An integrated multiscaling strategy based on a particle swarm algorithm for inverse scattering problems

The application of a multiscale strategy integrated with a stochastic technique to the solution of nonlinear inverse scattering problems is presented. The approach allows the explicit and effective handling of many difficulties associated with such problems ranging from ill-conditioning to nonlinearity and false solutions drawback. The choice of a finite dimensional representation for the unknowns, due to the upper bound to the essential dimension of the data, is iteratively accomplished by means of an adaptive multiresolution model, which offers a considerable flexibility for the use of the information on the scattering domain acquired during the iterative steps of the multiscaling process. Even though a suitable representation of the unknowns could limit the local minima problem, the multiresolution strategy is integrated with a customized stochastic optimizer based on the behavior of a particle swarm, which prevents the solution from being trapped into false solutions without a large increasing of the overall computational burden. Selected examples concerned with a two-dimensional microwave imaging problem are presented for illustrating the key features of the integrated stochastic multiscaling strategy.     

介质散射的双线性高阶叠层基函数矩量法分析

提出了一种基于双线性思想的高阶基函数降低矩量法分析介质目标电磁散射问题时的未知量.论文给出了双线性高阶叠层基函数的构造过程, 并将其应用于介质的面积分方程分析中.数值算例比较了不同阶数时所需未知量以及计算精度, 表明该高阶叠层基函数在满足相同积分方程的计算精度时能比低阶基函数节省未知量.     

Effective exploitation of the a priori information through a microwave imaging procedure based on the SMW for NDE/NDT applications

This paper presents an innovative microwave technique, which is suitable for the detection of defects in nondestructive-test and nondestructive-evaluation (NDT/NDE) applications where a lot of a priori information is available. The proposed approach is based on the equations of the inverse scattering problem, which are solved by means of a minimization procedure based on a genetic algorithm. To reduce the number of problem unknowns, the available a priori information is efficiently exploited by introducing an updating procedure for the electric field computation based on the Sherman-Morrison-Woodbury formula. The results of a representative set of numerical experiments as well as comparisons with state-of-the-art methods are reported. They confirm the effectiveness, feasibility, and robustness of the proposed approach, which shows some interesting features by a computational point of view as well.     

二维有耗介质目标重建的Newtoin迭代方法

本文给出了一种由已知的散射场数据重建二线非均匀有耗目标的复介电常数的迭代算法。由积分方程出发，利用点匹配技术导出了依赖于未知参数的解析逆散射公式。由此可以以解析的形式计算场量对未知参数的导数（Jacobian和Hessian矩阵）。本文采用Newton优化方法迭代末解道散射问题，具有二次收敛特性。为了克服逆散射中解的不适定性，连续采用多个方向的TM波照射目标，并采集目标区域外的散射场数据，以及采用共轭梯度法（CGM）求解逆问题．数值结果表明了本文所提方法的可行性和灵活性。     

A boundary element approach to the scattering from inhomogeneousdielectric bodies

A boundary element method (BEM) for the analysis of the electromagnetic scattering from inhomogeneous dielectric structures is presented. The problem is formulated in terms of a single integral equation reducing by half the number of unknowns required with respect to a conventional approach based on two coupled integral equations     

Efficient electromagnetic analysis of line-fed aperture antennas in thick conducting screens

This paper presents a numerical and experimental verification of an approximate but efficient integral equation technique for the scattering by apertures in conducting planes with finite thicknesses. The approach is based on a perturbation method and modified Green's functions that take into account the finite metallization thickness. The computational effort and time needed for solving the problem are the same as in zero-thickness case. When compared to full-wave cavity treatment of thick apertures, the method is (depending on the number of unknowns) at least an order of magnitude faster. The method can be applied even to apertures of arbitrary shapes where computing the cavity's Green's functions is a difficult task. The results of simulations using the new approach show good agreement when compared to both results from full-wave cavity approach and measurements.     

Reduction of the number of unknowns in large stacked planarstructures by a fringe aperture formulation

For scattering problems comprising a combination of planar structures, the total number of unknowns may be significantly reduced if an aperture formulation is employed rather than a patch formulation. The rationale behind using the aperture formulation is based on the recognition that the decay rate of the scattered aperture field is independent of the size of the scatterer. Therefore, any scatterer may be surrounded by an aperture of fixed width over which an integral equation is formulated. The area of this aperture is proportional to the perimeter of the scatterer rather than its area, and it becomes much smaller compared with the entire scatterer area as the size of the scatterer increases, hence the reduction in the number of independent unknowns. A truncation criterion for the finite aperture is determined via a numerical study of the aperture field behavior for various angles of incidence. In addition, the a priori knowledge of the physical optics component is also taken into account, reducing the unknown function to an aperture field component that is the outcome of the remaining fringe current only. The total current distribution can be subsequently derived from this field by adding the known physical optics field and invoking the inverse of the Green's function in the spectral domain. This analysis of isolated planar scatterers results in a spectral scattering matrix representation that is subsequently used for cascading of stacked structures     

Boundary integrodifferential equations for electromagnetic scattering problems in three dimensions

On the basis of two vector representations of electromagnetic fields we introduce a new system of boundary integrodifferential equations for the solution of scattering problems in three dimensions. The unknowns of this system present two scalar functions, namely, the "" coefficients of Atkinson-Wilcox expansion; electromagnetic field being reconstructed with these functions by means of certain recursive-differential operators. We define an algebraic analog of the equations by expanding unknowns into Fourier series with respect to spherical harmonics. Verification of the approach is done on the basis of the solution of well-known canonical problems.     

