microwave image reconstruction utilizing log magnitude and unwrapped phase to improve high contrast object recovery reconstructing images of large high contrast objects with microwave methods has proved difficult successful images have generally been obtained by using a priori information to constrain the image reconstruction to recover the correct electromagnetic property distribution in these situations the measured electric field phases as a function of receiver position around the periphery of the imaging field of view vary rapidly often undergoing changes of greater than spl pi radians especially when the object contrast and illumination frequency increase here the authors introduce a modified form of a maxwell equation model based image reconstruction algorithm which directly incorporates log magnitude and phase of the measured electric field data by doing so measured phase variation can be unwrapped and distributed over more than one rieman sheet in the complex plane simulation studies and microwave imaging experiments demonstrate that significant image quality enhancements occur with this approach for large high contrast objects simple strategies for visualizing and unwrapping phase values as a function of the transmitter and receiver positions within our microwave imaging array are described metrics of the degree of phase variation expressed in terms of the amount and extent of phase wrapping are defined and found to be figures of merit which estimate when it is critical to deploy the new image reconstruction approach in these cases the new algorithm recovers high quality images without resorting to the use of a priori information on object contrast and or size as previously required

microwave tomography using topology optimization techniques microwave tomography is a technique in which microwaves illuminate a specimen and measurements of the scattered electrical field are used to determine and depict the specimen s dielectric and conductive properties this article presents a new method to perform the reconstruction the reconstruction method is illustrated by assuming time harmonic scattering in two space dimensions in a setup tailored for medical applications we prove that the resulting constrained nonlinear least squares problem admits a solution the governing helmholtz equation is discretized by using the finite element method and the dielectric properties are allowed to attain different values at each element within a given region the reconstruction algorithm uses methodologies borrowed from topology optimization of linearly elastic structures numerical examples illustrate the reconstruction method in a parameter range typical for human tissue and for the challenging case where the size of the object is in the same order as the wavelength a reasonable estimate of the dielectric properties is obtained by using one observation per 20 unknowns when the permittivity is allowed to vary continuously within a given interval using a priori information that the permittivity attains only certain values results in a good estimate and a sharp image as opposed to topology optimization for structures there is no indication of mesh dependency and checkerboarding when forcing the permittivity to attain discrete values

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

a new value picking regularization strategy application to the 3 d electromagnetic inverse scattering problem the nonlinear electromagnetic inverse scattering problem of reconstructing a possibly quasi piecewise constant inhomogeneous complex permittivity profile is solved by iterative minimization of a pixel based data fit cost function because of the ill posedness it is necessary to introduce some form of regularization many authors apply a smoothing constraint on the reconstructed permittivity profile but such regularization smooths away sharp edges in this paper a simple yet effective regularization strategy the value picking vp regularization is proposed this new technique is capable of reconstructing piecewise constant permittivity profiles without degrading the edges it is based on the knowledge that only a few different permittivity values occur in such profiles the values of which need not be known in advance vp regularization does not impose this a priori information in a strict sense such that it can be applied also to profiles that are only approximately piecewise constant the vp regularization is introduced in the solution of the inverse problem by adding a choice function to the data fit cost function for every permittivity unknown in the discretized problem when minimized the choice function forces the corresponding permittivity unknown to be close to one member of a set of auxiliary variables the vp values which are continuously updated throughout the iterations to minimize the regularized cost function a half quadratic gauss newton optimization technique is presented finally a stepwise relaxed vp regularization scheme is proposed in which the number of vp values is gradually increased this scheme is tested with synthetic and measured scattering data obtained from inhomogeneous 3d targets and is shown to achieve high reconstruction quality

free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule the generalized differential quadrature rule proposed recently by these authors is applied here to the free vibration analyses of solid circular plates with radially varying thickness and elastic restraints the thickness can vary radially in any given continuous form and it varies exponentially and linearly in this work two regularity conditions corresponding to the plate center are expressed in explicit formulae since they have been inexactly or even wrongly expressed in the literature such errors are pointed out in the application of the differential quadrature techniques and in the expression of the regularity conditions at the plate center numerical results are presented for a number of plates illustrating the versatility and accuracy of the approach

linearized cauchy data inversion method for two dimensional buried target imaging we propose a novel inversion algorithm to image buried objects in inhomogeneous media from the electromagnetic data on the outer boundary our method is based on exploiting the cauchy data to derive a new born like linearization of the inverse problem the main advantage of this formulation is to avoid the use of the background green function and therefore is computationally more efficient it also provides better accuracy than classical born approximation in the case of stratified media our approach can be coupled with any appropriate continuation method we discuss here the coupling with a continuation method based on the use of approximate transmission conditions the feasibility and robustness of our methodology is validated through numerical experiments for single and multiple targets

