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

homoclinic orbits in the near integrable double discrete sine gordon equation we establish the existence of homoclinic orbits for the near integrable double discrete sine gordon ddsg equation under periodic boundary conditions the hyperbolic structure and homoclinic orbits are constructed through the backlund transformation and lax pair a geometric perturbation method based on mel nikov analysis is used to establish necessary criteria for the persistent of temporally homoclinic orbits for the class of ddsg equations with dissipative perturbations

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

tomographic reconstruction of three dimensional volumes using the distorted born iterative method although real imaging problems involve objects that have variations in three dimensions a majority of work examining inverse scattering methods for ultrasonic tomography considers 2 d imaging problems therefore the study of 3 d inverse scattering methods is necessary for future applications of ultrasonic tomography in this work 3 d reconstructions using different arrays of rectangular elements focused on elevation were studied when reconstructing spherical imaging targets by producing a series of 2 d image slices using the 2 d distorted born iterative method dbim the effects of focal number f speed of sound contrast deltac and scatterer size were considered for comparison the 3 d wave equation was also inverted using point like transducers to produce fully 3 d dbim image reconstructions in 2 d slicing blurring in the vertical direction was highly correlated with the transmit receive elevation point spread function of the transducers for low deltac the eventual appearance of overshoot artifacts in the vertical direction were observed with increasing deltac these diffraction related artifacts were less severe for smaller focal number values and larger spherical target sizes when using 3 d dbim the overshoot artifacts were not observed and spatial resolution was improved however results indicate that array configuration in 3 d reconstructions is important for good image reconstruction practical arrays were designed and assessed for image reconstruction using 3 d dbim

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

numerical chaos symplectic integrators and exponentially small splitting distances two discrete versions of duffing s equation are derived as reductions of discretizations of the nonlinear schrodinger nls equation inheriting the properties of the nsl discretizations one is shown to be integrable and using a mel nikov type analysis the other discretization is shown to be nonintegrable arguments are given why it is possible for the nonintegrable scheme to restore the homoclinic orbit at an exponentially fast rate which is faster than the order of the approximation as h 0 this suggests why there can be fundamental differences between symplectic and nonsymplectic discretizations of certain continuous hamiltonian systems

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

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

perturbation of a hopf bifurcation by an external time periodic forcing contenrs i introduction ii the mathematical model iii dynamics of the poincark map in the non resonant and weakly resonant cases iv dynamics of the poincark map in the p l resonant case v dynamics of the poincart map in the p 2 resonant case vi dynamics of the poincark map in the p 3 resonant case

continuation method for nonlinear complementarity problems via normal maps abstract in a recent paper by chen and mangasarian c chen o l mangasarian a class of smoothing functions for nonlinear and mixed complementarity problems computational optimization and applications 2 1996 97 138 a class of parametric smoothing functions has been proposed to approximate the plus function present in many optimization and complementarity related problems this paper uses these smoothing functions to approximate the normal map formulation of nonlinear complementarity problems ncp properties of the smoothing function are investigated based on the density functions that defines the smooth approximations a continuation method is then proposed to solve the ncps arising from the approximations sufficient conditions are provided to guarantee the boundedness of the solution trajectory furthermore the structure of the subproblems arising in the proposed continuation method is analyzed for different choices of smoothing functions computational results of the continuation method are reported

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

two dimensional microwave imaging approach based on a genetic algorithm a multi illumination multiview approach to microwave imaging is proposed which is based on a genetic algorithm ga the inverse problem is recast in an optimization problem solved in the framework of the born approximation the formulation of the approach is described and images of reconstructed circular multilayer cylinders are reported

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

non integrability and continuation of fixed points of 2 n dimensional perturbed twist maps abstract in this paper a simple criterion to prove non integrability of symplectic perturbed twist mappings in 2 n dimensions is developed for sufficiently small perturbations in addition an upper bound for the number of isolating integrals the system can possess is provided a criterion for the analytic continuation of isolated periodic orbits in case of a small nonzero perturbation of twist maps is found the evaluation of their linear stability character by obtaining a simplified expression of the eigenvalues of the jacobian matrix concludes the theoretical part the theory is finally applied to a twist map perturbed by the suris potential and also a four dimensional map with physical interest

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

mel nikov s function for two dimensional mappings this paper calculates explicitly the mel nikov function for general perturbations of two dimensional maps possessing a saddle connection this result may be considered as the discrete analogue of ziglin s calculation of the mel nikov function for time periodic perturbations of two dimensional continuous flows key words integrable planar maps perturbations homoclinic orbits mel nikov s function poisson summation formula

