an infinity norm bound for the inverse of dashnic zusmanovich type matrices with applications abstract an upper bound for the infinity norm for the inverse of dashnic zusmanovich type matrices is given it is proved that the upper bound is sharper than the well known varah s bound for strictly diagonally dominant matrices by introducing a new subclass of p matrices dashnic zusmanovich type b matrices dz type b matrices and using the proposed infinity norm bound an error bound is given for the linear complementarity problems of dz type b matrices we also give a new pseudospectra localization to measure the distance to instability

on the convergence of a class of parallel decomposition type relaxation methods a class of parallel decomposition type accelerated overrelaxation methods suitable to the simd systems is established and sufficient and or necessary conditions ensuring its convergence are concluded when the coefficient matrices of the linear systems of equations are respectively l matrices h matrices and symmetric positive definite matrices

efficient reconstruction of dielectric objects based on integral equation approach with gauss newton minimization reconstruction of unknown objects by microwave illumination requires efficient inversion for measured electromagnetic scattering data in the integral equation approach for reconstructing dielectric objects based on the born iterative method or its variations the volume integral equations are involved because the imaging domain is fully inhomogeneous when solving the forward scattering integral equation the nystrom method is used because the traditional method of moments may be inconvenient due to the inhomogeneity of the imaging domain the benefits of the nystrom method include the simple implementation without using any basis and testing functions and low requirement on geometrical discretization when solving the inverse scattering integral equation the gauss newton minimization approach with a line search method lsm and multiplicative regularization method mrm is employed the lsm can optimize the search of step size in each iteration whereas the mrm may reduce the number of numerical experiments for choosing the regularization parameter numerical examples for reconstructing typical dielectric objects under limited observation angles are presented to illustrate the inversion approach

parallel hybrid iteration methods for block bordered linear systems a class of parallel hybrid iteration method and its accelerated overrelaxation variant are established for solving the large sparse block bordered system of linear equations and their convergence are proved when the coefficient matrix of the linear system is an m matrix an h matrix and a symmetric positive definite matrix respectively

electrical impedance tomography of translationally uniform cylindrical objects with general cross sectional boundaries an algorithm is developed for electrical impedance tomography eit of finite cylinders with general cross sectional boundaries and translationally uniform conductivity distributions the electrodes for data collection are assumed to be placed around a cross sectional plane therefore the axial variation of the boundary conditions and the potential field are expanded in fourier series for each fourier component a two dimensional 2 d partial differential equation is derived thus the 3 d forward problem is solved as a succession of 2 d problems and it is shown that the fourier series can be truncated to provide substantial savings in computation time the finite element method is adopted and the accuracy of the boundary potential differences gradients thus calculated is assessed by comparison to results obtained using cylindrical harmonic expansions for circular cylinders a 1016 element and 541 node mesh is found to be optimal the algorithm is applied to data collected from phantoms and the errors incurred from the several assumptions of the method are investigated

singular value analysis of the jacobian matrix in microwave image reconstruction for non linear inverse scattering problems utilizing gauss newton methods the jacobian matrix encodes rich information concerning the system performance and algorithm efficiency in this paper we perform an analytical evaluation of a single iteration jacobian matrix based on a previously derived nodal adjoint representation concepts for studying linear ill posed problems such as the degree of ill posedness are used to assess the impact of important system parameters on the expected image quality analytical singular value decomposition svd of the jacobian matrix for a circular imaging domain is derived along with the numerical svd for optimizing imaging system configurations the results show significant reductions in the degree of ill posedness when signal frequency antenna array density and property parameter sampling are increased specifically the decay rate in the singular spectrum of the jacobian decreases monotonically with signal frequency being approximately 1 3 of its 0 1 ghz value at 3 ghz is improved with antenna array density up to about 35 equally spaced circumferentially positioned elements and drops significantly with increased property parameter sampling to more than twice the amount of measurement data these results should serve as useful guidelines in the development of design specifications for an optimized hardware installation

microwave imaging of nonsparse domains using born iterative method with wavelet transform and block sparse bayesian learning a microwave technique utilizing the combination of wavelet transform block sparse bayesian learning bsbl and born iterative method bim is proposed to image nonsparse domains the wavelet transform is implemented to convert the nonsparse domain into a sparse domain then bsbl framework based on expectation maximization em algorithm is applied on the bim model to reconstruct the original profile of the nonsparse domain the presented imaging results of a nonsparse model indicate that the proposed technique in comparison with traditional microwave imaging or compressive sensing cs algorithms achieve very low normalized error rate ner at a short computational time using only small number of antennas the accuracy robustness and effectiveness of the proposed method are further assessed by employing it to detect a hemorrhagic brain stroke in a realistic numerical head model which is a nonsparse domain the obtained results indicate the capability for the technique to detect an early stroke in the realistic nonsparse environment of the human head using only six antennas

