Image reconstruction from TE scattering data using equation ofstrong permittivity fluctuation

Compared to the TM case, the inverse scattering problem for the TE incident field is more complicated due to its stronger nonlinearity. This work provides an effective method for the reconstruction of two-dimensional (2-D) inhomogeneous dielectric objects from TE scattering data. The algorithm applies the distorted Born iterative method to the integral equation of strong permittivity fluctuation to reconstruct scatterers with high-permittivity contrast. Numerical simulations are performed and the results show that the distorted Born iterative method (DBIM) for strong permittivity fluctuation (SPF-DBIM) converges faster and can obtain better reconstructions for objects with larger dimensions and higher contrasts in comparison with ordinary DBIM. A frequency hopping technique is also applied to further increase the contrast     

二维有耗介质体电磁反演的时域玻恩迭代方法

本文利用时域非线性优化方法求解二维有耗介质的体的逆散射问题获得了很好的结果。并对正散射的求解精度做了改进。     

时域玻恩迭代的改进方法

本文提出了一种能够加速收敛的助推法，把助推法应用于时域非线性优化方法求解二维有耗介质体的逆散射问题，获得了很好的结果。     

Detection of buried dielectric cavities using the finite-differencetime-domain method in conjunction with signal processing techniques

We address the problem of detecting low-dielectric contrast cavities buried deep in a lossy ground by using the finite-difference time-domain (FDTD) method in conjunction with signal processing techniques for extrapolation and object identification. It is well known that very low frequency probing is needed for deep penetration into the lossy ground, owing to a rapid decay of electromagnetic (EM) waves at higher frequencies. It is also recognized that numerical modeling using the FDTD method becomes very difficult, if not impossible, when the operating frequency becomes as low as 1 Hz. To circumvent this difficulty, we propose a hybrid approach in this paper that combines the FDTD method with signal processing techniques, e.g., rational function approximation and neural networks (NNs). Apart from the forward problem of modeling buried cavities, we also study the inverse scattering problem-that of estimating the depth of a buried object from the measured field values at the surface of the Earth or above. Numerical results for a buried prism are given to illustrate the application of the proposed technique     

半无限大空间中无耗二维电磁目标的微波成像新方法

本文提出利用模拟得到的时域散射信息对埋于半无限大空间中的无耗二维电磁目标进行微波成像的新方法时域变分迭代法(time-domain variational iterative method,TVIM)。这是一种基于电磁体等效原理、变分原理和傅立叶变换的迭代方法,每次迭代各计算正问题和逆问题一次,正问题采用时域有限差分(finite-difference time-domain)方法处理。列举了一些典型的数值反演实例,并与有关文献结果作了比较,考察了TVIM的收敛性能、反演复杂目标能力、抗随机噪声等反演性能,并从理论上简要分析了形成TVIM良好反演性能的原因。     

多重网格技术与波恩迭代法 相结合的反演新方法

本文将多重网格技术与波恩迭代法(BIM)相结合,利用时域散射数据对二维无耗非均匀介质剖面进行了反演.在反演迭代过程中,待反演目标区域的离散网格由粗逐渐变细.由于在反演的初期,目标区域离散网格较粗,离散反演积分方程所得到的矩阵方程的维数较小、条件数较低,使得该方法具有稳定性好、更容易收敛到真解的特点.通过反演实例表明,该方法极大地降低了反演过程的计算量,与传统的BIM方法相比能更精确地反演高对比度的散射目标.更为重要的是本文方法简单可行、可以与其它任何反演方法相结合.     

A matched-filter-based reverse-time migration algorithm forground-penetrating radar data

Ground-penetrating radar (GPR) is a remote sensing technique used to obtain information on subsurface features from data collected over the surface. The process of collecting data may be viewed as mapping from the object space to an image space. Since most GPRs use broad beam width antennas, the energy reflected from a buried structure is recorded over a large lateral aperture in the image spare, migration algorithms are used to reconstruct an accurate scattering map by refocusing the recorded scattering events to their true spatial locations through a backpropagation process. The goal of this paper is to present a pair of finite-difference time-domain (FDTD) reverse-time migration algorithms for GPR data processing. Linear inverse scattering theory is used to develop a matched-filter response for the GPR problem. The reverse-time migration algorithms, developed for both bistatic and monostatic antenna configurations, are implemented via FDTD in the object space. Several examples are presented     

探地雷达中的衍射层析算法

给出了二维情况下进行地下目标反演的线性衍射层析算法。该方法采用线性Born近似和傅里叶变换,避免了一般非线性逆散射算法的逐步迭代,因而可用于地下目标的快速检测和位置标定。本文的衍射层析算法考虑了空气地面交界面的影响并计入了凋落场。计算结果表明,该方法可以较好地描述低对比度目标的位置、轮廓和介电参数等信息,也可用于高对比度目标的检测和定位。     

Linear tomographic inversion of stepped-frequency GPR data: experimental results on two test-sites

This paper deals with the tomographic inversion of experimental data acquired by a stepped-frequency ground penetrating radar (SFGPR).The experimental SFGPR has been designed for archaeological prospecting and makes it possible to exploit a multi-view/multi-static/multi-frequency configuration. The tomographic algorithm is based on a linear model of the electromagnetic scattering to reconstruct the shape of strongly scattering targets. It has been already validated against experimental data for objects in free-space and synthetic data for buried scatterers.Here, we present experimental results for buried objects starting from measurements collected at two test-sites. The first one has been a dedicated outdoor test facility which has allowed to test the experimental setup and the inversion algorithm in controlled conditions; the second one has been an archeological test-site.     

