A neural network image reconstruction technique for electrical impedance tomography

Reconstruction of images in electrical impedance tomography requires the solution of a nonlinear inverse problem on noisy data. This problem is typically ill-conditioned and requires either simplifying assumptions or regularization based on a priori knowledge. The authors present a reconstruction algorithm using neural network techniques which calculates a linear approximation of the inverse problem directly from finite element simulations of the forward problem. This inverse is adapted to the geometry of the medium and the signal-to-noise ratio (SNR) used during network training. Results show good conductivity reconstruction where measurement SNR is similar to the training conditions. The advantages of this method are its conceptual simplicity and ease of implementation, and the ability to control the compromise between the noise performance and resolution of the image reconstruction.     

Image reconstruction by conditional entropy maximisation for PET system

The authors show that the conditional entropy maximisation algorithm is a generalised version of the maximum likelihood algorithm for positron emission tomography (PET). Promising properties of the conditional entropy maximisation algorithm are as follows: an assumption is made that the entropy of the information content of the data should be maximised; it is a consistent way of selecting an image from the very many images that fit the measurement data; this approach takes care of the positivity of the reconstructed image pixels, since entropy does not exist for negative image pixel values; and inclusion of prior distribution knowledge in the reconstruction process is possible. Simulated experiments performed on a PET system have shown that the quality of the reconstructed image using the entropy maximisation method is good. A Gibbs distribution is used to incorporate prior knowledge into the reconstruction process. The mean squared error (MSE) of the reconstructed images shows a sharp new dip, confirming improved image reconstruction. The entropy maximisation method is an alternative approach to maximum likelihood (ML) and maximum a posteriori (MAP) methodologies.     

基于块稀疏的电阻抗成像算法

该文提出一种基于自适应块稀疏字典学习的电阻抗图像重建算法,构建了分块稀疏字典,较好地保留了重建图像的细节信息;同时,将字典学习与图像重建交替进行,并将迭代重建的中间结果作为稀疏字典的训练样本,有效提高了字典学习效果。数值仿真与实验重建结果表明,新方法对电阻抗成像系统测量噪声具有较好的鲁棒性,能准确重构电导率分布图像,特别是对突变细节的准确恢复。     

Impedance imaging of lung ventilation: do we need to account forchest expansion?

Electrical Impedance Tomography (EIT) uses surface electrical measurements to image changes in the conductivity distribution within a medium. When used to measure lung ventilation, however, measurements depend both on conductivity changes in the thorax and on rib cage movement. Given that currently available reconstruction techniques assume that only conductivity changes are present, certain errors are introduced. A finite element model (FEM) is used to calculate the effect of chest expansion on the reconstructed conductivity images. Results indicate that thorax expansion accounts for up to 20% of the reconstructed image amplitude and introduces an artifact in the center of the image tending to “move” the reconstructed lungs closer together. Although this contribution varies depending on anatomical factors, it is relatively independent of inspiration depth. For certain applications in which one is only interested in changes in the level of physiological activity, the effect of the expansion can be neglected because it varies linearly with impedance changes. It is concluded that chest expansion can contribute significantly to the conductivity images of lung ventilation and should be taken into account in the interpretation of these images     

一种多目标优化重建方法在气体浓度层析成像中的应用

为了克服传统的少射线图像重建方法-ART对噪声敏感而导致的重建图像质量差的问题,在考虑气体扩散时其浓度二维分布特点的基础上,提出了一种利用多目标优化的方法来重建气体二维浓度分布图的方法.实验表明,该算法对改善气体浓度层析成像中的噪声对重建结果的影响具有较好的效果.     

Noninvasive imaging of bioimpedance distribution by means of current reconstruction magnetic resonance electrical impedance tomography

We have developed a novel magnetic resonance electrical impedance tomography (MREIT) algorithm-current reconstruction MREIT algorithm-for noninvasive imaging of electrical impedance distribution of a biological system using only one component of magnetic flux density. The newly proposed algorithm uses the inverse of Biot-Savart Law to reconstruct the current density distribution, and then, uses a modified J-substitution algorithm to reconstruct the conductivity image. A series of computer simulations has been conducted to evaluate the performance of the proposed current reconstruction MREIT algorithm with simulation settings for breast cancer imaging applications, with consideration of measurement noise, current injection strength, size of simulated tumors, spatial resolution, and position dependency. The present simulation results are highly promising, demonstrating the high spatial resolution, high accuracy in conductivity reconstruction, and robustness against noise of the proposed algorithm for imaging electrical impedance of a biological system. The present MREIT method may have potential applications to breast cancer imaging and imaging of other organs.     