microwave medical imaging based on sparsity and an iterative method with adaptive thresholding we propose a new image recovery method to improve the resolution in microwave imaging applications scattered field data obtained from a simplified breast model with closely located targets is used to formulate an electromagnetic inverse scattering problem which is then solved using the distorted born iterative method dbim at each iteration of the dbim method an underdetermined set of linear equations is solved using our proposed sparse recovery algorithm imatcs our results demonstrate the ability of the proposed method to recover small targets in cases where traditional dbim approaches fail furthermore in order to regularize the sparse recovery algorithm we propose a novel l 2 based approach and prove its convergence the simulation results indicate that the l 2 regularized method improves the robustness of the algorithm against the ill posed conditions of the em inverse scattering problem finally we demonstrate that the regularized imatcs dbim approach leads to fast accurate and stable reconstructions of highly dense breast compositions

a block qmr method for computing multiple simultaneous solutions to complex symmetric systems the solution of complex symmetric indefinite systems of equations where multiple solutions are required is considered the quasi minimum residual qmr method ideally suited for these matrices is generalized using the block lanczos algorithm to solve multiple solutions simultaneously this modification alone is shown through numerical examples involving large sparse matrices from finite element discretization of maxwell s equations to accelerate the convergence by a factor almost as great as the number of simultaneous solutions a natural convergence criterion for this method is presented that is shown to be as effective as and easier to compute than the usual equation residual finally a numerical comparison of the classical incomplete cholesky and a variant of the ilu t preconditioners is given showing superior performance by the latter

viable three dimensional medical microwave tomography theory and numerical experiments three dimensional microwave tomography represents a potentially very important advance over 2d techniques because it eliminates associated approximations which may lead to more accurate images however with the significant increase in problem size computational efficiency is critical to making 3d microwave imaging viable in practice in this paper we present two 3d image reconstruction methods utilizing 3d scalar and vector field modeling strategies respectively finite element fe and finite difference time domain fdtd algorithms are used to model the electromagnetic field interactions in human tissue in 3d image reconstruction techniques previously developed for the 2d problem such as the dual mesh scheme iterative block solver and adjoint jacobian method are extended directly to 3d reconstructions speed improvements achieved by setting an initial field distribution and utilizing an alternating direction implicit adi fdtd are explored for 3d vector field modeling the proposed algorithms are tested with simulated data and correctly recovered the position size and electrical properties of the target the adjoint formulation and the fdtd method utilizing initial field estimates are found to be significantly more effective in reducing the computation time finally these results also demonstrate that cross plane measurements are critical for reconstructing 3d profiles of the target

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

comparison of te and tm inversions in the framework of the gauss newton method the gauss newton inversion method in conjunction with a regularized formulation of the inverse scattering problem is used to invert transverse electric te and transverse magnetic tm data the utilized data sets consist of experimental data provided by the institut fresnel as well as synthetic data the te inversion outperformed the tm inversion when utilizing near field scattering data collected using only a few transmitters and receivers however very little difference was found between te and tm inversions when using far field scattering data it is conjectured that the reason for the better performance of the near field te result is that the near field te data contains more information than the near field tm data at each receiver point in all cases considered herein the te inversion required equal or fewer iterations than the tm inversion the per iteration computational complexity of both te and tm inversions is discussed in the framework of the gauss newton inversion method actual costs are consistent with the computational complexity analysis that is given

overview and classification of some regularization techniques for the gauss newton inversion method applied to inverse scattering problems different regularization techniques used in conjunction with the gauss newton inversion method for electromagnetic inverse scattering problems are studied and classified into two main categories the first category attempts to regularize the quadratic form of the nonlinear data misfit cost functional at different iterations of the gauss newton inversion method this can be accomplished by utilizing penalty methods or projection methods the second category tries to regularize the nonlinear data misfit cost functional before applying the gauss newton inversion method this type of regularization may be applied via additive multiplicative or additive multiplicative terms we show that these two regularization strategies can be viewed from a single consistent framework

vibration of annular sector plates from three dimensional analysis accurate three dimensional elasticity solutions are presented for the free vibration analysis of annular sector plates with arbitrary but continuous boundary conditions the ritz procedure is used to minimize the integral energy functional which is formulated in a cylindrical polar coordinate system in the derivation of the governing eigenvalue equation the vibratory characteristics of annular sector plates with variations in boundary condition sector angle and thickness are examined the accuracy of the method is validated through appropriate convergence and comparison studies the first known results presented here provide a basis for understanding the physics of vibrations of annular sector plates and can be used to assess numerical results obtained from various refined two dimensional theories