detection of buried inhomogeneous elliptic cylinders by a memetic algorithm the paper studies the application of a global optimization procedure to the detection of buried inhomogeneities the object inhomogeneities are schematized as multilayer infinite dielectric cylinders with elliptic cross sections an efficient recursive analytical procedure is used for the forward scattering computation a functional is constructed in which the field is expressed in a series solution of mathieu functions starting with the input scattered data the iterative minimization of the functional is performed by a new optimization method called memetic algorithm

the existence results for obstacle optimal control problems this paper is concerned with the existence of an optimal control problem for a quasi linear elliptic obstacle variational inequality in which the obstacle is taken as the control firstly we get some existence results under the assumption of the leading operator of the variational inequality with a monotone type mapping in section 2 in section 3 as an application without the assumption of the monotone type mapping for the leading operator of the variational inequality we prove that the leading operator of the variational inequality is a monotone type mapping existence of the optimal obstacle is proved the method used here is different from y y zhou x q yang k l teo the existence results for optimal control problems governed by a variational inequality j math anal appl 321 2006 595 608

infinity norm bounds for the inverse of nekrasov matrices from the application point of view it is important to have a good upper bound for the maximum norm of the inverse of a given matrix a in this paper we will give two simple and practical upper bounds for the maximum norm of the inverse of a nekrasov matrix

a modified gradient method for two dimensional problems in tomography abstract a method for reconstructing the complex index of refraction of a bounded two dimensional inhomogeneous object of known geometric configuration from measured scattered field data is presented this work is an extension of recent results on the direct scattering problem wherein the governing domain integral equation was solved iteratively by a successive over relaxation technique the relaxation parameter was chosen to minimize the residual error at each step convergence of this process was established for indices of refraction much larger than required for convergence of the born approximation for the inverse problem the same technique is applied except in this case both the index of refraction and the field are unknown iterative solutions for both unknowns are postulated with two relaxation parameters at each step they are determined by simultaneously minimizing the residual errors in satisfying the domain integral equation and matching the measured data this procedure retains the nonlinear relation between the two unknowns numerical results are presented for a number of representative two dimensional objects the algorithm is shown to be effective in cases where the iterative solution of the direct problem is rapidly convergent

evaluation of diffusion coefficient based on multiple forward solutions abstract this note is concerned with the identification of the unknown diffusion coefficient for a parabolic equation it introduces an iterative algorithm that can be used to recover the unknown function the algorithm assumes an initial guess for the unknown function and obtains a background field it obtains an equation for the error field it then formulates three forward problems for the error field these three formulations share the same unknown function which is the correction to the assumed value of the unknown diffusion coefficient by equating the responses of these three formulations the algorithm obtains two working equations for the unknown function a number of numerical examples are also used to study the performance of the algorithm

the existence results for optimal control problems governed by a variational inequality in this paper we establish the existence of the optimal control for an optimal control problem where the state of the system is defined by a variational inequality problem with monotone type mappings moreover as an application we get several existence results of an optimal control for the optimal control problem where the system is defined by a quasilinear elliptic variational inequality problem with an obstacle

a comparison of material classification techniques for ultrasound inverse imaging the conjugate gradient method with edge preserving regularization cgep is applied to the ultrasound inverse scattering problem for the early detection of breast tumors to accelerate image reconstruction several different pattern classification schemes are introduced into the cgep algorithm these classification techniques are compared for a full sized two dimensional breast model one of these techniques uses two parameters the sound speed and attenuation simultaneously to perform classification based on a bayesian classifier and is called bivariate material classification bmc the other two techniques presented in earlier work are univariate material classification umc and neural network nn classification bmc is an extension of umc the latter using attenuation alone to perform classification and nn classification uses a neural network both noiseless and noisy cases are considered for the noiseless case numerical simulations show that the cgep bmc method requires 40 fewer iterations than the cgep method and the cgep nn method requires 55 fewer the cgep bmc and cgep nn methods yield more accurate reconstructions than the cgep method a quantitative comparison of the cgep bmc cgep nn and gn umc methods shows that the cgep bmc and cgep nn methods are more robust to noise than the gn umc method while all three are similar in computational complexity

