Computational approach based on a particle swarm optimizer for microwave imaging of two-dimensional dielectric scatterers

A computational approach based on an innovative stochastic algorithm, namely, the particle swarm optimizer (PSO), is proposed for the solution of the inverse-scattering problem arising in microwave-imaging applications. The original inverse-scattering problem is reformulated in a global nonlinear optimization one by defining a suitable cost function, which is minimized through a customized PSO. In such a framework, this paper is aimed at assessing the effectiveness of the proposed approach in locating, shaping, and reconstructing the dielectric parameters of unknown two-dimensional scatterers. Such an analysis is carried out by comparing the performance of the PSO-based approach with other state-of-the-art methods (deterministic, as well as stochastic) in terms of retrieval accuracy, as well as from a computational point-of-view. Moreover, an integrated strategy (based on the combination of the PSO and the iterative multiscaling method) is proposed and analyzed to fully exploit complementary advantages of nonlinear optimization techniques and multiresolution approaches. Selected numerical experiments concerning dielectric scatterers different in shape, dimension, and dielectric profile, are performed starting from synthetic, as well as experimental inverse-scattering data.     

Fast and accurate solutions of extremely large integral-equation problems discretised with tens of millions of unknowns

The solution of extremely large scattering problems that are formulated by integral equations and discretised with tens of millions of unknowns is reported. Accurate and efficient solutions are performed by employing a parallel implementation of the multilevel fast multipole algorithm. The effectiveness of the implementation is demonstrated on a sphere problem containing more than 33 million unknowns, which is the largest integral-equation problem ever solved to our knowledge     

Two-dimensional SPICE-linked multiresolution impedance method for low-frequency electromagnetic interactions

A multiresolution impedance method for the solution of low-frequency electromagnetic interaction problems typically encountered in bioelectromagnetics is presented. While the impedance method in its original form is based on the discretization of the scattering objects into equal-sized cells, our formulation decreases the number of unknowns by using an automatic mesh generation method that does not yield equal-sized cells in the modeling space. Results indicate that our multiresolution mesh generation scheme can provide a 50%-80% reduction in cell count, providing new opportunities for the solution of low-frequency bioelectromagnetic problems that require a high level of detail only in specific regions of the modeling space. Furthermore, linking the mesh generator to a circuit simulator such as SPICE permits the addition of arbitrarily complex passive and active circuit elements to the generated impedance network, opening the door to significant advances in the modeling of bioelectromagnetic phenomena.     

An overview of the hybrid MM/Green's function method inelectromagnetics

An overview is presented of a hybrid technique for solving electromagnetic radiation and scattering problems by combining the method of moments (MM) with a special Green's function. The method, referred to as an MM/Green's function solution, combines the ability of MM solutions to treat geometrically complex bodies with the accuracy and computational efficiency of Green's function solutions. Compared to a standard MM solution, the MM/Green's function solution reduces the number of unknowns and thus the computer storage requirements. In most cases the CPU time for the MM/Green's function solution is considerably less than that for a standard MM solution. An example problem of TM scattering by a semicircular strip in the presence of a circular cylinder is solved by the MM, and by the MM/Green's function technique with a matrix, exact eigenfunction, and high-frequency Green's function     

Lossless inverse scattering, digital filters, and estimation theory

Methods to construct rational solutions of the lossless inverse scattering (LIS) problem for one-port passive digital systems are described. The first method is recursive and can be viewed as a generalization of the celebrated Schur algorithm. The second method is global and leads to a parametrization of what we call fundamental solutions from which all LIS solutions may be constructed. Quite a few classical problems in estimation theory and network theory may be viewed as special cases of the LIS problem. With each fundamental solution there is a solution of a corresponding estimation problem leading to a prediction and a modeling filter for a given stochastic process.     

An Analytical Methodology for Solving Complex Stochastic Network Problems

An analytical methodology (GERT) using the linear signal flowgraph topology is recommended for solution of problems related to complex stochastic networks, as a convenient alternative to commonly used Monte Carlo simulation technique. The novelty of this paper is in the use Laplace transforms in defining thewfunction associated with each branch of the network, which permits solution of the network in its entirety. Adaptability of stochastic networks in a valid representation of common control system delay problems and capability of the analytical methodology in obtaining solutions by a mechanistic procedure are illustrated by analyzing a register access delay problem. Finally, the analytical solution is compared with Monte Carlo simulation results.     

