The very early time electromagnetic system (VETEM) is an efficient tool for the detection of buried objects in very lossy earth, which allows a deeper penetration depth compared to the ground-penetrating radar. In this paper, the inversion of VETEM data is investigated using three-dimensional (3-D) inverse scattering techniques, where multiple frequencies are applied in the frequency range from 0-5MHz. For small and moderately sized problems, the Born approximation and/or the Born iterative method have been used with the aid of the singular value decomposition and/or the conjugate gradient method in solving the linearized integral equations. For large-scale problems, a localized 3-D inversion method based on the Born approximation has been proposed for the inversion of VETEM data over a large measurement domain. Ways to process and to calibrate the experimental VETEM data are discussed to capture the real physics of buried objects. Reconstruction examples using synthesized VETEM data and real-world VETEM data are given to test the validity and efficiency of the proposed approach.

It has been observed that super resolution is possible in the electromagnetic imaging. In the first part of the paper, the possible resolution of image is investigated in the inversion of farfield data using the diffraction tomographic (DT) algorithm, where two cases are considered when the object is in a homogeneous space and in an air-earth half space. The study shows that the resolution of image for inversion of far-field data has been limited theoretically to 0.3536-0.5 wavelength using the DT algorithm in homogeneous-space problems, and it is even worse in half-space problems. If the transmitters and receivers are located in the near-field regime, however, the image resolution is less than 0.25 wavelength, which is the super-resolution phenomenon. In the second part of the paper, the physical reason for the super-resolution phenomenon is investigated using different electromagnetic inverse scattering methods. The study has demonstrated that the information of evanescent waves in the measurement data and its involvement in inversion algorithms is the main reason for the super resolution. Four inversion algorithms are considered for half-space problems: the DT algorithm, the spatial-domain Born approximation (BA), the Born iterative method (BIM), and the distorted BIM (DBIM). The first two belong to linear inverse scattering, while the last two belong to nonlinear inverse scattering. Further analysis shows that DBIM provides a better super resolution than BIM, and BIM provides a better super resolution than BA. Numerical simulations validate the above conclusions.

The extended Born approximation (ExBorn) has been shown an efficient formulation in the electromagnetic (EM) scattering by dielectric objects in both free-space and air-earth half-space problems. In most cases, ExBorn is much more accurate than the conventional Born approximation at low frequencies. When the frequency is high or the contrast of dielectric objects is large, however, the ExBorn approximation becomes inaccurate. In this paper, new approximations are proposed for the EM scattering by dielectric objects buried in a lossy earth, which are also suitable for the case of free space. It has been shown that the zeroth-order form of new approximations is completely equivalent to ExBorn. Hence, high-order approximations can be regarded as high-order ExBorn. Closed-form formulations are derived for the new approximations. Using the fast Fourier transform (FFT), these formulations can be implemented efficiently at a cost of log, where is the number of unknowns and is a small number. Numerical simulations show that high-order ExBorn approximations are much more accurate than the ExBorn approximation.

Based on the addition theorem, the principle of a multilevel ray-propagation fast multipole algorithm (RPFMA) and fast far-field approximation (FAFFA) has been demonstrated for three-dimensional (3-D) electromagnetic scattering problems. From a rigorous mathematical derivation, the relation among RPFMA, FAFFA, and a conventional multilevel fast multipole algorithm (MLFMA) has been clearly stated. For very large-scale problems, the translation between groups in the conventional MLFMA is expensive because the translator is defined on an Ewald sphere with many sampling K directions. When two groups are well separated, the translation can be simplified using RPFMA, where only a few sampling K directions are required within a cone zone on the Ewald sphere. When two groups are in the far-field region, the translation can be further simplified by using FAFFA where only a single K is involved in the translator along the ray-propagation direction. Combining RPFMA and FAFFA with MLFMA, three algorithms RPFMA-MLFMA, FAFFA-MLFMA, and RPFMA-FAFFA-MLFMA have been developed, which are more efficient than the conventional MLFMA in 3-D electromagnetic scattering and radiation for very large structures. Numerical results are given to verify the efficiency of the algorithms.

An efficient multiregion model has been proposed for the fast implementation of the electromagnetic scattering by perfectly electrical conducting (PEC) targets and the radiation of point sources or wire antennas near PEC targets. In the multiregion model, the PEC target under consideration is divided by multiple regions depending on the position of point source/antenna or the incident direction of plane waves. Then the method of moments (MoM) is used on the first region, which is close to the source or is the illuminated region, to obtain the accurate electric current. The mutual coupling between different regions are considered approximately based on the magnetic-field integral equation, from which closed-form approximations for electric currents on other regions are derived. Because MoM is only performed on the first region, the number of unknowns in the new model is much fewer than that in the full MoM analysis, making the new model much more efficient. Compared with the published hybrid methods, the multiregion model gives a more reasonable physical explanation, and provides a better accuracy in both currents and scattered fields. Numerical simulations for two-dimensional (2-D) problems (transverse-magnetic/transverse-electric) and 3-D problems are given to test the validity and efficiency of the proposed modeling.