Low frequency inverse scattering

Derived is an acoustic and electromagnetic low frequency direct scattering approximation in terms of the characteristic function of a scatterer. An inverse scattering solution for the complete moments tensor of this characteristic function is obtained. It is shown that this inverse scattering solution is a generalization of Rayleigh's law, yielding the Rayleigh law volume of the scatterer for the moments tensor of rank zero. The moments tensors of rank one and two are the spatial position centroid and the principal dimensions (and their spatial orientation) of the scatterer respectively.     

Convexly constrained linear inverse problems: iterativeleast-squares and regularization

We consider robust inversion of linear operators with convex constraints. We present an iteration that converges to the minimum norm least squares solution; a stopping rule is shown to regularize the constrained inversion. A constrained Laplace inversion is computed to illustrate the proposed algorithm     

Solving inverse problems with piecewise linear estimators: from Gaussian mixture models to structured sparsity

A general framework for solving image inverse problems with piecewise linear estimations is introduced in this paper. The approach is based on Gaussian mixture models, which are estimated via a maximum a posteriori expectation-maximization algorithm. A dual mathematical interpretation of the proposed framework with a structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared with traditional sparse inverse problem techniques. We demonstrate that, in a number of image inverse problems, including interpolation, zooming, and deblurring of narrow kernels, the same simple and computationally efficient algorithm yields results in the same ballpark as that of the state of the art.     

High frequency inverse scattering and the Luneberg-Kline asymptoticexpansion

The problem of estimating the relative distance to individual scatterers within a complicated multiscatter target from radar backscattered signals is addressed. The scattered signal amplitudes produced by these scatterers are estimated. Such information can be useful for detection and identification of targets. An extension is described of the linear prediction algorithm for estimating these quantities applied to a signal model given by the Luneberg-Kline asymptotic expansion for electromagnetic scattering. This model includes the geometrical optics signal model as a special case     

An inverse scattering method based on contour deformations by means of a level set method using frequency hopping technique

A shape reconstruction method for electromagnetic tomography based on contour deformations by means of a level set method is proposed. The level set method adds quite valuable features to the inverse procedure such as natural regularization of the contours and automatic breaking and merging capability. The frequency hopping technique turns out to be a key point of the inverse scattering procedure. The numerical results clearly indicate that the use of this inversion algorithm yields to accurate reconstructions of one or several objects from one initial guess object, even with noise-contaminated data and limited coverage of the fields.     

On the Bojarski-Lewis inverse scattering method

We assume that the backscattered electromagnetic far-field of a perfectly conducting scatterer is known for all aspects and for frequencies greater in magnitude than some positive numberm. Then using standard integral equation techniques, we show how numerical instability enters into the Bojarski-Lewis inverse scattering method. Since the assumed knowledge of the backscattered field is even more complete than can be expected with radar, these results show that for radar applications the Bojarski-Lewis method is numerically unstable. Moreover we show, as expected, that the degree of instability depends directly uponm. The more low frequency information we haves (i.e, the smallermis), the more stable the method is. In the concluding remarks is noted a recent constrained Bojarski-Lewis method that overcomes much of the instability of the original unconstrained method studied here.     

Inverse obstacle scattering for homogeneous dielectric cylindersusing a boundary finite-element method

A method for reconstructing the shape and the permittivity of a penetrable homogeneous cylinder is described. It is the extension to penetrable cylinders of a previous work dealing with perfectly conducting cylinders. A low-frequency approximation is used to determine an initial guess. Then, a rigorous boundary integral method permits us to reconstruct arbitrary shapes and complex permittivities. It is based on an iterative conjugate gradient algorithm requiring the solving of two direct diffraction problems only. A simple and original regularization scheme is presented, which ensures the robustness of the algorithm. Numerical examples with lossy embedding media and additional random noise for both E∥ and H∥ polarizations are given     

大尺度电磁散射与逆散射问题的深度学习方法

大尺度电磁散射与逆散射一直是科学研究和工程应用的热点和难点,亟待发展将电磁模型与数据挖掘有机融合的高性能求解方法,针对此,提出了一种针对大尺度电磁散射与逆散射问题的深度学习模型.该模型不仅继承了深度神经网络结构简单、运算速度快等优点,而且还能高精度地解决大尺度电磁散射与逆散射问题.实验结果表明:文中提出的深度学习方法可为解决现有大尺度电磁测算融合和电磁逆散射的计算成本昂贵的难题提供新思路、开辟新方向.     

