38,200 research outputs found
Direct and Inverse Computational Methods for Electromagnetic Scattering in Biological Diagnostics
Scattering theory has had a major roll in twentieth century mathematical
physics. Mathematical modeling and algorithms of direct,- and inverse
electromagnetic scattering formulation due to biological tissues are
investigated. The algorithms are used for a model based illustration technique
within the microwave range. A number of methods is given to solve the inverse
electromagnetic scattering problem in which the nonlinear and ill-posed nature
of the problem are acknowledged.Comment: 61 pages, 5 figure
Recursive integral method for transmission eigenvalues
Recently, a new eigenvalue problem, called the transmission eigenvalue
problem, has attracted many researchers. The problem arose in inverse
scattering theory for inhomogeneous media and has important applications in a
variety of inverse problems for target identification and nondestructive
testing. The problem is numerically challenging because it is non-selfadjoint
and nonlinear. In this paper, we propose a recursive integral method for
computing transmission eigenvalues from a finite element discretization of the
continuous problem. The method, which overcomes some difficulties of existing
methods, is based on eigenprojectors of compact operators. It is
self-correcting, can separate nearby eigenvalues, and does not require an
initial approximation based on some a priori spectral information. These
features make the method well suited for the transmission eigenvalue problem
whose spectrum is complicated. Numerical examples show that the method is
effective and robust.Comment: 18 pages, 8 figure
Compressive Sensing Theory for Optical Systems Described by a Continuous Model
A brief survey of the author and collaborators' work in compressive sensing
applications to continuous imaging models.Comment: Chapter 3 of "Optical Compressive Imaging" edited by Adrian Stern
published by Taylor & Francis 201
A spectral projection method for transmission eigenvalues
In this paper, we consider a nonlinear integral eigenvalue problem, which is
a reformulation of the transmission eigenvalue problem arising in the inverse
scattering theory. The boundary element method is employed for discretization,
which leads to a generalized matrix eigenvalue problem. We propose a novel
method based on the spectral projection. The method probes a given region on
the complex plane using contour integrals and decides if the region contains
eigenvalue(s) or not. It is particularly suitable to test if zero is an
eigenvalue of the generalized eigenvalue problem, which in turn implies that
the associated wavenumber is a transmission eigenvalue. Effectiveness and
efficiency of the new method are demonstrated by numerical examples.Comment: The paper has been accepted for publication in SCIENCE CHINA
Mathematic
Fredholm factorization of Wiener-Hopf scalar and matrix kernels
A general theory to factorize the Wiener-Hopf (W-H) kernel using Fredholm Integral Equations (FIE) of the second kind is presented. This technique, hereafter called Fredholm factorization, factorizes the W-H kernel using simple numerical quadrature. W-H kernels can be either of scalar form or of matrix form with arbitrary dimensions. The kernel spectrum can be continuous (with branch points), discrete (with poles), or mixed (with branch points and poles). In order to validate the proposed method, rational matrix kernels in particular are studied since they admit exact closed form factorization. In the appendix a new analytical method to factorize rational matrix kernels is also described. The Fredholm factorization is discussed in detail, supplying several numerical tests. Physical aspects are also illustrated in the framework of scattering problems: in particular, diffraction problems. Mathematical proofs are reported in the pape
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