Jiguang Sun

Through-Wall Detection of Human Being's Movement by UWB Radar

Ultrawideband (UWB) radar technology has emerged as one of the preferred choices for through-wall detection due to its high range resolution and good penetration. The resolution is a result of high bandwidth of UWB radar and helpful for better separation of multiple targets in complex environment. Detection of human targets through a wall is interesting in many applications. One significant characteristic of human is the periodic motion, such as breathing and limb movement. In this letter, we apply the UWB radar system in through-wall human detection and present the methods based on fast Fourier transform and S transform to detect and identify the humans life characteristic. In particular, we can extract the center frequencies of life signals and locate the position of human targets from experimental data with high accuracy. Compared with other research studies in through-wall detection, this letter is concentrated in the processing and identifying of the life signal under strong clutter. It has a high signal-to-noise ratio and simpler to implement in complex environment detection. We can use the method to search and locate the survivor trapped under the building debris during earthquake, explosion, or fire.

The inverse electromagnetic scattering problem for anisotropic media

The inverse electromagnetic scattering problem for anisotropic media plays a special role in inverse scattering theory due to the fact that the (matrix) index of refraction is not uniquely determined from the far field pattern of the scattered field even if multi-frequency data are available. In this paper, we describe how transmission eigenvalues can be determined from the far field pattern and be used to obtain upper and lower bounds on the norm of the index of refraction. Numerical examples will be given for the case when the scattering object is an infinite cylinder and the inhomogeneous medium is orthotropic.

Analytical and computational methods for transmission eigenvalues

The interior transmission problem is a boundary value problem that arises in the scattering of time-harmonic waves by an inhomogeneous medium of compact support. The associated transmission eigenvalue problem has important applications in qualitative methods in inverse scattering theory. In this paper, we first establish optimal conditions for the existence of transmission eigenvalues for a spherically stratified medium and give numerical examples of the existence of both real and complex transmission eigenvalues in this case. We then propose three finite element methods for the computation of the transmission eigenvalues for the cases of a general non-stratified medium and use these methods to investigate the accuracy of recently established inequalities for transmission eigenvalues.

Iterative Methods for Transmission Eigenvalues

Transmission eigenvalues have important applications in inverse scattering theory. They can be used to obtain useful information of the physical properties, such as the index of refraction, of the scattering target. Despite considerable effort devoted to the existence and estimation for the transmission eigenvalues, the numerical treatment is limited. Since the problem is nonstandard, classical finite element methods result in non-Hermitian matrix eigenvalue problems. In this paper, we focus on the computation of a few lowest transmission eigenvalues which are of practical importance. Instead of a non-Hermitian problem, we work on a series of generalized Hermitian problems. We first use a fourth order reformulation of the transmission eigenproblem to construct functions involving an associated generalized eigenvalue problem. The roots of these functions are the transmission eigenvalues. Then we apply iterative methods to compute the transmission eigenvalues. We show the convergence of the numerical schemes. The effectiveness of the methods is demonstrated using various numerical examples.

Estimation of transmission eigenvalues and the index of refraction from Cauchy data

Recently the transmission eigenvalue problem has come to play an important role and received a lot of attention in inverse scattering theory. This is due to the fact that transmission eigenvalues can be determined from the far field data of the scattered wave and used to obtain estimates for the material properties of the scattering object. In this paper, we show that transmission eigenvalues can also be obtained from the near field Cauchy data. In particular, we use the gap reciprocity method to estimate the lowest transmission eigenvalue. To determine the index of refraction, we apply an optimization scheme based on a finite element method for transmission eigenvalues. Numerical examples show that the method is stable and effective.

Algorithm 922: A Mixed Finite Element Method for Helmholtz Transmission Eigenvalues

Transmission eigenvalue problem has important applications in inverse scattering. Since the problem is non-self-adjoint, the computation of transmission eigenvalues needs special treatment. Based on a fourth-order reformulation of the transmission eigenvalue problem, a mixed finite element method is applied. The method has two major advantages: 1) the formulation leads to a generalized eigenvalue problem naturally without the need to invert a related linear system, and 2) the nonphysical zero transmission eigenvalue, which has an infinitely dimensional eigenspace, is eliminated. To solve the resulting non-Hermitian eigenvalue problem, an iterative algorithm using restarted Arnoldi method is proposed. To make the computation efficient, the search interval is decided using a Faber-Krahn type inequality for transmission eignevalues and the interval is updated at each iteration. The algorithm is implemented using Matlab. The code can be easily used in the qualitative methods in inverse scattering and modified to compute transmission eigenvalues for other models such as elasticity problem.

A Multigrid Method for Helmholtz Transmission Eigenvalue Problems

In this paper, we analyze the convergence of a finite element method for the computation of transmission eigenvalues and corresponding eigenfunctions. Based on the obtained error estimate results, we propose a multigrid method to solve the Helmholtz transmission eigenvalue problem. This new method needs only linear computational work. Numerical results are provided to validate the efficiency of the proposed method.

Finite Element Methods for Maxwell's Transmission Eigenvalues

The transmission eigenvalue problem plays a critical role in the theory of qualitative methods for inhomogeneous media in inverse scattering theory. Efficient computational tools for transmission eigenvalues are needed to motivate improvements to theory, and, more importantly, are parts of inverse algorithms for estimating material properties. In this paper, we propose two finite element methods to compute a few lowest Maxwells transmission eigenvalues which are of interest in applications. Since the discrete matrix eigenvalue problem is large, sparse, and, in particular, non-Hermitian due to the fact that the problem is neither elliptic nor self-adjoint, we devise an adaptive method which combines the Arnoldi iteration and estimation of transmission eigenvalues. Exact transmission eigenvalues for balls are derived and used as a benchmark. Numerical examples are provided to show the viability of the proposed methods and to test the accuracy of recently derived inequalities for transmission eigenvalues.

A coupled BEM and FEM for the interior transmission problem in acoustics

Abstract The interior transmission problem (ITP) is a boundary value problem arising in inverse scattering theory, and it has important applications in qualitative methods. In this paper, we propose a coupled boundary element method (BEM) and a finite element method (FEM) for the ITP in two dimensions. The coupling procedure is realized by applying the direct boundary integral equation method to define the so-called Dirichlet-to-Neumann (DtN) mappings. We show the existence of the solution to the ITP for the anisotropic medium. Numerical results are provided to illustrate the accuracy of the coupling method.

An inverse scattering problem for a partially coated buried obstacle

We consider an inverse scattering problem for a perfect conductor that is partially coated by a dielectric. We investigate a method for determining the shape of the object from the Cauchy data of the total field measured on the boundary of a domain containing the object in its interior. We then give a variational characterization of the supremum of the surface impedance and validate the method with some numerical examples. Applications are given to the target identification of a buried partially coated perfect conductor from a knowledge of the electric and magnetic field on the surface of the earth.