max norm estimation for the inverse of block matrices abstract maximum norm bound of the inverse of a given matrix is an important issue in a wide range of applications motivated by this fact we will extend the list of matrix classes for which upper bounds for max norms can be obtained these classes are subclasses of block h matrices and they stand in a general position with corresponding point wise classes efficiency of new results will be illustrated by numerical examples

frechet derivatives for some bilinear inverse problems in many inverse problems a functional of u is given by measurements where u solves a partial differential equation of the type l p u su q here q is a known source term and l p s are operators with p as an unknown parameter of the inverse problem for the numerical reconstruction of p the heuristically derived frechet derivative r of the mapping r p rightarrow measurementfunctional of u is often used we show for three problems a transport problem in optical tomography an elliptic equation governing near infrared tomography and the wave equation in moving media that r is the derivative in the strict sense our method is applicable to more general problems than are established methods for similar inverse problems

full wave three dimensional microwave imaging with a regularized gauss newton method theory and experiment a reconstruction algorithm is detailed for three dimensional full vectorial microwave imaging based on newton type optimization the goal is to reconstruct the three dimensional complex permittivity of a scatterer in a homogeneous background from a number of time harmonic scattered field measurements the algorithm combines a modified gauss newton optimization method with a computationally efficient forward solver based on the fast fourier transform method and the marching on in source position extrapolation procedure a regularized cost function is proposed by applying a multiplicative additive regularization to the least squares datafit this approach mitigates the effect of measurement noise on the reconstruction and effectively deals with the non linearity of the optimization problem it is furthermore shown that the modified gauss newton method converges much faster than the broyden fletcher goldfarb shanno quasi newton method promising quantitative reconstructions from both simulated and experimental data are presented the latter data are bi static polarimetric free space measurements provided by institut fresnel marseille france

time harmonic impedance tomography using the t matrix method a time harmonic formulation for the electrical impedance tomography eit inverse problem accounting for electrodynamic effects is derived this work abandons the standard electrostatic impedance model for a full wave t matrix model the advantage of this method is an accurate physical model that includes finite frequency effects such as diffusion phenomena and electrode contact impedance effects this model offers the potential for increased resolution and larger invertible contrast objects than other methods when used on experimental data because it may represent a more realistic physical model also an accurate gradient matrix is used in the newton iterative method so the image reconstruction converges in a few iterations these advantages are realized with no increase in the computational complexity of this algorithm compared to the static finite element model a calibration technique is suggested for measurement systems to test the validity of a theoretical model that includes electrode contact impedance effects

regularized reconstruction in electrical impedance tomography using a variance uniformization constraint this paper describes a new approach to reconstruction of the conductivity field in electrical impedance tomography our goal is to improve the tradeoff between the quality of the images and the numerical complexity of the reconstruction method in order to reduce the computational load we adopt a linearized approximation to the forward problem that describes the relationship between the unknown conductivity and the measurements in this framework we focus on finding a proper way to cope with the ill posed nature of the problem mainly caused by strong attenuation phenomena this is done by devising regularization techniques well suited to this particular problem first we propose a solution which is based on tikhonov regularization of the problem second we introduce an original regularized reconstruction method in which the regularization matrix is determined by space uniformization of the variance of the reconstructed conductivities both methods are nonsupervised i e all tuning parameters are automatically determined from the measured data tests performed on simulated and real data indicate that tikhonov regularization provides results similar to those obtained with iterative methods but with a much smaller amount of computations regularization using a variance uniformization constraint yields further improvements particularly in the central region of the unknown object where attenuation is most severe we anticipate that the variance uniformization approach could be adapted to iterative methods that preserve the nonlinearity of the forward problem more generally it appears as a useful tool for solving other severely ill posed reconstruction problems such as eddy current tomography

a class of parallel hybrid two stage iteration methods for block bordered linear systems a class of parallel hybrid two stage iteration method and its accelerated overrelaxation variant are established for solving the large sparse block bordered system of linear equations and their convergence are proved when the coefficient matrix of this linear system is an m matrix and an h matrix respectively

optimal control in some variational inequalities we study a nonconvex nondifferentiable problem of optimal control where the state of the system is defined by an elliptic variational inequality with obstacle and where the cost function is quadr

