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

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

torsion of a micropolar elastic prism of square cross section abstract an analytical solution is presented for the problem of torsion of a prismatical bar of square cross section of a micropolar cosserat elastic solid warp of the cross sections is found to differ from the warp in a classically elastic solid contrary to the classical case a non zero shear strain is predicted to occur at the edge of the bar novel experimental modalities are suggested on the basis of this analytical solution

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

envelope theory in spectral geometry it is shown that the discrete spectrum of schrodinger hamiltonians of the form h vf may be represented by the semiclassical expression enl minr 0 k f nl r vf r the k functions are found to be invariant with respect to coupling and shifts k af b k f for pure power laws f r sgn q rq and the log potential they are also invariant with respect to scale and have the simple forms pnl q r 2 and lnl r 2 respectively k functions are also derived for sech squared and hulthen potentials if f g h where g is a smooth transformation then the envelope approximation is expressed in terms of k by the relation k f k h when the transformation g has definite convexity then the approximation immediately yields eigenvalue bounds for all n and l the theory is used to prove the log power theorem lnl pnl 0 which in turn generates a simple eigenvalue formula for the log potential

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

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

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

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

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

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

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

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

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

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

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

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

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

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