Weighted least-squares criteria for seismic traveltime tomography

Methods are developed for design of linear tomographic reconstruction algorithms with specified properties. Assuming a starting model with constant slowness, 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 traveltime data is as small as possible; (3) the variance of the reconstructed slowness from the starting model is minimized; (4) rays with the greatest length have the least influence on the reconstructed slowness, and (5) cells with most ray coverage tend to deviate least from the background value. The resulting algorithm maps the reconstruction problem into a vector space where the contribution to the inversion from the background slowness remains invariant, while the optimum contribution in orthogonal directions are found. For a starting model with constant slowness, the reconstruction algorithm has analogous properties     

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     

Image reconstruction in magnetic resonance conductivity tensor imaging (MRCTI)

Almost all magnetic resonance electrical impedance tomography (MREIT) reconstruction algorithms proposed to date assume isotropic conductivity in order to simplify the image reconstruction. However, it is well known that most of biological tissues have anisotropic conductivity values. In this study, four novel anisotropic conductivity reconstruction algorithms are proposed to reconstruct high resolution conductivity tensor images. Performances of these four algorithms and a previously proposed algorithm are evaluated in several aspects and compared.     

Electrical impedance endo-tomography: imaging tissue from inside

This paper describes a new method for scanning the conductivity of a tissue or an organ using a multielectrode impedance probe placed at the center of the region of interest. The long-term objective of the study is the evaluation, using an urethral impedance probe, of the lesion produced by ultrasound ablathermy of localized prostate cancer. The probe consists of electrodes placed at the surface of an insulating cylinder. The injected current passes around the cylinder and spreads in the medium surrounding the probe. This paper presents the theoretical bases of this method, the calculated sensitivity distributions of electrode configurations involving a pair of diametrically opposed electrodes and an application in vitro. The experimental set-up consisted of a water tank and a 16-electrode prototype probe 50 mm in diameter. Data sets were collected in the presence of conductivity perturbations produced by small size insulators or conductors and a 7.5% constant perturbation model. The presented images, although reconstructed using a simple retro-projection algorithm, demonstrate the feasibility of the method. Improvements in data collection and image reconstruction are possible.     

Magnetic resonance electrical impedance tomography (MREIT): simulation study of J-substitution algorithm

We developed a new image reconstruction algorithm for magnetic resonance electrical impedance tomography (MREIT). MREIT is a new EIT imaging technique integrated into magnetic resonance imaging (MRI) system. Based on the assumption that internal current density distribution is obtained using magnetic resonance imaging (MRI) technique, the new image reconstruction algorithm called J-substitution algorithm produces cross-sectional static images of resistivity (or conductivity) distributions. Computer simulations show that the spatial resolution of resistivity image is comparable to that of MRI. MREIT provides accurate high-resolution cross-sectional resistivity images making resistivity values of various human tissues available for many biomedical applications.     

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.     

A reconstruction algorithm for breast cancer imaging with electrical impedance tomography in mammography geometry

The conductivity and permittivity of breast tumors are known to differ significantly from those of normal breast tissues, and electrical impedance tomography (EIT) is being studied as a modality for breast cancer imaging to exploit these differences. At present, X-ray mammography is the primary standard imaging modality used for breast cancer screening in clinical practice, so it is desirable to study EIT in the geometry of mammography. This paper presents a forward model of a simplified mammography geometry and a reconstruction algorithm for breast tumor imaging using EIT techniques. The mammography geometry is modeled as a rectangular box with electrode arrays on the top and bottom planes. A forward model for the electrical impedance imaging problem is derived for a homogeneous conductivity distribution and is validated by experiment using a phantom tank. A reconstruction algorithm for breast tumor imaging based on a linearization approach and the proposed forward model is presented. It is found that the proposed reconstruction algorithm performs well in the phantom experiment, and that the locations of a 5-mm-cube metal target and a 6-mm-cube agar target could be recovered at a target depth of 15 mm using a 32 electrode system.     

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.     

A reconstruction algorithm for electrical impedance tomography data collected on rectangular electrode arrays

A three-dimensional reconstruction algorithm in electrical impedance imaging is presented for determining the conductivity distribution beneath the surface of a medium, given surface voltage data measured on a rectangular array of electrodes. Such an electrode configuration may be desirable for using electrical impedence tomography to detect tumors in the human breast. The algorithm is based on linearizing the conductivity about a constant value. Here, we describe a simple implementation of the algorithm on a four-electrode--by-four-electrode array and the reconstructions obtained from numerical and experimental tank data. The results demonstrate significantly better spatial resolution in the plane of the electrodes than with respect to depth.     