image reconstruction of perfectly conducting objects by a cascaded method in this paper we propose a method which combines a particle swarm optimization pso algorithm with a newton kantorovitch algorithm for image reconstruction of perfectly conducting objects first the inverse problem is recast as a global nonlinear optimization problem which is solved by a pso then the solution obtained by the pso is taken as an initial guess for the newton kantorovitch algorithm to obtain the more accuracy solution in a few iterations the inversion algorithm which is based on the rigorous mathematics makes use of the received scattered field and appropriate boundary condition to derive a set of nonlinear integral equations the moment method is used to transform the nonlinear integral equations into matrix form then the pseudoinverse transformation is employed to overcome the ill posedness to obtain a convergent and stable solution the particle swarm optimization algorithm is employed to find out the global extreme solution of the object function numerical results show that the performance of this cascaded method is better than the individual pso and the individual newton kantorovitch algorithm satisfactory reconstruction has been obtained by using this cascaded method

fast l p solution of large sparse linear systems application to seismic travel time tomography least squares inversion tends to be sensitive to small changes in the assumptions in the statistical lexicon it is not robust least squares solutions of noisy ill conditioned systems often exhibit unphysical high frequency oscillations which have to be damped or smoothed in some fashion the iteratively reweighted least squares irls algorithm provides a means of computing approximate lp solutions 1 p we will show that irls can be combined with the preconditioned conjugate gradient algorithm in order to solve large sparse rectangular systems of linear algebraic equations very efficiently further for p 1 the resulting algorithm is extremely stable it seems to give reasonably smooth solutions without minute adjustment of the parameters and does not become unstable if an overly optimistic error estimate is used it also has the ability to reject or at least significantly diminish the influence of outliers in the data and does not require the use of damping in addition we will show how to efficiently include diagonal weighting of the observations and parameters in order to incorporate a priori information into the inversion this combined inversion algorithm has wide applicability in real world inverse theory parameter estimation filtering etc where data are noisy and not uniformly reliable numerical examples of the l1 inversion of noisy seismic travel time data will be shown

state constrained control problems governed by variational inequalities we will consider various types of problems of minimizing some given cost functional over all pairs of states and controls subject to some parabolic or elliptic variational inequality and some state constraints our aim is to derive the first order optimality conditions for optimal pairs of these problems

on the regularity of an obstacle control problem an optimal control problem of the obstacle for an elliptic variational inequality is considered in which the obstacle is regarded as the control to get the regularity of the optimal pair a new related control problem is introduced by proving the existence of an optimal pair to such a new control problem the regularity of the optimal pair to the original problem is obtained it turns out that the regularity obtained is sharp in general some other interesting properties of the optimal pair are also established

existence of solutions for a class of elliptic variational inequalities in this paper the existence of solutions to the variational inequalities involving the p laplacian type operator div j u on an unbounded domain in rn is discussed

electrical impedance tomography using induced currents the mathematical basis of a new imaging modality induced current electrical impedance tomography eit is investigated the ultimate aim of this technique is the reconstruction of conductivity distribution of the human body from voltage measurements made between electrodes placed on the surface when currents are induced inside the body by applied time varying magnetic fields in this study the two dimensional problem is analyzed a specific 9 coil system for generating nine different exciting magnetic fields 50 khz and 16 measurement electrodes around the object are assumed the partial differential equation for the scaler potential function in the conductive medium is derived and finite element method fem is used for its solution sensitivity matrix which relates the perturbation in measurements to the conductivity perturbations is calculated singular value decomposition of the sensitivity matrix shows that there are 135 independent measurements it is found that measurements are less sensitive to changes in conductivity of the object s interior while in this respect induced current eit is slightly inferior to the technique of injected current eit using sheffield protocol its sensitivity matrix is better conditioned the images obtained are found to be comparable to injected current eit images in resolution design of a coil system for which parameters such as sensitivity to inner regions and condition number of the sensitivity matrix are optimum remains to be made

existence of solutions for quasilinear elliptic obstacle problems two existence results for a class of obstacle problems are obtained by using a result developed in this paper

euclidean norm estimates of the inverse of some special block matrices in this paper we start from the known lower bounds for minimal singular value of the matrices possessing certain kind of the diagonal dominance property and derive euclidean norm estimates of the inverses of several new subclasses of the block h matrices the motivation comes from applications where the matrix in question has distinguished block structure which can be exploited to obtain useful information an example arising from ecological modeling illustrates the benefits of the presented approach

