the object. In many industrial and medical applications of EIT, the conductivity distribution is discontinuous – due to, e.g. phase or tissue boundaries. Previous studies have shown that such features in the conductivity can be preserved by using total variation (TV) prior model in the EIT image reconstruction. Recently, both 2D and 3D TV models have been utilized in EIT simulation studies. This far, however, EIT reconstructions with TV models have been evaluated experimentally only in 2D cases or translationally invariant 3D cases. In this paper, an experimental study of EIT with a TV prior in a 3D geometry is presented. In addition, we propose the selection of the prior parameters in the TV model based on the prior information of materials in the target, and their conductivity ranges. The results demonstrate the robustness of the proposed parameter selection strategy, and verify that the use of the TV prior yields sharp reconstructions in 3D EIT.     

A three-dimensional image reconstruction algorithm for electrical impedance tomography using planar electrode arrays

We present a three-dimensional non-iterative reconstruction algorithm developed for conductivity imaging with real data collected on a planar rectangular array of electrodes. Such an electrode configuration as well as the proposed imaging technique is intended to be used for breast cancer detection. The algorithm is based on linearizing the conductivity about a constant value and allows real-time reconstructions. The performance of the algorithm was tested on numerically simulated data and we successfully detected small inclusions with conductivities three or four times the background lying beneath the data collection surface. The results were fairly stable with respect to the noise level in the data and displayed very good spatial resolution in the plane of electrodes.     

Regularized modified Newton-Raphson technique applied to electrical impedance tomography

Electrical Impedance Tomography (EIT) is gaining importance as a monitoring tool for process engineering. The main reasons for this are its nonintrusive measurement property and its relatively cheap hardware. However, the image reconstruction still remains a problem especially under heavy process conditions with little prior information. Many researchers have devoted their attention to this problem, but robust algorithms working on real noisy data are scarce. The authors present a regularized, modified Newton-Raphson algorithm that gives satisfying results on both static and dynamic processes. The number of pixels used by the algorithm are identical to the number of true non-zero eigenvalues, thereby diminishing the effect of ill-conditioning. The algorithm uses a user-defined pixel mesh that is mapped onto a standard finite-element mesh so that the user is able to easily adapt the mesh to the problem under investigation. © 1998 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 9, 60–65, 1998     

Image reconstruction using simulated annealing in electrical impedance tomography: a new approach

Image reconstruction in electrical impedance tomography (EIT) deals with an ill-posed and non-linear inverse problem. It has the objective of minimizing the difference between simulated (virtual) object data and electric voltage measurements performed on a non-simulated (real) object. In this paper, a new approach to the simulated annealing method applied to the reconstruction of EIT images is described. The main advantage of this approach is that all conductivity parameters are updated simultaneously. Most methods that employ simulated annealing to the problem of EIT usually evaluate each conductivity parameter individually resulting in high computational cost. The algorithm was tested both with computationally generated data and with measurements performed on a physical tank. In both cases, the method was able to make data inversion, determining the position, the dimensions and the conductivity of materials in an opaque object plane.     

一种基于模型的光学层析图像重建方法

光学层析图像重建是个病态问题,测量误差会在重建过程中被放大,对此,提出一种以广义高斯马尔可夫随机场模型为先验信息的光学层析图像重建方法.重建过程是对目标函数的优化过程,目标函数关于光学参数的梯度计算是算法中的难点,因此,提出一种基于梯度树的梯度计算方法.文中分别给出了吸收系数和散射系数的重建结果,并引入三个指标因子衡量重建图像的质量,进而列出不同重建算法下,重建图像的指标值.最后通过对重建结果和指标因子取值的比较,分析基于模型的重建算法的有效性.     

气体浓度层析成像重建算法性能比较与研究

针对少射线成像算法在研究气体浓度层析成像中的重要作用,对常用的几种少射线成像算法的性能进行了详细分析和比较,同时构造了一个多目标函数用于气体浓度优化重建成像。通过实验与常用的几种算法的重建性能相比,多目标优化重建算法具有良好的鲁棒性和抗噪性。在含5%测量误差的情况下,ART 重建结果与原始浓度分布的欧氏距离达 0.1680,而多目标优化重建算法下的该值仅为 0.0325。     

反射型超声衍射CT迭代重建算法

本文以傅立叶衍射定理为基础,将非均匀傅立叶变换和迭代法相结合,用正则化方法处理迭代的收敛问题,建立了反射型超声衍射成像算法。数据直接在频域中的非均匀频率点上比较,避免了频域内插引入的误差。本算法也减少了采样数据量,降低了运算的复杂度。实验结果表明,在迭代次数不多情况下,重建图像可以达到较好的视觉效果。     

