a new boundary element method for bending of plates on elastic foundations abstract the bending of plates on a winkler foundation according to kirchhoff s theory is solved by using an original boundary integral equation method involving the fundamental solution for plate flexure problems an integral representation for the second member pressure of the foundation of the equation is given by discretizing the integral equation it is possible to eliminate the boundary unknowns so that one is reduced to solving a linear system the solutions of which are deflections inside the domain to illustrate the potentialities of this method several problems with various boundary conditions loads and values of the modulus of the foundation are successfully solved

complete electrode model of electrical impedance tomography approximation properties and characterization of inclusions in electrical impedance tomography one tries to recover the spatial admittance distribution inside a body from boundary measurements in theoretical considerations it is usually assumed that the boundary data consists of the neumann to dirichlet map when conducting real world measurements the obtainable data is a linear finite dimensional operator mapping electrode currents onto electrode potentials in this paper it is shown that when using the complete electrode model to handle electrode measurements the corresponding current to voltage map can be seen as a discrete approximation of the traditional neumann to dirichlet operator this approximating link is utilized further in the special case of constant background conductivity with inhomogeneities it is demonstrated how inclusions with strictly higher or lower conductivities can be characterized by the limit behavior of the range of a boundary operator determined through electrode measurements when the electrodes get infinitely small and cover all

plate buckling loads by the boundary element method a boundary element solution of the plate buckling problem is extended and refined to accommodate any combination of loading and support conditions it is complemented by a similar boundary element formulation yielding the prebuckling membrane state of stress for non uniform distributions of edge loads both continuous and discontinuous models of various orders of approximation for boundary as well as domain unknowns have been employed and their effect on the accuracy of the solution algorithm assessed the computer code incorporates automatic mesh generation schemes for both the boundary and the domain through which a wide range of plate geometries can be discretized and analysed further gains in both efficiency and accuracy are achieved by taking advantage of any support and loading symmetries and reducing the formulation to a standard eigenvalue problem a large number of plate examples are solved to optimize the choice of various modelling parameters and to establish the reliability of the proposed analysis

b spline level set method for shape reconstruction in electrical impedance tomography a b spline level set bls based method is proposed for shape reconstruction in electrical impedance tomography eit we assume that the conductivity distribution to be reconstructed is piecewise constant transforming the image reconstruction problem into a shape reconstruction problem the shape interface of inclusions is implicitly represented by a level set function lsf which is modeled as a continuous parametric function expressed using b spline functions starting from modeling the conductivity distribution with the b spline based lsf we show that the shape modeling allows us to compute the solution by restricting the minimization problem to the space spanned by the b splines as a consequence the solution to the minimization problem is obtained in terms of the b spline coefficients we illustrate the behavior of this method using simulated as well as water tank data in addition robustness studies considering varying initial guesses differing numbers of control points and modeling errors caused by inhomogeneity are performed both simulation and experimental results show that the bls based approach offers clear improvements in preserving the sharp features of the inclusions in comparison to the recently published parametric level set method

utilizing prior information in the estimation of volume fraction distribution for many industrial processes the bulk volume fraction of one phase such as gas or solid can be of considerable importance for this reason it is often controlled within certain limits and therefore is known at least vaguely tomographic imaging of volume fraction can provide very valuable information not only on the bulk volume fraction but also on the spatial distribution of the phase of interest prior information on the bulk volume fraction can assist in tomographic inversion even if this information is not precise in this paper we propose an electrical impedance tomography approach for imaging volume fraction distribution a vague bulk volume fraction prior is utilized in the estimation two dimensional numerical examples are used to demonstrate the proposed method copyright 2005 john wiley sons ltd

existence and uniqueness for electrode models for electric current computed tomography the following experiment is considered to a body of given conductivity a number of electrodes are attached through which current is sent on the same electrodes the resulting voltages are measured this experiment can be described by a number of mathematical models k s cheng et al ieee transactions on biomedical engineering 36 1989 pp 918 924 these models are discussed and their predictions compared with experiment in particular a model is exhibited that is capable of predicting the experimentally measured voltages to within 0 1 percent for this model existence and uniqueness of the associated electrical potential is proved