Two-step inverse scattering method for one-dimensional permittivityprofiles

A numerical method to invert the dielectric permittivity profile from the Riccati equation using the Newton-Kantorovich iterative scheme is described. Instead of handling the equations in terms of usual geometrical depth, we determine the profile as a function of the electromagnetic path length since the convergence and the stability of the solution are found to be significantly better in this case. The initial profile used as a starting point for the inversion is obtained by another method employing successive reconstruction of dielectric interfaces and homogeneous layers in a step-like form. This method, though not always accurate, is fast and well suited for the approximate reconstruction of the profile, thus creating ideal starting conditions for the previous approach. As a result, the computation time is considerably reduced, without using any a priori information. The approach is applicable to both continuous and discontinuous profiles of high contrast and exhibits a good stability of the solution with respect to noisy input data. A lossy medium profile can also be inverted provided the overall thickness of the inhomogeneous slab and the background permittivity are known     

Minimum-time approach to obstacle avoidance constrained by envelope protection for autonomous UAVs

An integrated approach is needed for combining path planning for obstacle avoidance with envelop protection to ensure that a UAV is operated within its safe operational limits while maneuvering in obstacle fields. This paper presents a minimum-time approach to this problem by treating obstacle avoidance and envelope protection as inequality constraints in a state space formulation. The approach is used to study the guidance of a rotary wing UAV for aggressive maneuvering in avoiding an obstacle while staying within its operational envelope. The Nonlinear Trajectory Generator (NTG) is used as a real-time optimization solver, and load factor and rotor flapping angle are considered as limit parameters. A nonlinear simulation model of a rotary wing test bed within the Georgia Tech Unmanned Aerial Vehicle Simulation Tool (GUST) is used to evaluate the proposed approach.     

An inverse scattering approach based on the differential E-formulation

An inverse scattering technique based on the differential E-formulation in the frequency domain is proposed. The inversion is achieved by minimizing a cost functional, taking into account the discrepancy between measured and estimated field values, while the Helmholtz wave equation is set as constraint. The Fre/spl acute/chet derivatives of the cost functional with respect to the scatterer properties are derived analytically by means of the calculus of variations. Edge elements are used for the numerical treatment of the problem.     

A fast convergent method in electromagnetic inverse scattering

The authors present a fast convergent technique of the Born iterative method for nonlinear two-dimensional lossless object profile inversion using time-domain data. The magnitudes of the scattered fields at different frequencies are weighted according to the properties of the object. It is shown that the technique can speed up the convergence of the Born iterative method     

On the feasibility of an inverse scattering method

This communication continues the investigation of Lewis' inverse scattering method started in [1]. The purpose here is first to show that the previously mentioned results can be significantly improved and then to point out the requirements for an experimental setup.     

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     

Time-domain inverse scattering method for cross-borehole radar imaging

In this paper, we consider a solution method of the inverse problem of imaging two-dimensional (2D) objects buried underground by cross-hole radar data in the time domain. In addition to less information on the targets due to restriction on the arrangement of transmitters and receivers than for full-view cases such as imaging of objects in free space, the large search region between boreholes makes solving the inverse problem difficult. Although iterative optimization approaches take long computing time, these approaches give much better image qualities for high-contrast objects than linear inversions such as a diffraction tomography. However, the reconstruction in a large search region with limited-view measurements often fails trapped in a local minimum. To overcome this difficulty, we propose a two-step iterative approach: the first step is to reduce the search region to a smaller one and the second step is the accurate reconstruction of the targets in the small region. Both steps are based on an iterative optimization approach, i.e., the forward-backward time-stepping method previously proposed. This two-step approach is tested for detection of tunnel-like objects surrounded by a heterogeneous background medium to evaluate its performance. Numerical results indicate the efficiency of the approach and its ability of circumventing local minima.     