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

convergent scattering series solution of the inhomogeneous helmholtz equation via renormalization group and homotopy continuation approaches abstract the inhomogeneous helmholtz equation can be represented by an equivalent integral equation of the lippmann schwinger type since it is very costly to solve the lippmann schwinger equation exactly via matrix inversion researchers often try to use the popular born series which represents a physics based iterative solution however the popular born series is only guaranteed to converge if the contrast volume is sufficiently small we here use renormalization group rg and homotopy continuation hc approaches to derive novel scattering series solutions of the lippmann schwinger equation which are guaranteed to converge for arbitrary large contrast volumes perturbations our rg approach is based on the use of an auxillary set of scale dependent scattering potentials and green s operators which gradually evolve toward the real physical scattering potential and the physical green s operator respectively we show that the auxillary green s operators satisfies the renormalization group law and we derive the corresponding renormalization group flow equation by using familiar scaling arguments the hc approach comes from pure mathematics and is based on the deformation of a relatively simple reference equation initial condition into a more complicated target equation the lippmann schwinger equation for the physical scattering potential via a parameter that varies continuously between 0 and 1 our hc approach is more general than the rg approach since it involves a convergence control operator but the two approaches are nevertheless closely connected we show that the rg flow and hc equations can be implemented very efficiently using the fast fourier transform fft algorithm also we present a very efficient iterative scheme based on a combination of the zeroth order deformation equation with a floating initial we illustrate our results with a numerical example related with seismic wavefield modeling in strongly scattering media

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

on the singularity analysis of intersecting separatrices in near integrable dynamical systems abstract it has been recently proved by s l ziglin that transversal intersections of separatrices invariant manifolds in near integrable hamiltonian systems of two degrees of freedom imply the existence of multi valued solutions with infinitely many riemann sheets ziglin s theorem is illustrated here on a simple example and then extended and applied to non hamiltonian analytic flows x f x eg x t with x x y and g x t g x t 2 which for e 0 possess the painleve property on the other hand the theoretically expected logarithmic singularities for e 0 are obtained explicitly in solutions near the intersecting separatrices thus we conjecture that dynamical systems with the painleve property can have no separatrix intersections and hence no strange attractors etc these singularities are then numerically located and found to form certain very interesting chimney patterns in the complex t plane on which they accumulate densely the upper part of the chimneys away from the re t axis is asymptotically quite insensitive to changes in parameter values or initial conditions the singularity pattern itself however becomes denser and each chimney is seen to gradually collapse towards the re t axis as the amplitude of the driving term increases and the motion becomes more chaotic

existence of nontrivial homoclinic orbits for fourth order difference equations we obtain a sufficient condition for the existence of nontrivial homoclinic orbits for fourth order difference equations by using mountain pass theorem a weak convergence argument and a discrete version of lieb s lemma

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

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

melnikov potential for exact symplectic maps the splitting of separatrices of hyperbolic fixed points for exact symplectic maps of n degrees of freedom is considered the non degenerate critical points of a real valued function called the melnikov potential are associated to transverse homo clinic orbits and an asymptotic expression for the symplectic area between homoclinic orbits is given moreover if the unperturbed invariant manifolds are completely dou bled it is shown that there exist in general at least 4 primary homoclinic orbits 4 n in antisymmetric maps both lower bounds are optimal two examples are presented a 2n dimensional central standard like map and the hamiltonian map associated to a magnetized spherical pendulum several topics are studied about these examples existence of splitting explicit computations of melnikov potentials transverse homoclinic orbits exponentially small splitting etc

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

the mel nikov technique for highly dissipative systems we present explicit calculations that extend the applicability of the mel nikov technique to include a general class of highly dissipative systems in particular the dissipation may be in the form of large positive or negative damping the only required assumption is that each system of this class possesses a homoclinic or a heteroclinic orbit we also show that sufficiently small time sinusoidal perturbation of these systems results in nonempty transversal intersection of stable and unstable manifolds for all but at most discretely many frequencies the results are then demonstrated via computer simulation of the highly damped pendulum with constant plus small time sinusoidal forcing

discrete dichotomies and bifurcations from critical homoclinic orbits abstract perturbed discrete systems likexn 1 f xn g xn xn r n n z when the associated unperturbed map 0 is not invertible and has acriticalorbit n homoclinic to a hyperbolic fixed pointpare studied bycriticalwe mean that thef n are invertible for any integern 0 butf 0 is not invertible the main goal is to give sufficient conditions for a bifurcationfrom zero to many homoclinicswhen the parameter crosses zero we also give a melnikov like result assuring thepersistence of homoclinicsin a complete neighborhood of 0 this result is similar to the ones obtained for diffeomorphisms and flows