the factorization method applied to the complete electrode model of impedance tomography the factorization method is a tool for recovering inclusions inside a body when the neumann to dirichlet operator which maps applied currents to measured voltages is known in practice this information is never at hand due to the discreteness and physical properties of the measurement devices the complete electrode model of impedance tomography includes these physical characteristics but leads to a finite dimensional data set called the resistivity matrix the main result of this work is an approximation link relating the resistivity matrix to the neumann to dirichlet operator in the l 2 operator norm this result allows us to extend the factorization method to the framework of real life electrode measurements using a regularized series criterion which is easy to implement in practice the truncation index of the sequence criterion which represents the stopping index of the regularization scheme can be computed solely from the measured perturbed and finite dimensional data the functionality of

effects of measurement precision and finite numbers of electrodes on linear impedance imaging algorithms impedance imaging systems reconstruct approximations to the conductivity inside a body from electrical measurements made on the boundary the linearized problem was studied by calderon who showed that if the conductivity differs little from a constant then it can be reconstructed approximately in his work calderon assumed that arbitrary current densities can be applied anywhere on the body s surface and the resulting voltages perfectly measured in practice however imaging systems apply currents through a finite number of electrodes on the surface and measure the resulting voltages with a limited precision in this paper linear algorithms are described for approximating the electrical conductivity in a disk from finitely many limited precision measurements the effects of finite precision and electrode number on a two dimensional version of calderon s method are studied it is shown that as the measurement errors go to zero and the electrodes proliferate in a space filling manner the finite electro

generalized linearization techniques in electrical impedance tomography electrical impedance tomography aims at reconstructing the interior electrical conductivity from surface measurements of currents and voltages as the current voltage pairs depend nonlinearly on the conductivity impedance tomography leads to a nonlinear inverse problem often the forward problem is linearized with respect to the conductivity and the resulting linear inverse problem is regarded as a subproblem in an iterative algorithm or as a simple reconstruction method as such in this paper we compare this basic linearization approach to linearizations with respect to the resistivity or the logarithm of the conductivity it is numerically demonstrated that the conductivity linearization often results in compromised accuracy in both forward and inverse computations inspired by these observations we present and analyze a new linearization technique which is based on the logarithm of the neumann to dirichlet operator the method is directly applicable to discrete settings including the complete electrode model we also consider frechet derivatives of the logarithmic operators numerical examples indicate that the proposed method is an accurate way of linearizing the problem of electrical impedance tomography

finite element implementation of maxwell s equations for image reconstruction in electrical impedance tomography traditionally image reconstruction in electrical impedance tomography eit has been based on laplace s equation however at high frequencies the coupling between electric and magnetic fields requires solution of the full maxwell equations in this paper a formulation is presented in terms of the maxwell equations expressed in scalar and vector potentials the approach leads to boundary conditions that naturally align with the quantities measured by eit instrumentation a two dimensional implementation for image reconstruction from eit data is realized the effect of frequency on the field distribution is illustrated using the high frequency model and is compared with laplace solutions numerical simulations and experimental results are also presented to illustrate image reconstruction over a range of frequencies using the new implementation the results show that scalar vector potential reconstruction produces images which are essentially indistinguishable from a laplace algorithm for frequencies below 1 mhz but superior at frequencies reaching 10 mhz