Optimal experiments in electrical impedance tomography

Electrical impedance tomography (EIT) is a noninvasive imaging technique which aims to image the impedance within a body from electrical measurements made on the surface. The reconstruction of impedance images is a ill-posed problem which is both extremely sensitive to noise and highly computationally intensive. The authors define an experimental measurement in EIT and calculate optimal experiments which maximize the distinguishability between the region to be imaged and a best-estimate conductivity distribution. These optimal experiments can be derived from measurements made on the boundary. The analysis clarifies the properties of different voltage measurement schemes. A reconstruction algorithm based on the use of optimal experiments is derived. It is shown to be many times faster than standard Newton-based reconstruction algorithms, and results from synthetic data indicate that the images that it produces are comparable.     

Fast nonlinear image reconstruction for scanning impedance imaging

Scanning (electrical) impedance imaging (SII) is a novel high-resolution imaging modality that has the potential of imaging the electrical properties of thin biological tissues. In this paper, we apply the reciprocity principle to the modeling of the SII system and develop a fast nonlinear inverse method for image reconstruction. The method is fast because it uses convolution to eliminate the requirement of a numerical solver for the 3-D electrostatic field in the SII system. Numerical results show that our approach can accurately reveal the exact conductivity distribution from the measured current map for different 2-D simulation phantoms. Experiments were also performed using our SII system for a piece of butterfly wing and breast cancer cells. Two-dimensional current images were measured and corresponding quantitative conductivity images were restored using our approach. The reconstructed images are quantitative and reveal details not present in the measured images.     

基于连续插值逼近的电阻抗成象的图象ANIL建算法

本文提出了电阻抗成象的图象重建算法中一种新的电导率分布函数逼近方法连续插值函数逼近法.它充分利用有限元方法计算上的特点,在计算量不增加甚至有所减少的情况下,获得了比传统的分片常数逼近法更好的图象重建效果.     

Conductivity image reconstruction from defective data in MREIT: numerical simulation and animal experiment

Magnetic resonance electrical impedance tomography (MREIT) is designed to produce high resolution conductivity images of an electrically conducting subject by injecting current and measuring the longitudinal component, Bz, of the induced magnetic flux density B = (Bx, By, Bz). In MREIT, accurate measurements of Bz are essential in producing correct conductivity images. However, the measured Bz data may contain fundamental defects in local regions where MR magnitude image data are small. These defective Bz data result in completely wrong conductivity values there and also affect the overall accuracy of reconstructed conductivity images. Hence, these defects should be appropriately recovered in order to carry out any MREIT image reconstruction algorithm. This paper proposes a new method of recovering Bz data in defective regions based on its physical properties and neighboring information of Bz. The technique will be indispensable for conductivity imaging in MREIT from animal or human subjects including defective regions such as lungs, bones, and any gas-filled internal organs.     

Tomographic fluorescence imaging in tissue phantoms: a novel reconstruction algorithm and imaging geometry

A novel image reconstruction algorithm has been developed and demonstrated for fluorescence-enhanced frequency-domain photon migration (FDPM) tomography from measurements of area illumination with modulated excitation light and area collection of emitted fluorescence light using a gain modulated image-intensified charge-coupled device (ICCD) camera. The image reconstruction problem was formulated as a nonlinear least-squares-type simple bounds constrained optimization problem based upon the penalty/modified barrier function (PMBF) method and the coupled diffusion equations. The simple bounds constraints are included in the objective function of the PMBF method and the gradient-based truncated Newton method with trust region is used to minimize the function for the large-scale problem (39919 unknowns, 2973 measurements). Three-dimensional (3-D) images of fluorescence absorption coefficients were reconstructed using the algorithm from experimental reflectance measurements under conditions of perfect and imperfect distribution of fluorophore within a single target. To our knowledge, this is the first time that targets have been reconstructed in three-dimensions from reflectance measurements with a clinically relevant phantom.     