an approach to estimating building layouts using radar and jump diffusion algorithm estimating building layouts using exterior radar measurements is a challenging task involving electromagnetic modeling many unknown parameters and a limited number of sensors we propose using the jump diffusion algorithm as a powerful stochastic tool that can be used to estimate the number of walls their unknown positions and other parameters we develop an efficient iterative procedure that first uses low frequency transmissions to obtain rough estimates of the building layout these estimates are then used to initialize the estimation at higher frequencies thus obtaining more accurate results we show that with proper frequency selection the building layout can be estimated using radar measurements at only a few frequencies numerical examples are used to illustrate the performance of the proposed algorithm in practical situations

microwave imaging via distorted iterated virtual experiments the linearity of the scattering phenomenon with respect to primary sources allows to recombine a posteriori the available experiments and build in a synthetic fashion new virtual experiments starting from this circumstance an iterative procedure is proposed as an effective approach to tackle nonlinear inverse scattering problems in this procedure the virtual experiments the green s function and the corresponding physical inspired field approximations are updated at each iteration the structure and the complexity of the approach are comparable with those of the widely adopted distorted born iterative method but its performances are remarkably better thanks to extended validity of the exploited field approximation the overall approach also takes advantage of a compressive sensing inspired regularization scheme to promote sparsity in the search of piecewise constant dielectric profiles and further improve the accuracy of the imaging results examples with numerical and experimental data are given to assess the method

determining the resistors in a network in this paper it is shown that the resistors in a rectangular network can be determined by measurements at the boundary of the voltages generated by imposed currents an algorithm for using the boundary measurements to compute the resistances is also given

reconstruction of two dimensional permittivity distribution using the distorted born iterative method the distorted born iterative method dbim is used to solve two dimensional inverse scattering problems thereby providing another general method to solve the two dimensional imaging problem when the born and the rytov approximations break down numerical simulations are performed using the dbim and the method proposed previously by the authors int j imaging syst technol vol 1 no 1 p 100 8 1989 called the born iterative method bim for several cases in which the conditions for the first order born approximation are not satisfied the results show that each method has its advantages the dbim shows faster convergence rate compared to the bim while the bim is more robust to noise contamination compared to the dbim

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

inverse boundary value problems at the boundary continuous dependence we use the methods of microlocal analysis to give a new proof of a theorem of kohn and vogelius showing that the boundary values of a continuous isotropic conductivity can be recovered from voltage and current measurements at the boundary moreover we prove sharp estimates to establish the continuous dependence of the boundary values of the conductivity on the voltage to current maps

hp finite element discretisation of the electrical impedance tomography problem abstract this paper is concerned with the accurate recovery of the permittivity and conductivity from the solution of the electrical impedance tomography eit inverse problem given the knowledge of either the neumann to dirichlet or the dirichlet to neumann map the linearised eit inverse problem for the fourier regime is discretised by hp finite elements which allows the accurate calculation of the sensitivity matrix entries the variational algorithm of knowles 1998 31 is extended to allow the recovery of both material parameters by solution of the eit problem in the laplace regime the associated forward problem is again discretised by hp finite elements a series of numerical results are included to demonstrate the effectiveness of the proposed techniques

the finite element method contrast source inversion algorithm for 2d transverse electric vectorial problems the contrast source inversion algorithm is formulated using the finite element method for two dimensional transverse electric microwave imaging problems edge based triangular elements with vector basis functions are utilized to solve the te electromagnetic problem a single finite element method fem mesh is used to model both the electric field as well as the contrast source and contrast variables used in the inverse problem the electromagnetic field is modeled by taking the unknown values to be the tangential components of the transverse electric field along the edges of each triangular element the unknown contrast source and contrast variables are located at the centroids of every triangular element of the same fem mesh but only inside the imaging domain the adaptation of the fem contrast source inversion fem csi algorithm to 2d te problems on such an arbitrary mesh requires the implementation of special transformation operators which are presented herein the algorithm s capabilities are demonstrated by inverting the fresnel experimental te datasets as well as synthetically generated data

a recursive green s function method for boundary integral analysis of inhomogeneous domains the recursive green s function method rgfm for computation of fields scattered by two dimensional 2 d inhomogeneous dielectric bodies is presented the algorithm efficiently constructs the green s function for the inhomogeneous region by recursively combining known green s functions from smaller subdomains the fields on the scatterer surface are then computed using a boundary integral formulation proper implementation of the rgfm results in computational and storage complexities which scale as n sup 1 5 and n respectively where n is the total number of discrete cells in a domain comparisons of results obtained using the rgfm with those computed from moment method and exact solutions show the efficiency and accuracy of the technique