flexural vibration and buckling analysis of orthotropic plates by the boundary element method abstract a numerical solution technique by the boundary element method is developed in this paper for the flexural vibration and buckling analysis of elastic orthotropic plates according to kirchhoff s theory the integral formulations of the problem make use of the same fundamental solution as for the bending of orthotropic plates an assumed unknown transverse distributed loading defined inside the plate domain is introduced for representing the inertia forces of vibration and the in plane forces of buckling of the plate the integral equations necessary for solving the problem of interest are derived from the integral representations developed earlier for the bending analysis of orthotropic plates a simple discretization scheme for the plate boundary and its interior domain is adopted in this paper for establishing the integral equations thus obtained in matrix form after elimination of the conventional boundary unknowns the flexural vibration or the buckling problem of an orthotropic plate is finally reduced into an eigenvalue problem of a square matrix the eigenvalues and eigenvectors of that square matrix correspond respectively to the frequencies and the deflection mode shapes of the flexural vibration problem or to the critical loads and the curvature mode shapes of the buckling problem several computational examples of vibration and buckling problems with various boundary conditions are presented and the numerical results demonstrate in comparison with some published results a satisfactory accuracy of the proposed method

application of stochastic galerkin fem to the complete electrode model of electrical impedance tomography abstract the aim of electrical impedance tomography is to determine the internal conductivity distribution of some physical body from boundary measurements of current and voltage the most accurate forward model for impedance tomography is the complete electrode model which consists of the conductivity equation coupled with boundary conditions that take into account the electrode shapes and the contact resistances at the corresponding interfaces if the reconstruction task of impedance tomography is recast as a bayesian inference problem it is essential to be able to solve the complete electrode model forward problem with the conductivity and the contact resistances treated as a random field and random variables respectively in this work we apply a stochastic galerkin finite element method to the ensuing elliptic stochastic boundary value problem and compare the results with monte carlo simulations

optimal shape design by partial spectral data in this paper we are concerned with a shape design problem in which our target is to design up to rigid transformations and scaling the shape of an object given either its polarization tensor at multiple contrasts or the partial eigenvalues of its neumann poincare operator which are known as the fredholm eigenvalues we begin by proposing to recover the eigenvalues of the neumann poincare operator from the polarization tensor by means of the holomorphic functional calculus then we develop a regularized gauss newton optimization method for the shape reconstruction process we present numerical results to demonstrate the effectiveness of the proposed methods and to illustrate important properties of the fredholm eigenvalues and their associated eigenfunctions our results are expected to have important applications in the design of plasmon resonances in nanoparticles as well as in the multifrequency or pulsed imaging of small anomalies

resolution and stability analysis of an inverse problem in electrical impedance tomography dependence on the input current patterns electrical impedance tomography is a procedure by which one finds the conductivity distribution inside a domain from measurements of voltages and currents at the boundary this work addresses the i

variational principles for complex conductivity viscoelasticity and similar problems in media with complex moduli linear processes in media with dissipation arising in conductivity optics viscoelasticity etc are considered time periodic fields in such media are described by linear differential equations for complex valued potentials the properties of the media are characterized by complex valued tensors for example by complex conductivity or complex elasticity tensors variational formulations are suggested for such problems the functionals whose euler equations coincide with the original ones are constructed four equivalent variational principles are obtained two minimax and two minimal ones the functionals of the obtained minimal variational principles are proportional to the energy dissipation averaged over the period of oscillation the last principles can be used in the homogenization theory to obtain the bounds on the effective properties of composite materials with complex valued properties tensors

gauge symmetries of the master action in the batalin vilkovisky formalism we study the geometry of the lagrangian batalin vilkovisky bv theory on an antisymplectic manifold we show that gauge symmetries of the bv theory are essentially the symmetries of an even symplectic structure on the stationary surface of the master action

unilateral buckling of thin elastic plates by the boundary integral equation method the unilateral buckling of thin elastic plates according to kirchhoff s theory is studied by using a boundary integral method a representation for the second member of the equation is given in the matrix formulatiea boundary unknowns are eliminated therefore the unilateral buckling problem reduces to compute the eigenvalues and the eigenvectors of a matrix depending on the contact zone with the rigid foundation an iterative process allows this zone and the buckling load to be computed the capacities of the proposed method are illustrated by four examples

