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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 background medium for the inversion process. We demonstrate the accuracy of this new inversion technique by inverting experimentally collected biomedical data. For biomedical inversion, where a priori information about the target is often available, we show that the use of the a priori knowledge as a background medium, as opposed to an initial guess, often significantly improves the inversion results. This is shown through both single and multiple frequency examples taken from biological thorax, brain, and breast models. Index Terms--Biomedical imaging, electromagnetic fields, inverse problems, iterative methods.

In this paper, we report on temperature effects associated with elastic electromagnetic forming by pulsed electromagnetic fields in inhomogeneous, linear, and lossy media. In a previous paper, we discussed the electromagnetic forces associated with these pulsed electromagnetic fields. Here, we calculate the temperature rise from the equation of heat flow in an isolated object to be deformed. The temperature rise is included in the elastodynamic problem to be solved for the presence of electromagnetic forces, and as a consequence the thermoelastic field can be obtained. As an example, we calculate the thermoelastic field in a hollow cylindrical object. Index Terms--Conducting magnetic materials, elastic field, electromagnetic forming, electromechanical forces, temperature rise, thermoelastic field.

Microwave tomography is an imaging modality based on differentiation of dielectric properties of an object. The dielectric properties of biological tissues and its functional changes have high medical significance. Biomedical applications of microwave tomography are a very complicated and challenging problem, from both technical and image reconstruction point-of-views. The high contrast in tissue dielectric properties presenting significant advantage for diagnostic purposes possesses a very challenging problem from an image-reconstruction prospective. Different imaging approaches have been developed to attack the problem, such as two-dimensional (2-D) and three-dimensional (3-D), minimization, and iteration schemes. The goal of this research is to study imaging performance of the Newton and the multiplicative regularized contrast source inversion (MR-CSI) methods in 2-D geometry and gradient and MR-CSI methods in 3-D geometry using high-contrast, medium-size phantoms, and biological objects. Experiments were conducted on phantoms and excised segment of a pig hind-leg using a 3-D microwave-tomographic system operating at frequencies of 0.9 and 2.05 GHz. Both objects being of medium size (10-15 cm) possess high dielectric contrasts. Reconstructed images were obtained using all imaging approaches. Different approaches are evaluated and discussed based on its performance and quality of reconstructed images. Index Terms--Dielectric properties, high contrast, microwave imaging, tomography.

In this paper, we provide three direct procedures to extrapolate the early-time and the low-frequency response of a causal signal simultaneously in the time-and frequency domain. Compared with the extrapolation by orthonormal basis functions, direct extrapolation is straightforward and we do not need to evaluate the basis functions and search for the optimal scaling factor and the optimal number of basis functions. We show that the extrapolation introduced by Adve and Sarkar is equivalent to a Neumann-series solution of an integral equation of the second kind. It is further shown that this iterative Neumann expansion is an error-reducing method. We propose to solve this integral equation efficiently by employing a conjugate gradient iterative scheme. The convergence of this scheme is also demonstrated. We provide the matrix equations and show the equivalence to the integral equations, and demonstrate that the method of singular value decomposition (SVD) of solving the matrix equation provides accurate and stable results. Finally, a number of illustrative numerical examples are presented and the performances of the three direct methods are compared. Index Terms--Conjugate gradient (CG), early time, extrapolation, low frequency, Neumann series, singular value decomposition (SVD).

The deblurring process or image reconstruction is a mathematically ill-posted problem and therefore, regularization methods are usually employed to obtain a solution satisfying some criterion. Numerical testing shows that the proposed algorithm works effectively and efficiently in various practical applications.

In this paper, we discuss the electromechanical force densities associated with pulsed electromagnetic fields in inhomogeneous, linear media with conductive losses, in the context of a process of shaping metal objects. We show that the conductivity and the gradients in permittivity and in permeability lead to volume forces, while jump discontinuities in permittivity and permeability lead to surface forces. These electromagnetic forces are assumed to act as volume (body) source densities in the elastodynamic equations and as surface source densities in the corresponding boundary conditions that govern the elastic motion of deformable matter. As an example, we apply the theory to the calculation of the elastic field in a hollow cylindrical object made of a conducting magnetic or nonmagnetic material. We compare the numerical results with those for the classical theory of elasticity with concentrated forces on the boundaries of the material as the source of the elastodynamic field. Index Terms--Conducting magnetic materials, elastic field, electromechanical forces.

We present a robust iterative method to solve the inverse scattering problem in cases where the Born approximation is valid. We formulate this linearized inverse problem in terms of the unknown material contrast and the unknown contrast sources and we solve the problem by minimizing a cost functional consisting of two terms. The first term represents the differences between the actual data and the modeled data, while the second term represents the misfit in the constitutive relations between the contrast sources and the incident fields. In each iteration, the contrast sources and the contrast are reconstructed alternatingly, using subsequently a conjugate gradient step for the contrast source updates and a direct inversion of a diagonal matrix for the contrast. A further regularization with a multiplicative regularization factor is discussed. In this regularization procedure the relative variation of the contrast is minimized as well. As a test case we consider the two-dimensional (2-D) transverse magnetic polarization problem. Synthetic numerical examples are presented in order to compare the presented algorithm to the traditional Born algorithm. Results with respect to the inversion of experimental data are presented as well. In addition, some inversion results for the subsurface sensing problem, both in two and three dimensions, are presented. Index Terms--Born, conjugate gradient, iterative method, linear inversion.