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

a mel nikov approach to soliton like solutions of systems of discretized nonlinear schro dinger equations we investigate a class of n coupled discretized nonlinear schrodinger equations of interacting chains in a nonlinear lattice which in the limit of zero coupling become integrable ablowitz ladik differential difference equations we study the existence of stationary localized excitations in the form of soliton like time periodic states by reducing the system to a perturbed 2n dimensional symplectic map whose homoclinic orbits are obtained by a recently developed mel nikov analysis we find that depending on the perturbation homoclinic orbits can be accurately located from the simple zeros of a mel nikov vector and illustrate our results in the cases n 2 and 3

microwave imaging based on a markov random field model a new approach to microwave imaging of 2d inhomogeneous dielectric scatterers is presented the method is developed in the space domain and markov random fields are used to obtain a model of the distributions of dielectric features in the scattering region in this way a priori knowledge can be easily inserted in the imaging scheme this stochastic approach gives rise to a functional equation that can be minimized by using a simulated annealing algorithm an iterative scheme is derived that allows one to bypass the need for storing large matrices in the computer numerical simulation results confirming the capabilities and effectiveness of the proposed method are reported solutions have generally been obtained in few steps and seem better than those obtained by other imaging techniques in the space domain the capability of the algorithm to operate in a strongly noisy environment is also proved

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

splitting of a small separatrix loop near the saddle center bifurcation in area preserving maps abstract when the saddle center bifurcation occurs in an analytic family of area preserving maps a parabolic fixed point first appears at the origin and then this point bifurcates creating an elliptic fixed point and a hyperbolic one separatrices of the hyperbolic fixed point form a small loop around the elliptic point in general the separatrices intersect transversely and the splitting is exponentially small with respect to the perturbation parameter we derive an asymptotic formula which describes the splitting and study the properties of the pre exponential factor

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

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

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

sequential quadratic programming method for solution of electromagnetic inverse problems in this paper a new algorithm namely a reduced hessian sequential quadratic programming sqp method for solving electromagnetic inverse problems is proposed the electromagnetic inverse problem is considered to be a constrained nonlinear programming the reduced hessian sqp method finds the solution of this constrained nonlinear programming by solving a sequential of quadratic programming subproblems the reduced hessian scheme is applied to reduce the requirement of computational memory of the basic sqp method for large inverse problems numerical results are presented to demonstrate the efficiency and accuracy of the proposed method and some comparisons show that the proposed method has a better convergence and a faster speed than the previous methods

shrinkage thresholding enhanced born iterative method for solving 2d inverse electromagnetic scattering problem a numerical framework that incorporates recently developed iterative shrinkage thresholding ist algorithms within the born iterative method bim is proposed for solving the two dimensional inverse electromagnetic scattering problem ist algorithms minimize a cost function weighted between measurement data misfit and a zeroth first norm penalty term and therefore promote sharpness in the solution consequently when applied to domains with sharp variations discontinuities or sparse content the proposed framework is more efficient and accurate than the classical bim that minimizes a cost function with a second norm penalty term indeed numerical results demonstrate the superiority of the ist bim over the classical bim when they are applied to sparse domains permittivity and conductivity profiles recovered using the ist bim are sharper and more accurate and converge faster

quantitative microwave imaging method in lebesgue spaces with nonconstant exponents an innovative nonlinear inverse scattering approach in variable exponent lebesgue spaces is proposed for microwave imaging purposes the main objective of the approach is to overcome one of the main problems associated with reconstruction procedures developed in lebesgue spaces with constant exponent i e the need for the selection of the optimum lebesgue space norm parameter which is critical for obtaining accurate reconstructions and no exact rules exist for this choice the approach proposed in this paper is oriented to tomographic imaging applications at microwave frequencies for which the adopted inversion procedure is based on a gauss newton method which has been reformulated in the unconventional variable exponent lebesgue spaces the capabilities of the approach are demonstrated by a set of numerical simulations in which cylindrical dielectric targets are inspected moreover an experimental result is reported

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

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

the fast multipole method and fourier convolution for the solution of acoustic scattering on regular volumetric grids the fast multipole method fmm is applied to the solution of large scale three dimensional acoustic scattering problems involving inhomogeneous objects defined on a regular grid the grid arrangement is especially well suited to applications in which the scattering geometry is not known a priori and is reconstructed on a regular grid using iterative inverse scattering algorithms or other imaging techniques the regular structure of unknown scattering elements facilitates a dramatic reduction in the amount of storage and computation required for the fmm both of which scale linearly with the number of scattering elements in particular the use of fast fourier transforms to compute green s function convolutions required for neighboring interactions lowers the often significant cost of finest level fmm computations and helps mitigate the dependence of fmm cost on finest level box size numerical results demonstrate the efficiency of the composite method as the number of scattering elements in each finest level box is increased

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

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