improving the forward solver for the complete electrode model in eit using algebraic multigrid image reconstruction in electrical impedance tomography is an ill posed nonlinear inverse problem linearization techniques are widely used and require the repeated solution of a linear forward problem to account correctly for the presence of electrodes and contact impedances the so called complete electrode model is applied implementing a standard finite element method for this particular forward problem yields a linear system that is symmetric and positive definite and solvable via the conjugate gradient method however preconditioners are essential for efficient convergence preconditioners based on incomplete factorization methods are commonly used but their performance depends on user tuned parameters to avoid this deficiency we apply black box algebraic multigrid using standard commercial and freely available software the suggested solution scheme dramatically reduces the time cost of solving the forward problem numerical results are presented using an anatomically detailed model of the human head

electrical impedance tomography problem with inaccurately known boundary and contact impedances in electrical impedance tomography eit electric currents are injected into a body with unknown electromagnetic properties through a set of contact electrodes at the boundary of the body the resulting voltages are measured on the same electrodes and the objective is to reconstruct the unknown conductivity function inside the body based on these data all the traditional approaches to the reconstruction problem assume that the boundary of the body and the electrode skin contact impedances are known a priori however in clinical experiments one usually lacks the exact knowledge of the boundary and contact impedances and therefore approximate model domain and contact impedances have to be used in the image reconstruction however it has been noticed that even small errors in the shape of the computation domain or contact impedances can cause large systematic artefacts in the reconstructed images leading to loss of diagnostically relevant information in a recent paper kolehmainen 2006 we showed how in the 2 d case the errors induced by the inaccurately known boundary can be eliminated as part of the image reconstruction and introduced a novel method for finding a deformed image of the original isotropic conductivity using the theory of teichmuller mappings in this paper the theory and reconstruction method are extended to include the estimation of unknown contact impedances the method is implemented numerically and tested with experimental eit data the results show that the systematic errors caused by inaccurately known boundary and contact impedances can efficiently be eliminated by the reconstruction method

in vivo impedance imaging with total variation regularization we show that electrical impedance tomography eit image reconstruction algorithms with regularization based on the total variation tv functional are suitable for in vivo imaging of physiological data this reconstruction approach helps to preserve discontinuities in reconstructed profiles such as step changes in electrical properties at interorgan boundaries which are typically smoothed by traditional reconstruction algorithms the use of the tv functional for regularization leads to the minimization of a nondifferentiable objective function in the inverse formulation this cannot be efficiently solved with traditional optimization techniques such as the newton method we explore two implementations methods for regularization with the tv functional the lagged diffusivity method and the primal dual interior point method pd ipm first we clarify the implementation details of these algorithms for eit reconstruction next we analyze the performance of these algorithms on noisy simulated data finally we show reconstructed eit images of in vivo data for ventilation and gastric emptying studies in comparison to traditional quadratic regularization tv regulariza tion shows improved ability to reconstruct sharp contrasts

reconstruction of permittivity profile from boundary capacitance data we present numerical methods of reconstructing permittivity profile of material flow from data collected in electrical capacitance tomography ect based on a formula for the sensitivity maps from a partial differential equation model we propose a unified framework of iterative algorithms using updated sensitivity maps to properly incorporate the non linear nature of the problem and a regularization mechanism to address the ill posedness for two and three phase flows the total variation tv regularization method is shown to be effective in reconstructing the permittivity profiles accurately in a few iterations without any a priori knowledge of the unknown permittivity values

identification of small inhomogeneities of extreme conductivity by boundary measurements a theorem on continuous dependence we consider an electrostatic problem for a conductor consisting of finitely many small inhomogeneities of extreme conductivity embedded in a spatially varying reference medium firstly we establish an asymptotic formula for the voltage potential in terms of the reference voltage potential the location of the inhomogeneities and their geometry secondly we use this representation formula to prove a lipschitz continuous dependence estimate for the corresponding inverse problem this estimate bounds the difference in the location and in certain geometric properties of two sets of inhomogeneities by the difference in the boundary voltage potentials corresponding to a fixed current distribution