wavelet methods for inverting the radon transform with noisy data because the radon transform is a smoothing transform any noise in the radon data becomes magnified when the inverse radon transform is applied among the methods used to deal with this problem is the wavelet vaguelette decomposition wvd coupled with wavelet shrinkage as introduced by donoho 1995 we extend several results of donoho and others here first we introduce a new sufficient condition on wavelets to generate a wvd for a general homogeneous operator whose class includes the radon transform we show that a variant of donoho s method for solving inverse problems can be derived as the exact minimizer of a variational problem that uses a besov norm as the smoothing functional we give a new proof of the rate of convergence of wavelet shrinkage that allows us to estimate rather sharply the best shrinkage parameter needed to recover an image from noise corrupted data we conduct tomographic reconstruction computations that support the hypothesis that near optimal shrinkage parameters can be derived if one can estimate only two besov space parameters about an image f both theoretical and experimental results indicate that our choice of shrinkage parameters yields uniformly better results than kolaczyk s 1996 variant of donoho s method and the classical filtered backprojection method

convergence of a reconstruction method for the inverse conductivity problem the inverse conductivity problem is that of reconstructing a spatially varying isotropic conductivity in the interior of some region by means of steady state measurements taken at the boundary reconstruction schemes including least squares type minimization methods have been widely studied and implemented but convergence analysis has been largely ignored this paper establishes the convergence of a well known least squares minimization scheme the levenberg marquardt method on a regularized formulation of the inverse conductivity problem

scattering calculation and image reconstruction using elevation focused beams pressure scattered by cylindrical and spherical objects with elevation focused illumination and reception has been analytically calculated and corresponding cross sections have been reconstructed with a two dimensional algorithm elevation focusing was used to elucidate constraints on quantitative imaging of three dimensional objects with two dimensional algorithms focused illumination and reception are represented by angular spectra of plane waves that were efficiently computed using a fourier interpolation method to maintain the same angles for all temporal frequencies reconstructions were formed using an eigenfunction method with multiple frequencies phase compensation and iteration the results show that the scattered pressure reduces to a two dimensional expression and two dimensional algorithms are applicable when the region of a three dimensional object within an elevation focused beam is approximately constant in elevation the results also show that energy scattered out of the reception aperture by objects contained within the focused beam can result in the reconstructed values of attenuation slope being greater than true values at the boundary of the object reconstructed sound speed images however appear to be relatively unaffected by the loss in scattered energy the broad conclusion that can be drawn from these results is that two dimensional reconstructions require compensation to account for uncaptured three dimensional scattering

iterative forward and inverse algorithms based on domain integral equations for three dimensional electric and magnetic objects an iterative approach to full vector three dimensional inverse scattering problems where the unknown objects can have conductivity permittivity and permeability different from the known background medium is discussed since this problem involves a large number of unknowns it has to be solved effectively and efficiently so that the results can be obtained in timely manner the forward modeling is based on a domain integral equation approach formulated in terms of the electric and magnetic contrast sources normalized with the characteristic impedance of the background medium our numerical tests indicate that this formulation is prerequisite in order to arrive at a forward solution within an acceptable number of iterations and hence it is also of significant importance in the optimization process of the inverse problem the inverse scattering problem is attacked using the multiplicative regularized contrast source inversion method as known in the literature the complexity of this inverse method is approximately equal to the complexity of two equivalent forward algorithms of the conjugate gradient type furthermore this inverse method has been armed with a weighted l2 norm regularizer which has been included as a multiplicative constraint some representative numerical testings will be presented to illustrate the ability of the our numerical algorithms

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

direct reconstructions of conductivities from boundary measurements the problem of reconstructing an unknown electric conductivity from boundary measurements has applications in medical imaging geophysics and nondestructive testing a nachman ann of math 2 143 1996 pp 71 96 proved global uniqueness for the two dimensional inverse conductivity problem using a constructive method of proof based on this proof siltanen mueller and isaacson inverse problems 16 2000 pp 681 699 presented a new numerical reconstruction method that solves the nonlinear problem directly without iteration the method was verified with nonnoisy rotationally symmetric examples in this paper the method is extended by introducing a new regularization scheme which is analyzed theoretically and tested on symmetric and nonsymmetric numerical examples containing computer simulated noise