基于邻域信息和快速FCM的肺部电阻抗成像伪迹优化算法

针对电阻抗成像技术可视化过程中因“欠定”问题和“软场”效应所导致的重建图像伪迹问题,该文提出一种基于邻域信息和快速模糊C均值聚类(快速FCM)的无监督图像质量评价指标。基于该评价指标和Tikhonov正则化算法,提出了一种重建图像伪迹优化算法TR-NC。仿真结果表明,该算法能够有效地修正重建图像中的伪迹,修正后的重建图像的相关系数平均提高了18.45%,相对误差平均降低了22.2%;仿真体验实验结果表明,当目标电导率变化率大于30%时,该算法能够准确地检测到目标。由此可见,相比于传统的Tikhonov正则化算法,提出的修正算法在重建图像目标的数量和位置精确度方面都得到了显著提高,为电学层析技术在医学和工业等领域的应用实践提供了新的成像理论依据和技术参考。     

A New Method for Electric Impedance Imaging Using an Eddy Current With a Tetrapolar Circuit

A new contactless technique for electrical impedance imaging, using an eddy current managed along with the tetrapolar circuit method, is proposed. The eddy current produced by a magnetic field is superimposed on a constant current that is normally used in the tetrapolar circuit method, and thus is used to control the current distribution in the body. By changing the current distribution, a set of voltage differences is measured with a pair of electrodes. This set of voltage differences is used in the image reconstruction of the resistivity distribution. The least square error minimization method is used in the reconstruction algorithm. The principle of this method is explained theoretically. A backprojection algorithm was used to get 2-D images. Based on this principle, a measurement system was developed and model experiments were conducted with a saline-filled phantom. The estimated shape of each model in the reconstructed image was similar to that of the corresponding model. From the results of these experiments, it is confirmed that the proposed method is applicable to the realization of electrical conductivity imaging.     

Electrical conductivity imaging using gradient B, decomposition algorithm in magnetic resonance electrical impedance tomography (MREIT)

In magnetic resonance electrical impedance tomography (MREIT), we try to visualize cross-sectional conductivity (or resistivity) images of a subject. We inject electrical currents into the subject through surface electrodes and measure the z component Bz of the induced internal magnetic flux density using an MRI scanner. Here, z is the direction of the main magnetic field of the MRI scanner. We formulate the conductivity image reconstruction problem in MREIT from a careful analysis of the relationship between the injection current and the induced magnetic flux density Bz. Based on the novel mathematical formulation, we propose the gradient Bz decomposition algorithm to reconstruct conductivity images. This new algorithm needs to differentiate Bz only once in contrast to the previously developed harmonic Bz algorithm where the numerical computation of (inverted delta)2Bz is required. The new algorithm, therefore, has the important advantage of much improved noise tolerance. Numerical simulations with added random noise of realistic amounts show the feasibility of the algorithm in practical applications and also its robustness against measurement noise.     

Electrical impedance tomography of complex conductivitydistributions with noncircular boundary

Electrical impedance tomography (EIT) uses low-frequency current and voltage measurements made on the boundary of a body to compute the conductivity distribution within the body. Since the permittivity distribution inside the body also contributes significantly to the measured voltages, the present reconstruction algorithm images complex conductivity distributions. A finite element model (FEM) is used to solve the forward problem, using a 6017-node mesh for a piecewise-linear potential distribution. The finite element solution using this mesh is compared with the analytical solution for a homogeneous field and a maximum error of 0.05% is observed in the voltage distribution. The boundary element method (BEM) is also used to generate the voltage data for inhomogeneous conductivity distributions inside regions with noncircular boundaries. An iterative reconstruction algorithm is described for approximating both the conductivity and permittivity distributions from this data. The results for an off-centered inhomogeneity showed a 35% improvement in contrast from that seen with only one iteration, for both the conductivity and the permittivity values. It is also shown that a significant improvement in images results from accurately modeling a noncircular boundary. Both static and difference images are distorted by assuming a circular boundary and the amount of distortion increases significantly as the boundary shape becomes more elliptical. For a homogeneous field in an elliptical body with axis ratio of 0.73, an image reconstructed assuming the boundary to be circular has an artifact at the center of the image with an error of 20%. This error increased to 37% when the axis ratio was 0.64. A reconstruction algorithm which used a mesh with the same axis ratio as the elliptical boundary reduced the error in the conductivity values to within 0.5% of the actual values     