a laplace method for under determined bayesian optimal experimental designs abstract in long et al 2013 a new method based on the laplace approximation was developed to accelerate the estimation of the post experimental expected information gains kullback leibler divergence in model parameters and predictive quantities of interest in the bayesian framework a closed form asymptotic approximation of the inner integral and the order of the corresponding dominant error term were obtained in the cases where the parameters are determined by the experiment in this work we extend that method to the general case where the model parameters cannot be determined completely by the data from the proposed experiments we carry out the laplace approximations in the directions orthogonal to the null space of the jacobian matrix of the data model with respect to the parameters so that the information gain can be reduced to an integration against the marginal density of the transformed parameters that are not determined by the experiments furthermore the expected information gain can be approximated by an integration over the prior where the integrand is a function of the posterior covariance matrix projected over the aforementioned orthogonal directions to deal with the issue of dimensionality in a complex problem we use either monte carlo sampling or sparse quadratures for the integration over the prior probability density function depending on the regularity of the integrand function we demonstrate the accuracy efficiency and robustness of the proposed method via several nonlinear under determined test cases they include the designs of the scalar parameter in a one dimensional cubic polynomial function with two unidentifiable parameters forming a linear manifold and the boundary source locations for impedance tomography in a square domain where the unknown parameter is the conductivity which is represented as a random field

brst cohomology in classical mechanics the classical non quantum cohomology of the becchi rouet stora tyutin brst symmetry in phase space is defined and worked out no group action for the gauge transformations is assumed the results cover therefore the general case of an open algebra and are valid off shell each cohomology class contains all brst invariant functions with fixed ghost number an integer which differ from each other by a brst variation if the ghost number is negative there is only the trivial class whose elements are equivalent to zero if the ghost number is positive or zero there is a bijective correspondence between the brst classes and those of the exterior derivative along the gauge orbits these gauge orbits lie in the phase space surface on which the gauge generators are constrained to vanish the brst invariant functions of ghost numberp are then related to closedp forms along the orbits the addition of a brst variation corresponds to the addition of an exact form some comments about the quantum case are included the physical meaning of the classes with ghost number greater than zero is not discussed

a weighted minimum gradient problem with complete electrode model boundary conditions for conductivity imaging we consider the inverse problem of recovering an isotropic electrical conductivity from interior knowledge of the magnitude of one current density field generated by applying current on a set of electrodes the required interior data can be obtained by means of mri measurements on the boundary we only require knowledge of the electrodes their impedances and the corresponding average input currents from the mathematical point of view this practical question leads us to consider a new weighted minimum gradient problem for functions satisfying the boundary conditions coming from the complete electrode model cem of somersalo cheney and isaacson siam j appl math 52 1992 pp 1023 1040 we show that this variational problem has nonunique solutions the surprising discovery is that the physical data is still sufficient to determine the geometry of the connected components of the level sets of the minimizers we thus obtain an interesting phase retrieval result knowledge of the input current at the boundary allows determination of the full current vector field from its magnitude we characterize locally the nonuniqueness in the variational problem in two and three dimensions we also show that additional measurements of the voltage potential along a curve joining the electrodes yield unique determination of the conductivity the proofs involve a maximum principle and a new regularity up to the boundary result for the cem boundary conditions a nonlinear algorithm is proposed and implemented to illustrate the theoretical results

application of a series type method to vibration of orthotropic rectangular plates with mixed boundary conditions the object of this paper is to show an application of a series type method to the free vibration of an orthotropic rectangular plate with mixed boundary conditions the rectangular plate considered is elastically constrained or clamped along a few parts of its edge and simply supported on the remainder a frequency equation is derived to accommodate rectangular orthotropy of the plate by the extension of a previously developed method and subsequent algebraic manipulation leads to the improved equation yielding natural frequencies of the plate with very good accuracy the method is demonstrated for numerical examples where one two or three parts are constrained along the boundary of the square plate and the effects of varying constraint and orthotropic parameters on the natural frequencies and mode shapes are studied