Solution of inverse problems in image processing by waveletexpansion

We describe a wavelet-based approach to linear inverse problems in image processing. In this approach, both the images and the linear operator to be inverted are represented by wavelet expansions, leading to a multiresolution sparse matrix representation of the inverse problem. The constraints for a regularized solution are enforced through wavelet expansion coefficients. A unique feature of the wavelet approach is a general and consistent scheme for representing an operator in different resolutions, an important problem in multigrid/multiresolution processing. This and the sparseness of the representation induce a multigrid algorithm. The proposed approach was tested on image restoration problems and produced good results.     

Detection, location, and imaging of multiple scatterers by means of the iterative multiscaling method

In this paper, a new version of the iterative multiscaling method (IMM) is proposed for reconstructing multiple scatterers in two-dimensional microwave imaging problems. This paper describes the new procedure evaluating the effectiveness of the IMM previously assessed for single object detection. Starting from inverse scattering integral equations, the problem is recast in a minimization one by defining iteratively (at each level of the scaling procedure) a suitable cost function, firstly allowing a detection of the unknown objects, successively a location of the scatterers, and finally, a quantitative reconstruction of the scenario under test. Thanks to its properties, the approach allows an effective use of the information achievable from inverse scattering data. Moreover, the adopted kind of expansion is able to deal with all possible multiresolution combinations in an easy and computationally inexpensive way. Selected numerical examples concerning dielectric, as well as dissipative objects in noisy environments or starting from experimentally acquired data are reported in order to confirm the usefulness of the introduced tool and of the effectiveness of the proposed procedure.     

A multilevel formulation of the finite-element method forelectromagnetic scattering

Multigrid techniques for three-dimensional (3-D) electromagnetic scattering problems are presented. The numerical representation of the physical problem is accomplished via a finite-element discretization, with nodal basis functions. A total magnetic field formulation with a vector absorbing boundary condition (ABC) is used. The principal features of the multilevel technique are outlined. The basic multigrid algorithms are described and estimations of their computational requirements are derived. The multilevel code is tested with several scattering problems for which analytical solutions exist. The obtained results clearly indicate the stability, accuracy, and efficiency of the multigrid method     

A Multiresolution Stochastic Level Set Method for Mumford–Shah Image Segmentation

The Mumford–Shah model is one of the most successful image segmentation models. However, existing algorithms for the model are often very sensitive to the choice of the initial guess. To make use of the model effectively, it is essential to develop an algorithm which can compute a global or near global optimal solution efficiently. While gradient descent based methods are well-known to find a local minimum only, even many stochastic methods do not provide a practical solution to this problem either. In this paper, we consider the computation of a global minimum of the multiphase piecewise constant Mumford–Shah model. We propose a hybrid approach which combines gradient based and stochastic optimization methods to resolve the problem of sensitivity to the initial guess. At the heart of our algorithm is a well-designed basin hopping scheme which uses global updates to escape from local traps in a way that is much more effective than standard stochastic methods. In our experiments, a very high-quality solution is obtained within a few stochastic hops whereas the solutions obtained with simulated annealing are incomparable even after thousands of steps. We also propose a multiresolution approach to reduce the computational cost and enhance the search for a global minimum. Furthermore, we derived a simple but useful theoretical result relating solutions at different spatial resolutions.      

Multimode network representations for the scattering by an array ofthick parallel plates

In this paper, we describe two multimode network representations for the analysis of radiating array of thick parallel plates. Due to periodicity and infinite extent, only one period of the structure needs to be studied. The key step is then the derivation of the equivalent network representation for the transition from a free-space region limited by phase-shift walls to a parallel plate waveguide. Two solutions to the problem are discussed. In the first solution, the relevant boundary value problem is cast into a network form that leads to an integral equation. The equation is then solved with the method of moments (MoMs). In the second solution, the elements of the multimode coupling matrix representing the grating are evaluated directly in terms of their network definition. The two solutions are then compared and the relative merits are discussed. The main feature of the approach presented in this paper, is that once the network representation of the key transition is obtained, it allows for the study of a wide class of scattering problems involving, for instance, corrugated surfaces and single or cascaded thick gratings. Comparison with published data are also presented, indicating that the two network representations developed are indeed very accurate     