基于专家场先验模型的图像超分辨重建算法

为了进一步提高图像超分辨率重建的质量,针对非局部集中稀疏表示算法中重建图像的噪声问题,提出了一种基于专家场先验模型的图像超分辨率重建改进算法。首先,利用专家场模型从图像训练集中学习整幅图像的先验知识建立全局先验模型;然后将学习到的先验信息用于非局部集中稀疏表示模型求解最优稀疏表示系数;最后,得到高分辨率图像估计。该算法在超分辨率重建迭代运算的同时,同步更新专家场模型参数,因此在不显著增加运算复杂度的情况下,通过选取合适的先验约束,有效地增强了图像重建的效果。实验结果表明:相比非局部集中稀疏表示算法,文中算法对无噪和有噪降质图像均能取得较好的峰值信噪比结果,并且能够进一步提高有噪图像的去噪效果。     

A multiscale, statistically based inversion scheme for linearizedinverse scattering problems

The application of multiscale and stochastic techniques to the solution of a linearized inverse scattering problem is presented. This approach allows for the explicit and easy handling of many difficulties associated with problems of this type. Regularization is accomplished via the use of a multiscale prior stochastic model which offers considerable flexibility for the incorporation of prior knowledge and constraints. the authors use the relative error covariance matrix (RECM), introduced by E.L. Miller et al. (1995), as a tool for quantitatively evaluating the manner in which data contribute to the structure of a reconstruction. Given a set of scattering experiments, the RECM is used for understanding and analyzing the process of data fusion and allows the authors to define the space-varying optimal scale for reconstruction as a function of the nature (resolution, quality, and distribution of observation points) of the available measurement sets. Examples of the authors' multiscale inversion algorithm are presented using the Born approximation of an inverse electrical conductivity problem formulated so as to illustrate many of the features associated with inverse scattering problems arising in fields such as geophysical prospecting and medical imaging     

Weighted least-squares criteria for electrical impedance tomography

Methods are developed for the design of electrical impedance tomographic reconstruction algorithms with specified properties. Assuming a starting model with constant conductivity or some other specified background distribution, an algorithm with the following properties is found. (1) The optimum constant for the starting model is determined automatically. (2) The weighted least-squares error between the predicted and measured power dissipation data is as small as possible. (3) The variance of the reconstructed conductivity from the starting model is minimized. (4) Potential distributions with the largest volume integral of gradient squared have the least influence on the reconstructed conductivity, and therefore distributions most likely to be corrupted by contact impedance effects are deemphasized. (5) Cells that dissipate the most power during the current injection tests tend to deviate least from the background value. For a starting model with nonconstant conductivity, the reconstruction algorithm has analogous properties.     

Spherical harmonics microwave algorithm for shape and location reconstruction of breast cancer tumor

A reconstruction algorithm to simultaneously estimate the shape and location of three-dimensional breast cancer tumor is presented and its utility is analyzed. The approach is based on a spherical harmonic decomposition to capture the shape of the tumor. We combine a gradient descent optimization method with a direct electromagnetic solver to determine the coefficients in the harmonic expansion as well as the coordinates of the center of the tumor. The results demonstrate the potential advantage of collecting data using a multiple-view/tomographic-type strategy. We show how the order of the harmonic expansion must be increased to capture increasingly "irregularly" shaped tumors and explore the resulting increase in the central processing unit (CPU) time required by the algorithm. Our approach shows accurate reconstruction of the tumor image regardless of the source polarization. This work demonstrates the promise of the algorithm when used on data corrupted with Gaussian noise and when perfect knowledge of the tumor electrical properties is not available.