microwave imaging within the first order born approximation by means of the contrast field bayesian compressive sensing a new approach based the contrast field cf formulation of the microwave imaging problem that exploits the bayesian compressive sampling bcs paradigm is proposed for the reconstruction of sparse distributions of weak scatterers towards this end the original inverse scattering problem is recast to a probabilistic sparseness constrained optimization by introducing suitable hierarchical priors as sparsity constraints a fast relevance vector machine rvm is then employed to reconstruct the scatterers as well as to estimate the confidence level of the inversion representative numerical results are presented to illustrate the method as well as to assess its potentialities and limitations in terms of inversion accuracy computational efficiency and robustness comparisons with state of the art deterministic and stochastic reconstruction methodologies still within the born approximation ba are discussed as well

on the use of orthogonal polynomials in the rayleigh ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates series composed of recently proposed orthogonal polynomial functions are used in the rayleigh ritz method to generate results for a number of flexural vibration and buckling problems for rectangular isotropic and orthotropic plates it is demonstrated that the approach yields excellent results not only for natural frequencies and buckling loads but also for the more sensitive mode shape bending moment and shear force distribution problem

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

inverse scattering an iterative numerical method for electromagnetic imaging the authors propose a spatial iterative algorithm for electromagnetic imaging based on a newton kantorovich procedure for the reconstruction of the complex permittivity of inhomogeneous lossy dielectric objects with arbitrary shape starting from integral representation of the electric field and using the moment method this technique has been developed for 2 d for tm and te polarization cases objects as well as for 3 d objects its performance has been compared with spectral techniques of classical diffraction tomography the modified newton method and the pseudo inverse method

hamilton decompositions of regular expanders a proof of kelly s conjecture for large tournaments abstract a long standing conjecture of kelly states that every regular tournament on n vertices can be decomposed into n 1 2 edge disjoint hamilton cycles we prove this conjecture for large n in fact we prove a far more general result based on our recent concept of robust expansion and a new method for decomposing graphs we show that every sufficiently large regular digraph g on n vertices whose degree is linear in n and which is a robust outexpander has a decomposition into edge disjoint hamilton cycles this enables us to obtain numerous further results e g as a special case we confirm a conjecture of erd s on packing hamilton cycles in random tournaments as corollaries to the main result we also obtain several results on packing hamilton cycles in undirected graphs giving e g the best known result on a conjecture of nash williams we also apply our result to solve a problem on the domination ratio of the asymmetric travelling salesman problem which was raised e g by glover and punnen as well as alon gutin and krivelevich

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

microwave image reconstruction from 3 d fields coupled to 2 d parameter estimation an efficient gauss newton iterative imaging technique utilizing a three dimensional 3 d field solution coupled to a two dimensional 2 d parameter estimation scheme 3 d 2 d is presented for microwave tomographic imaging in medical applications while electromagnetic wave propagation is described fully by a 3 d vector field a 3 d scalar model has been applied to improve the efficiency of the iterative reconstruction process with apparently limited reduction in accuracy in addition the image recovery has been restricted to 2 d but is generalizable to three dimensions image artifacts related primarily to 3 d effects are reduced when compared with results from an entirely two dimensional inversion 2 d 2 d important advances in terms of improving algorithmic efficiency include use of a block solver for computing the field solutions and application of the dual mesh scheme and adjoint approach for jacobian construction methods which enhance the image quality such as the log magnitude unwrapped phase minimization were also applied results obtained from synthetic measurement data show that the new 3 d 2 d algorithm consistently outperforms its 2 d 2 d counterpart in terms of reducing the effective imaging slice thickness in both permittivity and conductivity images over a range of inclusion sizes and background medium contrasts

microwave biomedical data inversion using the finite difference contrast source inversion method we present a contrast source inversion csi technique which is based on a finite difference fd solver for use in microwave biomedical imaging the algorithm is capable of inverting complex permittivity biomedical data sets without the explicit use of a forward solver at each iteration the fd solver is based in the frequency domain utilizes perfectly matched layer pml boundary conditions and the stiffness matrix is solved via an lu decomposition and gaussian elimination an important feature of the fd csi algorithm is that the stiffness matrix associated with the fd solver depends only upon the background medium and frequency and thus the lu decomposition is only performed once before the iterative inversion process unlike the usual integral equation ie based inversion techniques the fd csi algorithm is readily capable of utilizing an arbitrary backarbitrary backgroundground medium for the inversion process