Generation of anisotropic-smoothness regularization filters for EIT

In the inverse conductivity problem, as in any ill-posed inverse problem, regularization techniques are necessary in order to stabilize inversion. A common way to implement regularization in electrical impedance tomography is to use Tikhonov regularization. The inverse problem is formulated as a minimization of two terms: the mismatch of the measurements against the model, and the regularization functional. Most commonly, differential operators are used as regularization functionals, leading to smooth solutions. Whenever the imaged region presents discontinuities in the conductivity distribution, such as interorgan boundaries, the smoothness prior is not consistent with the actual situation. In these cases, the reconstruction is enhanced by relaxing the smoothness constraints in the direction normal to the discontinuity. In this paper, we derive a method for generating Gaussian anisotropic regularization filters. The filters are generated on the basis of the prior structural information, allowing a better reconstruction of conductivity profiles matching these priors. When incorporating prior information into a reconstruction algorithm, the risk is of biasing the inverse solutions toward the assumed distributions. Simulations show that, with a careful selection of the regularization parameters, the reconstruction algorithm is still able to detect conductivities patterns that violate the prior information. A generalized singular-value decomposition analysis of the effects of the anisotropic filters on regularization is presented in the last sections of the paper.     

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.     

Electrical impedance tomography

Electrical impedance tomography (EIT) is an imaging modality that estimates the electrical properties at the interior of an object from measurements made on its surface. Typically, currents are injected into the object through electrodes placed on its surface, and the resulting electrode voltages are measured. An appropriate set of current patterns, with each pattern specifying the value of the current for each electrode, is applied to the object, and a reconstruction algorithm uses knowledge of the applied current patterns and the measured electrode voltages to solve the inverse problem, computing the electrical conductivity and permittivity distributions in the object. This article focuses on the type of EIT called adaptive current tomography (ACT) in which currents are applied simultaneously to all the electrodes. A number of current patterns are applied, where each pattern defines the current for each electrode, and the subsequent electrode voltages are measured to generate the data required for image reconstruction. A ring of electrodes may be placed in a single plane around the object, to define a two-dimensional problem, or in several layers of such rings, to define a three-dimensional problem. The reconstruction problem is described and two algorithms are discussed, a one-step, two-dimensional (2-D) Newton-Raphson algorithm and a one-step, full three-dimensional (3-D) reconstructor. Results from experimental data are presented which illustrate the performance of the algorithms     

Comparison between changes of ultracapacitors model parameters during calendar life and power cycling ageing tests

This paper deals with the performances fading of ultracapacitors under calendar life and power cycling tests. The used impedance model is analytical and based on physical quantities as double layer capacitance, specific area and electrolyte conductivity but also on elementary electrodes dispersion. This model is validated in frequency domain using the initial state of the tested ultracapacitor. Then, the two types of tests are presented and specified. A periodic characterization based on impedance spectroscopy is done in order to quantify the impedance changes during ageing tests. The obtained results confirm that impedance real part is increasing and the capacitance is decreasing during the two ageing tests, nevertheless the way they change is different. Indeed the impedance real part increase is independent of the frequency in calendar life test while, in power cycling test, this increase is accentuated at low frequencies. This difference will be explained thanks to impedance model parameters evolution. This study confirms that the two ageing tests affect differently the ultracapacitor performances.     

An iterative Newton-Raphson method to solve the inverse admittivityproblem

By applying electrical currents to the exterior of a body using electrodes and measuring the voltages developed on these electrodes, it is possible to reconstruct the electrical properties inside the body. This technique is known as electrical impedance tomography. The problem is nonlinear and ill conditioned meaning that a large perturbation in the electrical properties far away from the electrodes produces a small voltage change on the boundary of the body. This paper describes an iterative reconstruction algorithm that yields approximate solutions of the inverse admittivity problem in two dimensions. By performing multiple iterations, errors in the conductivity and permittivity reconstructions that result from a linearized solution to the problem are decreased. A finite-element forward-solver, which predicts voltages on the boundary of the body given knowledge of the applied current on the boundary and the electrical properties within the body, is required at each step of the reconstruction algorithm. Reconstructions generated from numerical data are presented that demonstrate the capabilities of this algorithm     