Fixed‐lag smoothing and state estimation in dynamic electrical impedance tomography

In electrical impedance tomography (EIT), an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the body. The conventional approach is to inject several different current patterns and use the associated data for the reconstruction of a single distribution. This is an ill‐posed inverse problem. In some applications the resistivity changes may be so fast that the target changes between the injection of the current patterns and thus the data do not correspond to the same target distribution. In these cases traditional reconstruction methods yield severely blurred resistivity estimates. We have earlier proposed to formulate the EIT problem as an augmented system theoretical state estimation problem. The reconstruction problem can then be solved with Kalman filter and Kalman smoother algorithms. In this paper, we use the so‐called fixed‐lag smoother to solve the dynamic EIT reconstruction problem. We show that data storage difficulties that are associated with the previously used fixed‐interval smoother can be avoided using the fixed‐lag smoother. The proposed methods are compared with simulated measurements and real data. Copyright © 2001 John Wiley & Sons, Ltd.     

Convergence study of 2D forward problem of electrical impedance tomography with high-order finite elements

A convergence study of the forward problem of electrical impedance tomography is performed using triangular high-order piecewise polynomial finite-element methods (p-FEM) on a square domain. The computation of p-FEM for the complete electrode model (CEM) is outlined and a novel analytic solution to the CEM on a square domain is presented. Errors as a function of mesh-refinement and computational time, as well as convergence rates as a function of contact impedance, are computed numerically for different polynomial approximation orders. It is demonstrated that p-FEM can generate more accurate forward solutions in less computational time, which implies more accurate simulated interior potentials, electrode voltages and conductivity Jacobians.     

超拉普拉斯重叠组稀疏先验的稀疏角度CT重建

对于稀疏角度下的投影数据,计算机断层扫描在图像重建中容易出现伪影和噪声较多的问题,难以满足工业及医学诊断要求。本文提出一种基于重叠组稀疏和超拉普拉斯先验的稀疏角度CT迭代图像重建算法。其中重叠组稀疏反映图像梯度稀疏性,从图像梯度的角度考虑相邻元素之间互相重叠交叉的关系。而超拉普拉斯先验能够精确地近似图像梯度的重尾分布,能够使得重建图像整体的质量提升。本文提出的算法模型采用交替方向乘子法,主分量最小化法和梯度下降法求解目标函数。实验结果表明,在稀疏角度CT重建的条件下,本文提出的算法在保留结构细节、抑制图像重建过程中产生的噪声和阶梯伪影方面有着一定的改善。

     

A new projection-based iterative image reconstruction algorithm for dual-energy computed tomography

Dual-energy CT can be represented as the dual-energy equations by decomposing the linear attenuation coefficient of the X-ray scanned object into two material basis functions of photoelectric absorption and Compton scatter. To solve the dual-energy equations, in this paper, we apply the mean-value theorem for integrals and propose a new projection-based iterative algorithm. We discuss the convergence of the proposed algorithm and carry out various numerical simulations for demonstrating its feasibility.     

Study on beam geometry and image reconstruction algorithm in fast neutron computerized tomography at NECTAR facility

Investigations on the fast neutron beam geometry for the NECTAR facility are presented. The results of MCNP simulations and experimental measurements of the beam distributions at NECTAR are compared. Boltzmann functions are used to describe the beam profile in the detection plane assuming the area source to be set up of large number of single neutron point sources. An iterative algebraic reconstruction algorithm is developed, realized and verified by both simulated and measured projection data. The feasibility for improved reconstruction in fast neutron computerized tomography at the NECTAR facility is demonstrated.     

超声层析成像的迭代重建

利用变形Born迭代方法,建立了超声衍射重建算法。在迭代过程中,为了解决超声逆散射问题中的非线性性,需要反复地求解前向散射方程和逆散射方程,以达到全场和未知函数的近似,较好地重建物体内部的断层图象。由于逆散射方程是一个不适定性的方程组,要用正则化方法处理方程的不适定性问题,使迭代方法收敛于问题的真实解,才能成功地应用于较高对比度物体的图象重建问题。用Picard准则对不适定问题进行了分析,给出了通过简单图形．确定模型受噪声污染情况以及正则化方法适用范围的方法。在重建实验中。对建立的图像重建算法进行了实验仿真。达到了较好的效果。