free vibration of continuous polar orthotropic annular and circular plates abstract the free vibration of a polar orthotropic annular plate supported on concentric circles is analyzed by the ritz method with use of lagrange multipliers a trial function for the deflection of the plate is expressed in terms of simple power series and a frequency equation for the plate is derived by the condition for minimizing the total potential energy with the constraint equations included in the numerical examples it is also shown that the method can directly yield quite accurate frequency values for a solid circular plate natural frequencies of annular and circular plates are calculated for wide ranges of the support location and orthotropic parameters

exact vibration solutions for circular mindlin plates with multiple concentric ring supports this paper presents an analytical approach to investigate the vibration behaviour of circular mindlin plates with multiple concentric ring supports a circular plate is first divided into multiple annular segments and a circular segment at the locations of the ring supports the governing differential equations and the solutions of these equations for the annular and circular segments based on the mindlin plate theory are presented a homogenous equation system governing the vibration of circular mindlin plates with ring supports is derived by imposing the essential and natural boundary and segment interface conditions the first known exact vibration frequencies for circular mindlin plates with multiple concentric ring supports are obtained and the modal shapes of displacement fields and stress resultants for several selected cases are presented the influence of the ring support locations plate boundary conditions and plate thickness ratios on the vibration behaviour of circular plates is discussed

newton kantorovitch algorithm applied to an electromagnetic inverse problem an efficient algorithm is presented to compute the shape of perfectly conducting cylinders via knowledge of scattering cross sections this choice of scattering data avoids the difficulties linked with the phase measurements or reconstructions the mathematical analysis is performed in terms of operator and functions and the fundamental instability of the problem is demonstrated then the stability is restored by means of a tikhonov miller regularization the efficiency of the method is outlined by numerical examples references are given which show that the same algorithm applies to other electromagnetic inverse problems especially to gratings

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

stochastic optimization methods applied to microwave imaging a review stochastic methods are now very common in electromagnetics among the various applications they have been recently proposed for solving inverse problems arising in radio frequency and microwave imaging some of the recently proposed stochastic inversion procedures are critically discussed e g genetic algorithms differential evolution methods memetic algorithms particle swarm optimizations hybrid techniques etc and the way they have been applied in this area the use of the ant colony optimization method which is a relatively new method in electromagnetics is also proposed various imaging modalities are considered tomography buried object detection and borehole sensing finally the main features making these approaches useful for imaging purposes are discussed and the currently considered strategies to reduce the computational load associated with stochastic optimization procedures delineated

application of the multiplicative regularized gauss newton algorithm for three dimensional microwave imaging we apply the so called multiplicative regularized gauss newton inversion algorithm for solving three dimensional electromagnetic microwave inverse problems this inversion algorithm automatically adjusts the regularization parameter and when combined with the total variation type regularization function it can provide inversion results with excellent edge preserving characteristics in addition in order to deal with an extensive memory requirement for the gauss newton method we employ an implicit jacobian calculation scheme by using this scheme we do not have to explicitly store the jacobian matrix hence we are able to significantly reduce the memory requirement of the gauss newton method albeit at an additional computational overhead furthermore in order to be able to handle a large scale computational problem both the forward and the inversion algorithms are parallelized using the mpi library where we obtain a nearly linear speedup factor we demonstrate efficiency and robustness of this algorithm by inverting synthetic data fresnel experimental data and biomedical experimental data

microwave data inversions using the source receiver compression scheme we apply a source receiver compression approach to reduce the computational time and memory usage of the nonlinear inversion approaches for interpreting three dimensional microwave data by detecting and quantifying the extent of redundancy in the data we assemble a reduced set of simultaneous sources and receivers that are weighted sums of the physical sources and receivers employed in the measurement setup because the number of these simultaneous sources and receivers can be significantly less than those of the physical sources and receivers the computational time and memory usage of any inversion method such as steepest descent nonlinear conjugate gradient contrast source inversion and quasi newton can be tremendously reduced the scheme is based on decomposing the data into their principal components using a singular value decomposition approach and the data compression is done through the elimination of eigenvectors corresponding to small eigenvalues consequently this will also suppress the effect of noise in the data as a concept demonstration we show that this approach has the potential of significantly reducing both computational time and memory usage of the gauss newton inversion method by few orders of magnitude