It is well-known that electromagnetic solutions of boundary integral equations for perfectly electrically conducting scatterers are nonunique for those frequencies which correspond to interior resonances of the scatterer. In this paper a simple and efficient computational method is developed, in which the interior integral representations, required to hold on an interior closed surface, are used as a sufficient constraint to restore uniqueness. We use the interior equations together with the second kind magnetic field integral equation, so that the ill-posedness of the interior equations does not give a problem. We develop a constrained conjugate gradient method that minimizes a cost functional consisting of two terms. The first term is the error norm with respect to the magnetic field boundary integral equation, while the second term is the error norm with respect to the interior equations over a closed interior surface, which is chosen as small as possible. Some numerical examples show the robustness and efficiency of the pertaining computational procedure. Index Terms--Boundary integral equation, conjugate gradient, interior resonance, uniqueness.

This paper deals with the scattered field data measured by a closed microwave scanner and discusses the removal of the effects of the metal casing as a preprocessing step before actual inversion of the data can take place. It is shown that Rayleigh's reciprocity theorem furnishes a relation between the scattered field data obtained in the closed microwave scanner and the scattered field data as if they were obtained by an open scanner without the metal casing. This relation leads to a system of linear equations, from which the desired scattered field data with respect to the equivalent open scanner are obtained. Index Terms--Inverse scattering, microwave scanner, reciprocity.

In this paper, the recently developed multiplicative regularized contrast source inversion method is applied to microwave biomedical applications. The inversion method is fully iterative and avoids solving any forward problem in each iterative step. In this way, the inverse scattering problem can efficiently be solved. Moreover, the recently developed multiplicative regularizer allows us to apply the method blindly to experimental data. We demonstrate inversion from experimental data collected by a 2.33-GHz circular microwave scanner using a two-dimensional (2-D) TM polarization measurement setup. Further some results of a feasibility study of the present inversion method to the 2-D TE polarization and the full-vectorial three-dimensional measurement will be presented as well. Index Terms--Experimental data, medical applications, microwave tomography, nonlinear inversion, three-dimensional.

The time-domain performance of a number of absorbing boundary conditions invoked on the boundary of a domain of computation, as well as of a perfectly matched layer surrounding such a domain, is carried out for a test configuration for which analytic expressions for the relevant field quantities exist. The test configuration consists of a small loop antenna radiating into a homogeneous, isotropic half-space. On the planar boundary of this half-space, either an absorbing boundary condition is invoked or a perfectly matched layer is started that is truncated at some finite depth of penetration. For a loop parallel to the boundary, closed-form analytic expressions for all field components of the spuriously reflected field are presented for all truncation conditions involved. A number of important features show up that might he masked in purely numerical implementations of the procedures under consideration. Index Terms--Absorbing boundary conditions, computational modeling, perfectly matched layers.

The problem of the location and characterization of a two-dimensional (2-D) subsurface object is formulated as the inverse problem for an effective scattering model. An arbitrary finite-sized buried object is described as a subsurface circular cylinder with the radius, permittivity, and position of its center to be determined. The inversion is performed in a nonlinearized way, minimizing the discrepancy between the actual scattered field and that of the effective scattering model. A simple and quick solution for a circular cylinder embedded in a lossy half space is introduced. As far as numerical efficiency is concerned, the obtained approximate algorithm is comparable to the free-space solution. The location algorithm has been tested with the two-dimensional models of plastic antipersonnel land mines. Index Terms: Detection and characterization of subsurface objects, ground penetrating radar, nonlinear inversion.

Cross-well induction logging as known in the oil industry is a method for determining the electrical conductivity distribution between boreholes from the low-frequency electromagnetic field measurements in the boreholes. In this paper, we discuss the reconstructions of the three-dimensional (3-D) conductivity distribution using the contrast source inversion (CSI) method. In order to improve the reconstruction results, the concept of the extended Born approximation has been used to arrive at a preconditioning operator. Results of a number of numerical examples show that by using this preconditioning operator, a large conductivity contrast of the unknown objects (factor of 100) can be reconstructed up to an acceptable degree of accuracy. Moreover, in each iteration, the computational effort to generate the preconditioning operator is negligible. Index Terms--Cross-well, induction logging, nonlinear inversion, three-dimensional.

Electrode logging as known in the oil industry is a method for determining the electrical conductivity distribution around a borehole or between two boreholes from the static-field (dc) measurements in the borehole. In this paper, we discuss the reconstruction of the three-dimensional (3-D) conductivity around a borehole in a highly deviated formation with invasion. At this moment, we have not included the borehole effect. To solve this problem, the full vector analysis is required. In most available algorithms, for the forward and inverse modeling of the resistivity data, the dipping bed environment is approximated using the staircase-discretization grid. In contrast, we have modeled the dipping-bed environment by introducing an oblique (nonorthogonal) coordinate system. By using the oblique coordinate system, we have gained some advantages over the usual approach. First, the use of the staircasing approximation for the dipping-bed environment can be avoided. This means that we reduce the discretization error, and we can suffice with less discretization points to obtain the results with the same degree of accuracy as the problem formulated in the Cartesian coordinate system. Secondly, the horizontally-symmetry constraints of the conductivity distribution can be included easily in the inversion procedure. Several numerical results are presented to demonstrate the performance of the inversion method using the synthetic 'measured' data, which are generated by solving a forward-scattering problem numerically with the help of the conjugate gradient fast fourier transform (CGFFT) method. Index Terms--Electrode logging, nonlinear inversion, oblique coordinate system, three-dimensional method.