基于稳健自适应频率采样的宽频电磁数值仿真

已有的基于Stoer-Bulirsch有理函数插值的自适应频率采样算法往往对插值间隔、收敛精度等参数非常敏感,算法稳定性差,甚至会出现伪收敛等问题.针对已有算法的上述缺陷,通过采用极点判断、插值区域二分、参数变换和多次收敛性检验等措施,提出了一种逐一增加采样点的自适应策略.形成了一种通用性强、稳定性好的自适应频率采样算法,可以用较少的采样点插值重构未知函数响应.并结合多层快速多极子方法,对宽频带目标电磁散射进行计算分析,实现采样频点的自适应选取,减少了计算量极大的精确数值计算的次数,提高了仿真效率.     

Experimental verification of a linear inverse scattering algorithm for the localization of planar interfaces

The problem of the localization and the determination of the extent of a void layer embedded in a masonry structure starting from the knowledge of the scattered field is addressed. The problem is recast as the subsequent localization of single interfaces by using an inverse scattering approach in frequency domain. Each interface is searched by assuming the dielectric properties of the wall known and inverting an appropriate linear model. Experimental validation of the approach is performed by means of scattered field measurements collected at different frequencies in controlled conditions for a tuff masonry illuminated by a bow-tie antenna.     

An adaptive multiscale inverse scattering approach to photothermal depth profilometry

Photothermal depth profilometry is formulated as a nonlinear inverse scattering problem. Starting with the one-dimensional heat diffusion equation, we derive a mathematical model relating arbitrary variation in the depth-dependent thermal conductivity to observed thermal wavefields at the surface of a material sample. The form of the model is particularly convenient for incorporation into a nonlinear optimization framework for is particularly convenient for incorporation into a nonlinear optimization framework for recovering the conductivity based on thermal wave data obtained at multiple frequencies. We develop an adaptive, multiscale algorithm for solving this highly ill-posed inverse problem. The algorithm is designed to produce an accurate, low-order representation of the thermal conductivity by automatically controlling the level of detail in the reconstruction. This control is designed to reflect both (1) the nature of the underlying physics, which says that scale should decrease with depth, and (2) the particular structure of the conductivity profile, which may require a sparse collection of fine-scale components to adequately represent significant features such as a layering structure. The approach is demonstrated in a variety of synthetic examples representative of nondestructive evaluation problems seen in the steel industry.The work of authors E. L. Miller and I. Yavuz was supported by a CAREER Award from the National Science Foundation MIP-9623721, an ODDR&E MURI under Air Force Office of Scientific Research contract F49620-96-1-0028, and the Army Research Office Demining MURI under grant DAAG55-97-1-0013. The work of authors L. Nicolaides and A. Mandelis was supported by a research contract from Material and Manufacturing Ontario (MMO).     

一种基于单形体正化的高光谱数据全约束线性解混方法

在端元已知情况下,线性混合模型的非负约束最小二乘无闭式解,需要多次迭代得收敛最优解,时间复杂度高.通过高光谱数据凸面几何特性分析,指出当数据为正单形体时,可经有限步骤快速得线性混合模型最优解.据此提出一种单形体正化的高光谱数据全约束线性解混方法,据已知端元进行单形体正化,采用和为一约束求解丰度系数,最后迭代剔除丰度负值端元得全约束解.实验结果表明该方法可获得传统全约束解一致的丰度估计,且效率大大提升.     

A high frequency inverse scattering model to recover the specular point curvature from polarimetric scattering matrix data

Based on the time-domain first-order correction to the physical optics current approximation, a relationship between the phase factors of the polarimetric scattering matrix elements and the principal curvatures at the specular point of a scatterer is established. The above phase-curvature relationship is tested by applying it to theoretical as well as experimental backscattering data obtained from a prolate spheroidal scatterer. The results of these tests not only determine the acceptability of the phase-curvature relationship; they also point out the spectral range over which the first-order correction to the physical optics currents is valid.