ultrasound tomography for simultaneous reconstruction of acoustic density attenuation and compressibility profiles a fast and efficient forward scattering solver is developed for use in ultrasound tomography the solver is formulated so as to enable the calculation of scattering from large and relatively high contrast objects with inhomogeneous physical properties that vary simultaneously in acoustic attenuation compressibility and density it is based on the method of moments in conjunction with a novel implementation of the conjugate gradient algorithm which requires the use of the adjoints of the scattering operators the solver takes advantage of the symmetric block toeplitz matrix with symmetric toeplitz blocks property of the green s function matrix to increase efficiency and only stores the first row of this matrix to reduce memory requirements this row is then used for the matrix vector multiplication using the fast fourier transform technique thus resulting in the computational complexity of o n log n the marching on source technique is also used to provide a good initial guess which allows the conjugate gradient technique to converge faster than initializing with an arbitrary guess this feature is important in tomographic inversion algorithms which require that the object to be imaged be interrogated via several incident fields forward scattering and inversion examples based on the conjugate gradient least squares regularized born iterative method are shown in two dimensions for objects varying in all three physical properties

on the analysis of laterally vibrating slender beams subject to various complicating effects the rayleigh ritz method with orthogonally generated polynomials as admissible functions is used to obtain a simple analysis of the free vibration problem of slender beams subject to various complicating effects these effects are the presence of concentrated masses and or concentrated moments of inertia intermediate supports axial loading and non uniformity of cross section such may exist separately or in any combination numerical results are presented for several example beams illustrating the accuracy and versatility of the approach

reconstruction of the permittivity profile using a nonlinear guided wave technique a new method is developed to reconstruct the permittivity profile of a dielectric slab in a guided wave formulation the propagation constants of the slab eigenmodes are used as input data for inversion of the boundary value problem for the nonlinear differential equation representing the condition of existence of the modes the permittivity profile is expanded into a set of special functions so that the propagation constant of a particular mode depends mainly on only one term of the set this ensures fast convergence of an iterative procedure to find the coefficients of expansion the method is shown to be valid for the discontinuous profiles of high contrast as well as for both symmetrical and asymmetrical profiles provided that in the last case additional measurements of the slab placed on a metal plate are performed several simulated and experimental examples are presented

gradient based optimization for poroelastic and viscoelastic mr elastography we describe an efficient gradient computation for solving inverse problems arising in magnetic resonance elastography mre the algorithm can be considered as a generalized adjoint method based on a lagrangian formulation one requirement for the classic adjoint method is assurance of the self adjoint property of the stiffness matrix in the elasticity problem in this paper we show this property is no longer a necessary condition in our algorithm but the computational performance can be as efficient as the classic method which involves only two forward solutions and is independent of the number of parameters to be estimated the algorithm is developed and implemented in material property reconstructions using poroelastic and viscoelastic modeling various gradient and hessian based optimization techniques have been tested on simulation phantom and in vivo brain data the numerical results show the feasibility and the efficiency of the proposed scheme for gradient calculation

higher order nonlinear diffraction tomography inversion of the rytov series nonlinear tomographic reconstruction algorithms are developed for inversion of data measured in scattering experiments in which the complex phase of the wavefields is modeled by an arbitrarily large possibly infinite number of terms in the rytov series the algorithms attain the form of a volterra series of nonlinear operators with the usual filtered backpropagation algorithm of diffraction tomography as the leading linear term a computer simulation study is included to illustrate the performance of the algorithms for the case of scattering objects with cylindrical symmetry

elasticity solutions for free vibrations of annular plates from three dimensional analysis abstract this article examines the vibrational characteristics of annular plates by using the three dimensional elasticity theory it aims to raise the quality of the investigation beyond that provided by the two dimensional plate theories by resorting to a full three dimensional analysis a polynomials ritz model based on sets of orthogonally generated polynomial functions to approximate the spatial displacements of the plates in cylindrical polar coordinates is presented the model is then used to extract the full vibration spectrum of natural frequencies and mode shapes the vibration responses due to the variations of boundary conditions and thickness are investigated frequency parameters and three dimensional deformed mode shapes are presented in vivid graphical forms the accuracy of the method is validated through appropriate convergence and comparison studies

hamilton decompositions of regular tournaments we show that every sufficiently large regular tournament can a lmost completely be decomposed into edge disjoint hamilton cycles more precisely for each 0 every regular tournament g of sufficiently large ordern contains at least 1 2 n edge disjoint hamilton cycles this gives an approximate solution to a conjecture of kelly from 1968 our result also extends to almost regular tournaments