a posteriori error estimate and convergence analysis for conductivity image reconstruction in mreit magnetic resonance electrical impedance tomography mreit takes advantage of internal information to solve its nonlinear inverse problem of recovering a conductivity distribution inside an imaging object when we inject current into the imaging object there occurs a distribution of internal magnetic flux density mathbf b b x b y b z in mreit we utilize a magnetic resonance imaging scanner with its main magnetic field in the z direction to acquire b z data the harmonic b z algorithm was invented in 2001 to reconstruct cross sectional conductivity images from b z data sets subject to multiple injection currents utilizing internal b z data it overcomes the inherent ill posedness in electrical impedance tomography we can set up the inverse problem in mreit as a coefficient identification problem of finding sigma appearing in nabla cdot sigma nabla u 0 from acquired data of the z component of nabla times sigma nabla u the harmonic b z algorithm has shown an excellent perfor

closing and abelizing operatorial gauge algebra generated by first class constraints a canonical transformation of operators of relativistic phase space is constructed which abelizes the basis of the operator valued gauge algebra of first class constraints the new operators of contraints commute among themselves the new hamiltonian commutes with the constraints dynamics of the new operators is physically equivalent to the initial one

statistical estimation of resistance conductance by electrical impedance tomography measurements this paper is built upon the assumption that in electrical impedance tomography vectors of voltages and currents are linearly dependent through a resistance matrix this linear relationship was confirmed experimentally and may be derived analytically under certain assumptions regarding electrodes isaacson 1991 given measurement data consisting of voltages and currents we treat this relationship as a linear statistical model thus our goal is not to reconstruct the image but directly estimate its electromagnetic properties reflected in the resistance and or conductance matrix using electrical impedance tomography eit measurements of voltages and currents on the periphery of the body since no inverse problem is involved the algorithm for estimation merely reduces to one matrix inversion we estimate the impedance resistance matrix using well established statistical inference techniques for linear regression models we provide a comprehensive treatment for a two dimensional homogeneous body of a circular shape by which many concepts of electrical impedance tomography such as width of electrodes the difference between voltage current and current voltage systems are illustrated our theory may be applied to various tests including eit hardware calibration and whether the medium is homogeneous these tests are illustrated on phantom agar data

free vibration solution for clamped orthotropic plates using lagrangian multiplier technique using the lagrangian multiplier technique an analysis was developed to compute the natural frequencies and mode shapes of clamped orthotropic laminated plates transverse shear deformation effects were included using a higher order plate theory predictions made with the developed analysis demonstrated excellent agreement with the available experimental test results and other analytical solutions the validated free vibration analysis has also been used to develop an analysis to predict the dynamic response of clamped orthotropic plates subjected to low velocity impact by a hard object

a new numerical method for the analysis of anisotropic thin plate bending problems abstract a new method is presented for the analysis of anisotropic thin plate bending problems this method appears to enjoy several advantages over other numerical methods for linear problems in concept the present method is quite simple using the influence function for an infinite plate of the same material the solution to the problem of interest is expressed as the superposition of the effect of the actual lateral load plus 2n unknown point loads located outside the region occupied by the plate these 2n loads are then determined through imposition of the boundary conditions at n selected locations an interesting numerical question arises regarding the selection of the 2n external points it is shown that proper distribution of these points leads to excellent results with minimal computer effort several example problems are presented demonstrating the ability of the method to deal with difficult geometries and boundary conditions and with material anisotropy