Genetic algorithms as applied to the numerical computation ofelectromagnetic scattering by weakly nonlinear dielectric cylinders

This paper deals with the application of an optimization procedure based on a genetic algorithm (GA) to the prediction of the electromagnetic fields scattered by weakly nonlinear dielectric objects. Starting by an integral approach and describing the nonlinearities of the constitutive parameters by the Volterra-type integrals, the nonlinear scattering problem is numerically solved by an iterative procedure developed for the minimization of a suitable defined cost function. A GA is applied in order to deal with a large number of unknowns related to the harmonic components of the nonlinear internal electromagnetic field. In a preliminary stage, the behavior of typical parameters of the GA is analyzed; then numerical solutions are carried out and compared with those provided by other methods. Finally, some considerations are made concerning the rate of convergence of the iterative procedure     

Absorbing boundary conditions on arbitrary boundaries for thescalar and vector wave equations

The solution of open region scattering problems involving inhomogeneous arbitrarily shaped objects may be performed through the use of partial differential equation techniques, which require enclosing the scatterer by an outer boundary on which an absorbing boundary condition (ABC) is applied. In order to minimize the size of the domain to be meshed and, consequently, the number of unknowns, if may be advisable to implement ABC's devised for outer boundaries of arbitrary shapes. Such ABC's are obtained for the 3D scalar and vector wave equations; they incorporate most of existing boundary conditions. When used in conjunction with a finite element technique, the numerical results derived by using a simplified form of these ABC's compare favourably to those obtained by using a rigorous hybrid finite element-integral equation formulation. These boundary conditions have been obtained in the frequency-domain framework; they may, however, be used in time-domain calculations     

基于DSM-CSI的非线性逆散射算法研究

由于反演问题中散射体所处区域和散射体个数信息的缺失,进而导致非线性逆散射方法的待重构空间维数高和运算代价高。基于线性逆散射方法在重构目标区域和目标个数信息的计算代价低,本文提出一种DSM（Di-rect Sampling Method）线性方法和CSI（Contrast Source Inversion）非线性方法相结合的非线性逆散射方法。该方法利用DSM方法的重构结果为CSI方法提供散射体所处区域和散射体个数的先验信息,进而降低待重构空间的维数以及非线性逆散射问题的计算量。实验计算结果证明了该方法的有效性。     

Fast spectral domain algorithm for rapid solution of integralequations

A fast spectral domain algorithm is presented for rapid solution of planar surface integral equations. The method of moments coupling integral matrix is formulated in the spectral domain but not explicitly calculated. Thus, in conjunction with an iterative equation solver, the pertinent matrix/vector products are evaluated with complexity O(n) where n is the number of unknowns. Validation and timing results are presented for an array analysis approach using a hybrid finite element (FE)-boundary integral implementation     

Joint state filtering and parameter estimation for linear stochastic time-delay systems

This paper presents the joint state filtering and parameter estimation problem for linear stochastic time-delay systems with unknown parameters. The original problem is reduced to the mean-square filtering problem for incompletely measured bilinear time-delay system states over linear observations. The unknown parameters are considered standard Wiener processes and incorporated as additional states in the extended state vector. To deal with the new filtering problem, the paper designs the mean-square finite-dimensional filter for incompletely measured bilinear time-delay system states over linear observations. A closed system of the filtering equations is then derived for a bilinear time-delay state over linear observations. Finally, the paper solves the original joint estimation problem. The obtained solution is based on the designed mean-square filter for incompletely measured bilinear time-delay states over linear observations, taking into account that the filter for the extended state vector also serves as the identifier for the unknown parameters. In the example, performance of the designed state filter and parameter identifier is verified for a linear time-delay system with an unknown multiplicative parameter over linear observations.     