a three dimensional model based inversion algorithm using radial basis functions for microwave data we present a three dimensional 3d model based inversion algorithm for inverting electromagnetic data in our approach the models are described by points in the 3d space and the so called radial basis functions are used as the interpolation functions for connecting these points the use of the radial basis functions renders the surface of the target intrinsically smooth the l2 norm and weighted l2 norm regularization schemes are employed to constrain the curvature and to further smooth the surface of the target we tested this inversion algorithm using both synthetic and experimental data sets the inversion results demonstrate that both the shapes and material properties of the target are well reconstructed as a complementary algorithm to the pixel based tomographic inversion algorithms the model based inversion algorithm has fewer parameters to invert hence it has a higher computational efficiency the model based inversion algorithm also gives the users the freedom to construct an initial model based on their knowledge and other related information it helps to reduce the non uniqueness in the data interpretation

simultaneous microwave imaging and parameter estimation using modified level set method a modified level set method mlsm is proposed to simultaneously reconstruct the shape and electrical properties of 2 d objects as a numerical technique the formal level set method lsm can retrieve the shape and position of objects using synthetic measurement data in general the constitutive parameters of an object e g its relative complex permittivity are among the a priori information needed for the lsm for mlsm an evolution strategy is proposed to simultaneously calculate both the shape and complex permittivity of a 2 d object the initial guesses in respect of the complex permittivity and shape of the target object converge on their real values as the cost function is minimized the cost function is regularized with two penalty terms to prevent sudden change in the shape of the object a curvature based regularization is used also laplacian regularizer is used to reduce fluctuations in the object s constitutive parameters during the process using different synthetic data sets the capabilities of mlsm in microwave imaging and parameter estimation are evaluated it is found that using mlsm it is possible to completely separate two adjacent objects separated by a distance of one fifteenth of a wavelength the proposed method can retrieve targets of different relative permittivities with less than 10 error one interesting feature of this method is its high fidelity in retrieving the immersed one tenth wavelength targets in highly contrasting up to as high as 8 1 domains in the case of targets with little contrast 10 the proposed method with more iterations can converge on a value which is 57 more than the actual value these features are valuable in distinguishing malignant tissue from normal tissue

buckling and vibrations of polar orthotropic annular plates of variable thickness abstract the effect of an hydrostatic in plane force together with the orthotropy on the axisymmetric vibrations of an annular plate of linearly varying thickness in the radial direction has been analyzed on the basis of classical theory of plates the numerical solution of the governing differential equation for two boundary conditions inner and outer both clamped inner clamped and outer simply supported at the periphery has been obtained by a spline technique transverse displacements moments in normalized form for a particular set of plate parameters and buckling loads in compression with thickness variation and various values of rigidity ratios have been computed for first two modes of vibrations a comparison of present results with those available in the literature shows a very good agreement

on the free transverse vibration of annular and circular thin sectorial plates subject to certain complicating effects abstract the rayleigh ritz method with orthogonally generated polynomials as admissible functions is used to obtain an eigenvalue equation for the free transverse vibration of thin annular sectorial plates circular sectorial plates are treated with this equation by permitting the inner radius to become negligibly small the plates may be of isotropic or polar orthotropic material of uniform or radially and or circumferentially varying thickness and may include interior circumferential or radial line supports numerical values for the natural frequency parameters of several different plates are presented and compared with previously published values where available

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

transverse vibrations of a rotating uniform cantilever beam with tip mass as predicted by using beam characteristic orthogonal polynomials in the rayleigh ritz method abstract natural frequencies and mode shapes of a rotating uniform cantilever beam with a tip mass are studied by using beam characteristic orthogonal polynomials in the rayleigh ritz method the set of orthogonal polynomials which satisfy the geometrical boundary conditions are generated by using the gram schmidt process the results are compared with those obtained by the myklestad method the extended galerkin method and finite element methods the variation of natural frequencies with the speed of rotation is plotted for several parameter combinations such as setting angle tip mass moment of inertia of tip mass etc mode shapes at different rotational speeds are also plotted use of orthogonal polynomials for the deflection shapes enables the computation of higher natural frequencies of any order to be accomplished without facing any numerical difficulties which is not the case when arbitrary polynomial expressions are used

compressive sensing imaging of non sparse 2d scatterers by a total variation approach within the born approximation the problem of imaging two dimensional non sparse scatterers with piecewise constant contrast is solved through an innovative total variation compressive sensing tv cs technique under born approximation ba the time harmonic two dimensional inverse scattering problem is reformulated into an equivalent augmented lagrangian one according to the tv cs formulation the resulting unconstrained functional is then minimized by means of a deterministic alternating direction algorithm selected results from a numerical assessment are discussed to give the interested reader some insights on the accuracy the flexibility the robustness and the efficiency of the tv cs inversion scheme also in comparison with available implementations of state of the art inversion methods still formulated within the ba