Efficient low-frequency inversion of 3-D buried objects with large contrasts

An efficient inversion method is proposed using Cui et al.'s high-order extended Born approximations to reconstruct the conductivity object function of three-dimensional dielectric objects buried in a lossy Earth. High-order solutions of the object function are obtained, which have closed-form relations to the linear inverse-scattering solution. Because such relations can be evaluated quickly using the fast Fourier transform, the high-order solutions have similar simplicity as the linear inversion. When the contrasts of buried objects are large, the high-order solutions are much more accurate due to the approximate consideration of multiple-scattering effects within the objects. Hence, good-resolution images can be obtained for large-contrast objects using the new method by only solving a linear inverse problem. Numerical experiments have shown the validity and efficiency of the proposed method.     

Inverse scattering of two-dimensional dielectric objects buried ina lossy earth using the distorted Born iterative method

An efficient inverse-scattering algorithm is developed to reconstruct both the permittivity and conductivity profiles of two-dimensional (2D) dielectric objects buried in a lossy earth using the distorted Born iterative method (DBIM). In this algorithm, the measurement data are collected on (or over) the air-earth interface for multiple transmitter and receiver locations at single frequency. The nonlinearity due to the multiple scattering of pixels to pixels, and pixels to the air-earth interface has been taken into account in the iterative minimization scheme. At each iteration, a conjugate gradient (CG) method is chosen to solve the linearized problem, which takes the calling number of the forward solver to a minimum. To reduce the CPU time, the forward solver for buried dielectric objects is implemented by the CG method and fast Fourier transform (FFT). Numerous numerical examples are given to show the convergence, stability, and error tolerance of the algorithm     

多极德拜色散媒质的时域电磁逆散射改进技术

在已有的经验模型中,多极德拜(Debye)模型最适合高精地描述生物组织、土壤、水等媒质的色散特性.为了同时反演这类媒质的电磁参数,本文提出了一种时域逆散射改进技术:分别应用迭代法和吉洪诺夫(Tikhonov)正则化技术克服逆问题的非线性和病态性困难;解析导出了目标泛函关于目标参数的梯度;迭代重建过程中,产生的正演、反演子问题分别选用时域有限差分(FDTD)法、共轭梯度(CG)法求解.噪声环境下,通过两个一维(1-D)的数值算例,初步证实了该技术的可行性和鲁棒性.     

Effective Solution of 3-D Scattering Problems via Series Expansions: Applicability and a New Hybrid Scheme

Accurate and reliable evaluation of the electromagnetic field scattered by dielectric objects is a canonical problem in the electromagnetic community. In the framework of integral equation formulations, iterative techniques, and in particular conjugate gradient (CG) schemes, are widely used. However, when the number of parameters grows, CG techniques may become too demanding from a computational point of view. In this paper, we show that many forward scattering problems can be conveniently solved by means of very simple series expansions, which allow a lower computational complexity and memory storage with respect to other iterative schemes. In particular, we consider three different series expansions, namely: 1) the traditional Born series; 2) the contrast source-extended Born series, which is recently introduced by rewriting the traditional source-type integral equations; and 3) a new series, which is a hybridization of the previous ones. Theoretical conditions for the applicability of the series expansions are discussed, and practical tools to foresee that a problem can be solved by means of these simple iterative schemes are provided. Numerical examples are reported for the sake of comparison and to assess performance     

An FDTD near- to far-zone transformation for scatterers buried instratified grounds

The finite-difference time-domain (EDTD) technique is being used with increasing frequency for modeling the scattering characteristics of buried objects. The FDTD has, for some time, been able to model the near-zone scattered fields of buried objects due to near-zone sources. This is adequate for modeling the scattered returns of ground-based ground-penetrating radar, but not for airborne radar. This paper describes an FDTD-compatible technique whereby far-zone scattered fields of objects buried in a stratified ground can be calculated. This technique uses the equivalence principle to model a buried object in terms of equivalent electric and magnetic currents. The fields radiated by these currents in the presence of a stratified ground are then calculated using the reciprocity theorem and the well-known field equations for plane waves in a stratified media. Numerical results are presented that show excellent agreement between this technique and both analytical and numerical results     