multifrequency trans admittance scanner mathematical framework and feasibility a trans admittance scanner tas is a device for breast cancer diagnosis based on numerous experimental findings that complex conductivities of breast tumors significantly differ from those of surrounding normal tissues in tas we apply a sinusoidal voltage between a hand held electrode and a scanning probe placed on the breast skin to make current travel through the breast the scanning probe has an array of electrodes at zero voltage we measure exit currents neumann data through the electrodes that provide a map of trans admittance data over the breast surface the inverse problem of tas is to detect a suspicious abnormality underneath the breast skin from the measured neumann data previous anomaly detection methods used the difference between the measured neumann data and a reference neumann data obtained beforehand in the absence of anomaly however in practice the reference data is not available and its computation is not possible since the inhomogeneous complex conductivity of the normal breast is unknown to deal with this problem we propose a frequency difference tas fdtas in which a weighted frequency difference of the trans admittance data measured at a certain moment is used for anomaly detection this paper provides a mathematical framework and the feasibility of fdtas by showing the relationship between the anomaly information and the weighted frequency difference of the neumann data

tikhonov regularization and prior information in electrical impedance tomography the solution of impedance distribution in electrical impedance tomography is a nonlinear inverse problem that requires the use of a regularization method the generalized tikhonov regularization methods have been popular in the solution of many inverse problems the regularization matrices that are usually used with the tikhonov method are more or less ad hoc and the implicit prior assumptions are thus in many cases inappropriate in this paper the authors propose an approach to the construction of the regularization matrix that conforms to the prior assumptions on the impedance distribution the approach is based on the construction of an approximating subspace for the expected impedance distributions it is shown by simulations that the reconstructions obtained with the proposed method are better than with two other schemes of the same type when the prior is compatible with the true object on the other hand when the prior is incompatible with the true object the method will still give reasonable estimates

effect of domain shape modeling and measurement errors on the 2 d d bar method for eit the d bar algorithm based on nachman s 2 d global uniqueness proof for the inverse conductivity problem nachman 1996 is implemented on a chest shaped domain the scattering transform is computed on this chest shaped domain using trigonometric and adjacent current patterns and the complete electrode model for the forward problem is computed with the finite element method in order to obtain simulated voltage measurements the robustness and effectiveness of the method is demonstrated on a simulated chest with errors in input currents output voltages electrode placement and domain modeling

projective electrical impedance reconstruction with two measurements this paper presents a projective reconstruction method of electrical impedance distribution using two boundary measurements of current voltage data the proposed method has a major advantage over existing electrical impedance tomography systems relatively high resolution impedance image in a near surface region underneath the voltage sensing probe that is placed on a skin surface we attach two pairs of electrodes on the border of the probe in such a way that each pair of electrodes generates electrical current flowing underneath the voltage sensing probe and two currents flow across each other a careful analysis of the measured data with respect to local perturbation of admittivity leads to the projective reconstruction method and its rationale numerical simulations show that the proposed method successfully reconstructs high resolution image of local perturbation of admittivity due to object position changes or admittivity value changes or the both in a near surface region underneath the probe

convergence and regularization for monotonicity based shape reconstruction in electrical impedance tomography the inverse problem of electrical impedance tomography is severely ill posed meaning that only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage recently it was shown that a simple monotonicity property of the related neumann to dirichlet map can be used to characterize shapes of inhomogeneities in a known background conductivity in this paper we formulate a monotonicity based shape reconstruction scheme that applies to approximative measurement models and regularizes against noise and modelling error we demonstrate that for admissible choices of regularization parameters the inhomogeneities are detected and under reasonable assumptions asymptotically exactly characterized moreover we rigorously associate this result with the complete electrode model and describe how a computationally cheap monotonicity based reconstruction algorithm can be implemented numerical reconstructions from both simulated and real life measurement data are presented

electrical conductivity reconstruction using nonlocal boundary conditions in this paper we study existence uniqueness and solution estimates to the mixed problem nabla cdot sigma nabla u 0 with dirichlet to neumann map boundary conditions and neumann boundary conditions we then show how this can be used in the reconstruction of sigma given the relationship between u and its normal derivative on the boundary portion where we do not apply the dirichlet to neumann map a numerical reconstruction scheme is also derived