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

on the lateral vibration of thin annular and circular composite plates subject to certain complicating effects abstract series comprising orthogonally generated polynomial functions are used in the rayleigh ritz method to obtain an eigenvalue equation for the flexural vibration of thin flat annular and circular plates the plates may be of isotropic or polar orthotropic material of uniform or radially varying thickness and may pass over intermediate concentric ring supports numerical results are presented for a number of plates illustrating the versatility and accuracy of the approach

use of two dimensional orthogonal polynomials for vibration analysis of circular and elliptical plates abstract a general numerical method is developed to estimate the natural frequencies and the mode shapes for transverse vibration of circular and elliptical plates a set of orthogonal plate functions is used as the admissible functions in the rayleigh ritz approach to approximate the eigenvalues and eigenvectors new starting functions are proposed which are used in a recurrence formula to generate the higher terms in the set of orthogonal plate functions to approximate the mode shapes for circular and elliptical plates these functions are general and easily formed for circular and elliptical plates having classical boundary conditions several numerical examples are solved to demonstrate the applicability and the accuracy of the new proposed plate functions

a multiplicative regularized gauss newton inversion for shape and location reconstruction a multiplicative regularized gauss newton inversion algorithm is proposed for shape and location reconstruction of homogeneous targets with known permittivities the data misfit cost functional is regularized with two different multiplicative regularizers the first regularizer is the weighted norm total variation which provides an edge preserving regularization the second one imposes a priori information about the permittivities of the objects being imaged using both synthetically and experimentally collected data sets we show that the proposed algorithm is robust in reconstructing the shape and location of homogeneous targets

nonlinear microwave imaging for breast cancer screening using gauss newton s method and the cgls inversion algorithm breast cancer screening using microwave imaging is emerging as a new promising technique as a supplement to x ray mammography to create tomographic images from microwave measurements it is necessary to solve a nonlinear inversion problem for which an algorithm based on the iterative gauss newton method has been developed at dartmouth college this algorithm determines the update values at each iteration by solving the set of normal equations of the problem using the tikhonov algorithm in this paper a new algorithm for determining the iteration update values in the gauss newton algorithm is presented which is based on the conjugate gradient least squares cgls algorithm the iterative cgls algorithm is capable of solving the update problem by operating on just the jacobian and the regularizing effects of the algorithm can easily be controlled by adjusting the number of iterations the new algorithm is compared to the gauss newton algorithm with tikhonov regularization and is shown to reconstruct images of similar quality using fewer iterations

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

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

numerical calculation of 2 d inhomogeneous media green s function and some applications in electromagnetic scattering problems a method of moments based numerical technique for the calculation of the electric type green s function of inhomogeneous media is presented for a 2 d configuration the problem is reduced to an integral equation by the use of a special representation through the decomposition of green s function into two parts which allows the singularity is being expressed conveniently however this representation yields multiple singular terms to appear on the right hand side of the integral equation system which are treated by an approximation of the related integral through an equivalent cell approach the method is validated by comparisons with classical solutions and some numerical examples are also given in order to show the applicability and the effectiveness

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

flexural vibration of shear deformable circular and annular plates on ring supports this paper presents an analysis of free flexural vibration of circular and annular mindlin plates lying on multiple internal concentric ring supports the rayleigh ritz method with an admissible displacement function expressed in terms of a set of simple polynomials is used to obtain the governing eigenvalue equation the natural frequencies of circular and annular mindlin plates with one or two ring supports having inner and outer peripheries with different combinations of free simply supported and clamped conditions are determined a comprehensive set of vibration results is presented and where possible these have been verified with existing solutions published in the open literature no previous theoretical results for thick annular plates supported with internal rings are known to exist thus the study should be useful and valuable to engineers and researchers