Scattering by an indentation satisfying a dyadic impedance boundarycondition

We derive a pair of boundary integral equations for the problem of scattering of an electromagnetic wave by an indentation in a perfectly conducting screen. The wall of the indentation obeys a dyadic impedance boundary condition. The unknowns are the electric current density on the wall of the indentation and the total tangential magnetic field in the opening of the indentation. We also derive integral representations for the fields everywhere in free space, including the far-field region. In all cases, the integrals involved extend over finite surfaces only     

Robust Kalman Filter Design for Markovian Jump Linear Systems with Norm-Bounded Unknown Nonlinearities

This paper considers the problems of stability and filtering for a class of linear hybrid systems with nonlinear uncertainties and Markovian jump parameters. The hybrid system under study involves a continuous-valued system state vector and a discretevalued system mode. The unknown nonlinearities in the system are time varying and norm bounded. The Markovian jump parameters are modeled by a Markov process with a finite number of states. First, we show the equivalence of the sets of norm-bounded linear and nonlinear uncertainties. Then, instead of the original hybrid linear system with nonlinear uncertainties, we consider the same system with linear uncertainties. By using a Riccati equation approach for this new system, a robust filter is designed using two sets of coupled Riccati-like equations such that the estimation error is guaranteed to have an upper bound.     

An effective near-field far-field transformation technique fromtruncated and inaccurate amplitude-only data

A general approach to the near-field far-field transformation from amplitude only near-field data is presented. The estimation of the far field is stated as an intersection finding problem and is solved by the minimization of a suitable functional. The difficulties related to the possible trapping of the algorithm by a false solution (common to any nonlinear inverse problem) are mitigated by setting the problem in the space of the squared field amplitudes (as already done in a number of existing papers) and by incorporating all the a priori knowledge concerning the system under test in the formulation of the problem. Accordingly, the a priori information concerning the far field, the near field outside the measurement region and the accuracy of the measurement setup and its dynamic range are properly taken into account in the objective functional. The intrinsic ill conditioning of the problem is managed by adopting a general, flexible, and nonredundant sampling representation of the field, which takes into account the geometrical characteristics of the source. As a consequence, the number of unknowns is minimized and a technique is obtained, which easily matches the available knowledge concerning the behavior of the field. The effectiveness of the approach is shown by reporting the main results of an extensive numerical analysis, as well as an experimental validation performed by using a very low cost near field facility available at the Electronic Engineering Department, University of Napoli, Italy     

Image recovery from Fourier domain measurements via classification using Bayesian approach and total variation regularization

In this paper we propose a Potts–Markov prior and total variation regularization associated with Bayesian approach to simultaneously reconstruct and segment piecewise homogeneous images in Fourier synthesis inverse problem. When the observed data do not fill uniformly the Fourier domain which is the case in many applications in tomographic imaging, or when the phase of the signal is lacking as in optical interferometry the results obtained by deterministic methods are not satisfactory. Such inverse problem is known to be nonlinear and ill-posed. It then needs to be regularized by introducing prior information. The particular a priori information on which we rely is the fact that the image is composed of a different regions finite known number. Such an appropriate modeling of the image gives the possibility of compensating the lack of information in the data thus giving satisfactory results. We define the appropriate Potts–Markov model to define parameters of label regions for such images and total variation to be used in a Bayesian estimation framework.     

Electromagnetic imaging for an imperfectly conducting cylinder

A computational approach to the imaging or inverse scattering of an imperfectly conducting cylinder is presented. A conducting cylinder of unknown shape and conductivity scatters the incident wave in free space and the scattered field is recorded on a circle surrounding the scatterer. By properly processing the scattered data, the shape and conductivity of the scatterer can be reconstructed. The problem is formulated in the form of nonlinear integral equations, which can be solved numerically by the Newton-Kantorovitch algorithm. The pseudoinverse technique is used to overcome the ill-posedness, and the condition number of the matrix is also discussed. Numerical examples are given to illustrate the capability of the inversion algorithm using the simulated scattered fields in both near and far zones. Multiple incident directions permit good reconstruction of shape and, to a lesser extent, conductivity in the presence of noise in measured data     

Three-Dimensional Microwave Breast Imaging: Dispersive Dielectric Properties Estimation Using Patient-Specific Basis Functions

Breast imaging via microwave tomography involves estimating the distribution of dielectric properties within the patient's breast on a discrete mesh. The number of unknowns in the discrete mesh can be very large for 3-D imaging, and this results in computational challenges. We propose a new approach where the discrete mesh is replaced with a relatively small number of smooth basis functions. The dimension of the tomography problem is reduced by estimating the coefficients of the basis functions instead of the dielectric properties at each element in the discrete mesh. The basis functions are constructed using knowledge of the location of the breast surface. The number of functions used in the basis can be varied to balance resolution and computational complexity. The reduced dimension of the inverse problem enables application of a computationally efficient, multiple-frequency inverse scattering algorithm in 3-D. The efficacy of the proposed approach is verified using two 3-D anatomically realistic numerical breast phantoms. It is shown for the case of single-frequency microwave tomography that the imaging accuracy is comparable to that obtained when the original discrete mesh is used, despite the reduction of the dimension of the inverse problem. Results are also shown for a multiple-frequency algorithm where it is computationally challenging to use the original discrete mesh.