comparison of an enhanced distorted born iterative method and the multiplicative regularized contrast source inversion method for 2d transverse magnetic tm microwave inversion multiplicative regularized contrast source inversion mr csi and the distorted born iterative method dbim are compared the comparison is based on a computational resource analysis inversion of synthetic data and inversion of experimentally collected data from both the fresnel and upc barcelona data sets all inversion results are blind but appropriate physical values for the reconstructed contrast are maintained the data sets used to test the algorithms vary widely in terms of the background media antennas and far near field considerations to ensure that the comparison is replicable an automatic regularization parameter selection method is used for the additive regularization within the dbim which utilizes a fast implementation of the l curve method and the laplacian regularizer while not used in the classical dbim we introduce an mr term to the dbim in order to provide comparable results to mr csi the introduction of this mr term requires only slight modifications to the classical dbim algorithm and adds little computational complexity the results show that with the addition of the mr term in the dbim the two algorithms provide very similar inversion results but with the mr csi method providing advantages for both computational resources and ease of implementation

optimal control of the obstacle in a quasilinear elliptic variational inequality abstract in this paper we consider an obstacle control problem where the state satisfies a quasilinear elliptic variational inequality and the control function is the obstacle the state is chosen to be close to the desire profile while the h 2 norms of the obstacle is not too large existence and necessary conditions for the optimal control are established

a prescaled multiplicative regularized gauss newton inversion a prescaled multiplicative regularized gauss newton inversion gni algorithm is proposed which utilizes a priori information about the expected ratio between the average magnitude of the real and imaginary parts of the true contrast as well as the expected ratio between the average magnitude of the gradient of the real and imaginary parts of the true contrast using both synthetically and experimentally collected data sets we show that this prescaled inversion algorithm is successful in reconstructing both real and imaginary parts of the contrast when there is a large imbalance between the average magnitude of these two parts where the standard multiplicative regularized gauss newton inversion algorithm fails we further show that the proposed prescaled inversion algorithm is robust and does not require the a priori information to be exact

fast solutions of the 2d inverse scattering problem based on a tsvd approximation of the internal field for the forward model an alternative formulation of the microwave tomography problem is proposed in order to reduce the computation time of the inversion procedure the well known multiplicative regularized contrast source inversion method is used as reference algorithm our formulation is based on a truncated singular value decomposition of the matrix involved in the most computationally intensive operations of the inversion algorithm after theoretical and practical investigation of the behavior of the singular values it is shown that the corresponding approximation does not yield any significant degradation of the quality of the solutions even for large complex permittivity contrasts while the computation times are reduced by a factor ranging between 1 1 and 6 with respect to the original method

the determination of a coefficient in an elliptic equation from average flux data abstract we consider the question of recovering the coefficient q from the equation u j q x u j j x subject to homogeneous dirichlet boundary conditions in a bounded domain r 2 the nonhomogeneous source terms j x j 1 form a basis for l 2 it will be proven that a unique determination is possible from data measurements consisting of measurements of the net flux r uj vds 1 leaving a subset of the boundary for each input source j a continuous dependence result and an algorithm that allows efficient numerical reconstruction of q x from finite data is presented

a mesh free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators a multiple scattering approach is presented to compute the solution of the helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere the solution is represented in terms of partial wave expansions and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces this approach yields high order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable numerical results are presented to demonstrate the accuracy and efficiency of the method

a class of parallel decomposition type relaxation methods for large sparse systems of linear equations abstract a class of parallel decomposition type accelerated over relaxation methods including four arbitrary parameters and suitable to the simd systems is established for solving the large sparse systems of linear equations in this paper and sufficient conditions ensuring its convergence are deduced when the coefficient matrices of the linear systems of equations are respectively l matrices h matrices and positive definite matrices in particular we investigate in detail the symmetric versions of these new methods and deduce a series of conveniently applicable conditions for determining the convergence of hese versions when the coefficient matrices of the linear systems of equations are symmetric positive definite matrices

low frequency reflection data augmentation by an inpainting method 1d acoustic media abstractthe augmentation of low frequencies is an important problem for inverting seismic reflection data through an acoustic scattering approach we have characterized how the data down to zero frequency grows in importance with increasing depth and the size of the velocity contrast we have developed a hermite distributed approximation functional hdaf inpainting method that provides a least squares fitting of the acoustic reflection data down to zero frequency the hdaf data fitting is applied to the first born approximation for compact velocity contrasts the top and bottom depth velocities are equal several fitting constraints are derived using a taylor expansion of the reflection data near zero frequency they provide a coupling with the first born approximation of the velocity contrast the method can be extended to the general geophysical case in which the final velocity i e is different from the starting velocity by use of the distorted wave born approximation numerical results for 1d t