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

enhancement of the krylov subspace regularization for microwave biomedical imaging although krylov subspace methods provide fast regularization techniques for the microwave imaging problem they cannot preserve the edges of the object being imaged and may result in an oscillatory reconstruction to suppress these spurious oscillations and to provide an edge preserving regularization we use a multiplicative regularizer which improves the reconstruction results significantly while adding little computational complexity to the inversion algorithm we show the inversion results for a real human forearm assuming the 2 d transverse magnetic illumination and a cylindrical object assuming the 2 d transverse electric illumination

proof of a conjecture of thomassen on hamilton cycles in highly connected tournaments a conjecture of thomassen from 1982 states that for every k there is an f k s o that every strongly f k connected tournament contains k edge disjoint hamilton cycles a classical theorem of camion that every strongly connected tournament contains a hamilton cycle implies that f 1 1 so far even the existence of f 2 was open in this paper we prove thomassen s conjecture by showing that f k o k 2 log 2 k this is best possible up to the logarithmic factor as a tool we show that every strongly 10 4 k log k connected tournament is k linked which improves a previous exponential bound the proof of the latter is based on a fundamental result

the flexural vibration of rectangular plates with point supports abstract orthogonally generated polynomial functions are used in the lagrangian multiplier method to study the free flexural vibration problem of point supported thin flat rectangular plates the analysis applies to isotropic and specially orthotropic plates having any combination of clamped simply supported or free edges with arbitrarily located point supports and to plates which are continuous over line supports parallel to the plate edges numerical results are presented for a number of specific problems illustrating the accuracy and versatility of the approach and which include natural frequencies and nodal patterns for a point supported plate which is continuous over two perpendicular line supports

axisymmetric vibrations of polar orthotropic annular plates of variable thickness in this study of the free axisymmetric vibrations of polar orthotropic annular plates of linearly varying thickness on the basis of the classical theory of plates the chebyshev collocation technique has been employed to solve the differential equation governing the transverse motion of such plates frequencies mode shapes and moments have been computed for three different boundary conditions for various values of the rigidity ratios the radii ratio and the taper parameter for the first two modes of vibration the results for isotropic annular plates of uniform and non uniform thickness show good agreement with those available in the literature

computation of modal stress resultants for completely free vibrating plates by lsfd method when the ritz method the galerkin s method and the finite element method are adopted for the vibration analysis of thin plates the natural frequencies and mode shapes can normally be obtained accurately however the corresponding modal stress resultants usually violate the natural boundary conditions at the free edges and contain erroneous oscillations therefore the accuracy of modal stress resultants obtained by such methods is uncertain in this study a meshfree least squares based finite difference method lsfd is proposed for evaluating the vibration solutions of completely free plates examples treated include circular plates elliptical plates lifting tab shaped plates and 45 right triangular plates it will be shown that the lsfd method not only furnishes accurate natural frequencies but also yields excellent modal stress resultants that satisfy the natural boundary conditions of the free edges and are smooth in their distribution over the plate domain

prediction correction method for electromagnetic imaging with current reconstruction a prediction correction methodology is presented for improving the numerical stability of the iterative process involved in the solution of nonlinear inverse scattering problems related to the electromagnetic imaging of dielectric objects in various methods developed so far each iteration is performed by only using the results obtained in the preceding iteration the results computed in the preceding iteration along with those acquired in previous iterations are employed selectively to make a prediction of the object function to be used in the next iteration as a consequence the numerical stability and the convergence of the iterative process are improved this is illustrated by numerical computation results obtained for lossless and for lossy dielectric bodies

a nested multi scaling inexact newton iterative approach for microwave imaging a microwave imaging technique based on the integration of the inexact newton method within a multi scaling strategy is proposed in the framework of the contrast field formulation of the electromagnetic inverse scattering the inversion problem is solved by means of a nested procedure that considers three different logical levels a an outer multi focusing loop aimed at implementing a synthetic zoom for focusing the scatterer support within the investigation domain b a local linearization of the original full nonlinear inverse scattering function and c a truncated landweber inner loop devoted to regularize the arising ill posed linear problem thanks to the features of the integrated approach a reliable inversion technique able to suitably face the non linearity and the ill posedness ill conditioning issues of the imaging problem is designed a numerical validation dealing with different objects measurement setups and noise conditions is carried out to assess the features and the potentialities as well as the limitations of the proposed strategy comparisons with bare approaches and other multi resolution formulations are presented as well

a novel microwave imaging approach based on regularization in l p banach spaces inverse problems arising in microwave imaging suffer from high ill posedness as it is well known it is necessary to employ regularized inversion methods in order to mitigate such behavior usually such approaches are formulated in standard hilbert spaces recently a more generic regularization theory working in banach spaces has been investigated in order to overcome some limitations of the hilbert space regularization in this paper a novel imaging algorithm performing a lp banach space regularization is proposed for 2 d electromagnetic inverse scattering problems the reconstruction capabilities of the methods are evaluated by using numerical and experimental data