Microwave imaging within the second-order Born approximation:stochastic optimization by a genetic algorithm

This paper addresses the problem of reconstructing the location, shape, and dielectric permittivity distribution of an inhomogeneous dielectric object from measurements of the field scattered by the object. The object is an inhomogeneous infinite cylinder of arbitrary cross section illuminated by a transverse magnetic incident electric field. The approach is based on the Lippmann-Schuringer integral equation for the electromagnetic inverse scattering problem, approximated by applying the second-order Born approximation, which allows an extension of the range of contrast values that can be accurately imaged. The numerical approach is developed in the spatial domain and makes use of a multi-illumination multiview processing. In particular, the inverse problem is recast in a global nonlinear optimization problem (including a penalty function), solved by a stochastic method based on a genetic algorithm. In this paper, the mathematical formulation of the approach is described and the results of several dielectric reconstructions are reported, including comparisons with analogous reconstructions performed within the linearized (first-order) Born approximation     

Subsurface Sensing of Buried Objects Under a Randomly Rough Surface Using Scattered Electromagnetic Field Data

This paper proposes a new inverse method for microwave-based subsurface sensing of lossy dielectric objects embedded in a dispersive lossy ground with an unknown rough surface. An iterative inversion algorithm is employed to reconstruct the geometry and dielectric properties of the half-space ground as well as that of the buried object. B-splines are used to model the shape of the object as well as the height of the rough surface. In both cases, the control points for the spline function represent the unknowns to be recovered. A single-pole rational transfer function is used to capture the dispersive nature of the background. Here, the coefficients in the numerator and denominator are the unknowns. The approach presented in this paper is based on the state-of-the-art semianalytic mode matching forward model, which is a fast and efficient algorithm to determine the scattered electromagnetic fields. Numerical experiments involving two-dimensional geometries and TM incident plane waves demonstrate the accuracy and reliability of this inverse method     

埋地三维复杂介质目标电磁散射特性分析

采用混合位积分方程（MPIE）和基于四面体元基函数的矩量法分析计算了埋地三维介质目标电磁散射问题,利用二级离散复镜像（DCIM）和广义函数束（GPOF）相结合的方法求解近场Sommerfeld积分,很好地解决了多层媒质中复杂目标电磁散射计算中的棘手问题,其方法简练、精确、高效,数值分析结果与有关文献吻合很好,证实了该方法的正确性和通用性。此外,该文还通过计算比较了不同观察点、不同目标埋地深度及介质参数的电磁散射特性。     

Derivation and comparison of SAR and frequency-wavenumber migration within a common inverse scalar wave problem formulation

Two common Fourier imaging algorithms used in ground penetrating radar (GPR), synthetic aperture radar (SAR), and frequency-wavenumber (F-K) migration, are reviewed and compared from a theoretical perspective. The two algorithms, while arising from seemingly different physical models: a point-scatterer model for SAR and the exploding source model for F-K migration, result in similar imaging equations. Both algorithms are derived from an integral equation formulation of the inverse scalar wave problem, which allows a clear understanding of the approximations being made in each algorithm and allows a direct comparison. This derivation brings out the similarities of the two techniques which are hidden by the traditional formulations based on physical scattering models. The comparison shows that the approximations required to derive each technique from the integral equation formulation of the inverse problem are nearly identical, and hence the two imaging algorithms and physical models are making similar assumptions about the solution to the inverse problem, thus clarifying why the imaging equations are so similar. Sample images of landmine-like targets buried in sand are obtained from experimental GPR data using both algorithms.     

Electromagnetic scattering interference between two shallow objects buried under 2-D random rough surfaces

A rigorous electromagnetic model has been used to analyze the scattering from two dielectric shallow objects buried under the two-dimensional (2-D) random rough ground (3-D scattering problem) as a means of predicting false alarms. The method of moments (MoM) accelerated by the steepest descent fast multipole method (SDFMM) is used to compute the equivalent electric and magnetic surface currents on all scatterers (i.e., the rough ground and the two buried objects). The roughness parameters influence the scattering interference mechanism of the two objects, however, a large separation distance (e.g., several correlation lengths) showed stronger effect for small ground roughness.     

FDTD分析探地雷达天线的辐射特性

探地雷达系统一般采用超宽带短脉冲信号,因而其天线系统必须具有较好的宽带性能。只有几种类型的宽带天线能够用于探地雷达系统中,如电阻加载的蝶形天线、TEM喇叭天线及其变形形式。本文将给出一种新型的探地雷达天线,该天线为置于镜像面上且具有离散指数电阻加载的单偶极子。文中将采用FDTD计算和分析该天线在自由空间和有耗媒质上方时的辐射特性。结果表明,通过选择一定的电阻加载形式,可使天线具有较好的辐射波形,从而能够满足实际探地雷达的需要。最后,通过地下目标散射场的理论结果和实验结果说明了本文所采用方法的正确性。