Scattering by Abrupt Discontinuities on Planar Dielectric Waveguides

Two unifying aspects of the problem of scattering by an abrupt discontinuity on a planar dielectric waveguide are considered. The first aspect is concerned with the numerical solution of the scattering problem through consideration of a corresponding bounded waveguide problem in which perfect electric or magnetic conductor bounds with variable locations are introduced. It is shown that the solutions to the bounded problem, when numerically integrated over a range of bound locations defined within half a wavelength, allow the complete mode spectra of the unbounded waveguide to be accurately accounted for. Scattering solutions for both TE- and TM-modes are presented for a wide range of discontinuities and, in the TE-mode case, are in agreement with results obtained using the method due to Rozzi [5]. The second aspect is concerned with the relationship between scattering and "inter-waveguide mode orthogonality." Based on a simple iterative scheme, a meaningful physical interpretation of the scattering process is developed. This allows the scattering to be classified as being of first or higher order, to be explained in terms of the physical characteristics of the mode fields.     

A multiscale, statistically based inversion scheme for linearizedinverse scattering problems

The application of multiscale and stochastic techniques to the solution of a linearized inverse scattering problem is presented. This approach allows for the explicit and easy handling of many difficulties associated with problems of this type. Regularization is accomplished via the use of a multiscale prior stochastic model which offers considerable flexibility for the incorporation of prior knowledge and constraints. the authors use the relative error covariance matrix (RECM), introduced by E.L. Miller et al. (1995), as a tool for quantitatively evaluating the manner in which data contribute to the structure of a reconstruction. Given a set of scattering experiments, the RECM is used for understanding and analyzing the process of data fusion and allows the authors to define the space-varying optimal scale for reconstruction as a function of the nature (resolution, quality, and distribution of observation points) of the available measurement sets. Examples of the authors' multiscale inversion algorithm are presented using the Born approximation of an inverse electrical conductivity problem formulated so as to illustrate many of the features associated with inverse scattering problems arising in fields such as geophysical prospecting and medical imaging     

On the use of spatio-temporal multiresolution analysis in method ofmoments solutions of transient electromagnetic scattering

A novel method of moments approach to the solution of time-domain integral-equation formulation of electromagnetic scattering problems is presented. The method is based on a spatio-temporal multiresolution analysis. This analysis facilitates a basis from which a small number of expansion functions is selected via an iterative procedure and utilized to model the unknown current distribution. In contrast to marching-on-in-time sequential procedures, the proposed method models the unknown current simultaneously at all the time steps within the time frame of interest. This new method is applied to a one-dimensional (1-D) problem of electromagnetic plane wave interaction with a dielectric slab. A comparison of the computed results with results based on the analytic solution demonstrates that the method is capable of attaining accurate results while achieving substantial reduction in computation time and resources     

Wavelet analysis of radar echo from finite-size targets

The wavelet analysis technique is applied to analyze the frequency-domain electromagnetic backscattered signal from finite-size targets. Since the frequency-domain radar echo consists of both small-scale natural resonances and large-scale scattering center information, the multiresolution property of the wavelet transform is well suited for analyzing such multiscale signals. Wavelet analysis examples of backscattered data from an open-ended waveguide cavity and a plasma cylinder are presented. Compared with the conventional short-time Fourier transform, the wavelet transform provides a more efficient representation of both the early-time scattering center data and the late-time resonances. The different scattering mechanisms are clearly resolved in the time-frequency representation     

一类随机动态过程基于q阶树的多尺度建模方法

利用多尺度随机模型能建立处理问题有效并行算法的这一优势,提出一类随机动态过程基于一般q阶树的多尺度建模方法。首先,利用Markov过程的条件独立性给出一类过程基于q阶树的多尺度表示方法;其次,基于q阶树多尺度表示和具体实例推导出多尺度模型中的状态转移矩阵、扰动阵、初始状态和相应的协方差矩阵等的具体形式,为具有Markov统计特性的过程或信号建立起多尺度随机模型,这将为有效地解决多源同类信息和多源异类信息的数据融合等实际问题提供了理论基础;最后,给出一类Gauss-Markov过程基于三阶树和五阶树多尺度表示的计算机仿真结果,进一步验证建立模型的实用性和有效性。     