Three-dimensional EIT imaging of breast tissues: system design and clinical testing

Results of development and testing of the new medical imaging system are described. The system uses a planar array consisting of 256 electrodes and enables obtaining images of the three-dimensional conductivity distribution in regions below the skin's surface up to several centimeters deep. The developed measuring system and image reconstruction algorithm can be used for breast tissue imaging and diagnostics, in particular for malignant tumor detection. Examples of tomographic images obtained in vivo during clinical tests are presented. The mammary gland, being an organ-target, alters at the background with such physiological events as menstrual cycle, pregnancy, lactation, and postmenopause. The objectives of this paper include estimation of the possibilities of electrical impedance mammography for investigation of mammary glands' state among women with different hormonal status. We found that electrical impedance mammograms from different groups had clear visual distinctions and statistically significant differences in mammary glands' conductivity. Our data on conductivity distribution in the mammary gland during different physiological periods will allow us to use it as normal values in the future, to continue this research on mammary glands with different pathology.     

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.     

Algorithmic Aspects of Topology Control Problems for Ad Hoc Networks

Topology control problems are concerned with the assignment of power values to the nodes of an ad hoc network so that the power assignment leads to a graph topology satisfying some specified properties. This paper considers such problems under several optimization objectives, including minimizing the maximum power and minimizing the total power. A general approach leading to a polynomial algorithm is presented for minimizing maximum power for a class of graph properties called monotone properties. The difficulty of generalizing the approach to properties that are not monotone is discussed. Problems involving the minimization of total power are known to be NP-complete even for simple graph properties. A general approach that leads to an approximation algorithm for minimizing the total power for some monotone properties is presented. Using this approach, a new approximation algorithm for the problem of minimizing the total power for obtaining a 2-node-connected graph is developed. It is shown that this algorithm provides a constant performance guarantee. Experimental results from an implementation of the approximation algorithm are also presented.     

Nonlinear analysis of microwave superconductor devices usingfull-wave electromagnetic model

This paper presents a full electromagnetic wave analysis for modeling the nonlinearity in high temperature superconductor (HTS) microwave and millimeter-wave devices. The HTS nonlinear model is based on the Ginzburg-Landau theory. The electromagnetic fields associated with the currents on the superconducting structure are obtained using a three-dimensional full wave solution of Maxwell's equations. A three-dimensional finite-difference time-domain algorithm simultaneously solves the resulting equations. The entire solution is performed in time domain, which is a must for this type of nonlinearity analysis. The macroscopic parameters of the HTS, the super fluid penetration depth and the normal fluid conductivity, are calculated as functions of the applied magnetic field. The nonlinear propagation characteristics for HTS transmission line, including the effective dielectric constant and the attenuation constant, are calculated, As the power on the transmission line increases, the phase velocity decreases and the line losses increase. The nonlinearity effects on the current distributions inside the HTS, the electromagnetic field distributions, and the frequency spectrum are also analyzed     

Parametric Simulation and Optimization of Cold-test Properties for a 220 GHz Broadband Folded Waveguide Traveling-wave Tube

Characterized with full-metal structure, high output power and broad bandwidth, microfabricated folded waveguide is considered as a robust slow-wave structure for millimeter wave traveling-wave tubes. In this paper, cold-test (without considering the real electron beam) properties were studied and optimized by 3D simulation on slow-wave structure, for designing a 220 GHz folded waveguide traveling-wave tube. The parametric analysis on cold-test properties, i.e., phase velocity, beam-wave interaction impedance and cold circuit attenuation, were conducted in half-period circuit with high frequency structure simulator, assisted by analytical model and equivalent circuit model. Through detailed parametric analyses, interference between specified structural parameters is found on determining beam-wave interaction impedance. A discretized matrix optimization for interaction impedance was effectively carried out to overcome the interference. A range of structural parameters with optimized interaction impedance distributions were obtained. Based on the optimized results, a broadband folded waveguide with cold pass-band of about 80 GHz, flat phase velocity dispersion and fairly high interaction impedance was designed for a 220 GHz central frequency traveling-wave tube. A three-dB bandwidth of 20.5 GHz and a maximum gain of 21.2 dB were predicted by small signal analysis for a 28 mm-long lossy circuit.