a new subclass of h matrices class of h matrices plays an important role in various scientific disciplines in economics for example however this class could be used in order to get various benefits in other linear algebra fields like determinant estimation perron root estimation eigenvalue localization improvement of convergence area of relaxation methods etc for that reason it seems important to find a subclass of h matrices as wide as possible and expressed by explicit conditions involving matrix elements only one step forward in this direction starting from gudkov matrices from one side and s sdd matrices from the other side will be presented in this paper

iterative reconstruction methods using regularization and optimal current patterns in electrical impedance tomography an iterative reconstruction method which minimizes the effects of ill conditioning is discussed based on the modified newton raphson algorithm a regularization method which integrates prior information into the image reconstruction was developed this improves the conditioning of the information matrix in the modified newton raphson algorithm optimal current patterns were used to obtain voltages with maximal signal to noise ratio snr a complete finite element model fem was used for both the internal and the boundary electric fields reconstructed images from phantom data show that the use of regularization optimal current patterns and a complete fem model improves image accuracy the authors also investigated factors affecting the image quality of the iterative algorithm such as the initial guess image iteration and optimal current updating

bounds for the infinity norm of the inverse for certain m and h matrices abstract the paper presents new two sided bounds for the infinity norm of the inverse for the so called pm matrices which form a subclass of the class of nonsingular m matrices and contain the class of strictly diagonally dominant matrices these bounds are shown to be monotone with respect to the underlying partitioning of the index set and the equality cases are analyzed also an upper bound for the infinity norm of the inverse of a ph matrix whose comparison matrix is a pm matrix is derived the known ostrowski ahlberg nilson varah and moraca bounds are shown to be special cases of the upper bound obtained

conjugate gradient method applied to inverse scattering problem a new reconstruction algorithm for diffraction tomography is presented the algorithm is based on the minimization of a functional which is defined as the norm of the discrepancy between the measured scattering amplitude and the calculated one for an estimated object function by using the conjugate gradient method to minimize the functional one can derive an iterative formula for getting the object function numerical results for some two dimensional scatterers show that the algorithm is very effective in reconstructing refractive index distributions to which the first order born approximation can not be applied in addition the number of iterations is reduced by using a priori information about the outer boundary of the objects furthermore the method is not so sensitive to the presence of noise in the scattered field data

max norm bounds for the inverse of s nekrasov matrices max norm bounds of the inverse of an h matrix appear in a wide range of applications motivated by this fact we will start with some preliminary estimations already obtained for s sdd matrices and present new applicable and practical bounds for a wider class of s nekrasov matrices then we will comment how the scaling technique proves that new bounds improve the known ones for nekrasov matrices finally we will illustrate new results by numerical examples

fast inverse scattering solutions using the distorted born iterative method and the multilevel fast multipole algorithm the distorted born iterative method dbim computes iterative solutions to nonlinear inverse scattering problems through successive linear approximations by decomposing the scattered field into a superposition of scattering by an inhomogeneous background and by a material perturbation large or high contrast variations in medium properties can be imaged through iterations that are each subject to the distorted born approximation however the need to repeatedly compute forward solutions still imposes a very heavy computational burden to ameliorate this problem the multilevel fast multipole algorithm mlfma has been applied as a forward solver within the dbim the mlfma computes forward solutions in linear time for volumetric scatterers the typically regular distribution and shape of scattering elements in the inverse scattering problem allow the method to take advantage of data redundancy and reduce the computational demands of the normally expensive mlfma setup additional benefits are gained by employing kaczmarz like iterations where partial measurements are used to accelerate convergence numerical results demonstrate both the efficiency of the forward solver and the successful application of the inverse method to imaging problems with dimensions in the neighborhood of ten wavelengths

an optimal control problem governed by quasi linear variational inequalities an optimal control problem governed by quasi linear variational inequality is considered the cost functional to be minimized contains the solution of a quasi linear variational inequality to get the existence regularity and necessary condition for the optimal pair a new related control problem is introduced by proving the existence of an optimal pair to such a new problem the existence and regularity of the optimal pair to the original problem are obtained it turns out that the regularity obtained is sharp in general some necessary conditions of the optimal pair are also obtained