Combining an extrapolation technique with the method of moments forsolving large scattering problems involving bodies of revolution

The purpose of this work is to combine an extrapolation technique with the method of moments (MoM) to solve scattering problems involving large bodies. It has been shown in a previous work that the current induced on the smooth parts of large scatterers may be represented as a series of complex exponential functions with a few terms. Based on this concept, a hybrid set of basis functions is constructed using entire domain functions of complex exponential type on the smooth portion of the scatterer, complemented by subdomain basis functions near edges and discontinuities. An extrapolation procedure is developed in which the scattering problem is first solved for a portion of the scatterer using the conventional MoM. Next, a set of entire-domain basis functions, whose behaviour could be extrapolated with an increase in the size of the scatterer, is extracted from this original solution. The procedure outlined has the very desirable feature that the total number of basis functions remains unchanged even as the scatterer size is increased, allowing for large scatterers to be handled with a relatively small number of unknowns. The extrapolation technique is applied to scattering problems from bodies of revolution (BORs), and numerical results for an open cylinder and a barrel-shaped BOR are presented     

Adaptive multiscale moment method (AMMM) for analysis of scatteringfrom perfectly conducting plates

Adaptive multiscale moment method (AMMM) is presented for the analysis of scattering from a thin perfectly conducting plate. This algorithm employs the conventional moment method and a special matrix transformation, which is derived from the tensor products of the two one-dimensional (1-D) multiscale triangular basis functions that are used for expansion and testing functions in the conventional moment method. The special feature of these new basis functions introduced through this transformation is that they are orthogonal at the same scale except at the initial scale and not between scales. From one scale to another scale, the initial estimate for the solution can be predicted using this multiscale technique. Hence, the compression is applied directly to the solution and the size of the linear equations to be solved is reduced, thereby improving the efficiency of the conventional moment method. The basic difference between this methodology and the other techniques that have been presented so far is that we apply the compression not to the impedance matrix, but to the solution itself directly using an iterative solution methodology. The extrapolated results at the higher scale thus provide a good initial guess for the iterative method. Typically, when the number of unknowns exceeds a few thousand unknowns, the matrix solution time exceeds generally the matrix fill time. Hence, the goal of this method is directed in solving electrically larger problems, where the matrix solution time is of concern. Two numerical results are presented, which demonstrate that the AMMM is a useful method to analyze scattering from perfectly conducting plates     

A Hierarchical Partitioning Strategy for an Efficient Parallelization of the Multilevel Fast Multipole Algorithm

We present a novel hierarchical partitioning strategy for the efficient parallelization of the multilevel fast multipole algorithm (MLFMA) on distributed-memory architectures to solve large-scale problems in electromagnetics. Unlike previous parallelization techniques, the tree structure of MLFMA is distributed among processors by partitioning both clusters and samples of fields at each level. Due to the improved load-balancing, the hierarchical strategy offers a higher parallelization efficiency than previous approaches, especially when the number of processors is large. We demonstrate the improved efficiency on scattering problems discretized with millions of unknowns. In addition, we present the effectiveness of our algorithm by solving very large scattering problems involving a conducting sphere of radius 210 wavelengths and a complicated real-life target with a maximum dimension of 880 wavelengths. Both of the objects are discretized with more than 200 million unknowns.      

A multiresolution study of effective properties of complexelectromagnetic systems

A systematic study of the across-scale coupling phenomenology in electromagnetic (EM) scattering problems is addressed using the theory of multiresolution decomposition and orthogonal wavelets. By projecting an integral equation formulation of the scattering problem onto a set of subspaces that constitutes a multiresolution decomposition of L₂ (R), one can derive two coupled formulations. The first governs the macroscale response, and the second governs the microscale response. By substituting the formal solution of the latter in the former, a new self-consistent formulation that governs the macroscale response component is obtained. This formulation is written on a macroscale grid, where the effects of the microscale heterogeneity are expressed via an across-scale coupling operator. This operator can also be interpreted as representing the effective properties of the microstructure. We study the properties of this operator versus the characteristics of the Green function and the microstructure for various electromagnetic problems, using general asymptotic considerations. A specific numerical example of TM scattering from a laminated complex structure is provided