Linear inverse problems in wave motion: nonsymmetric first-kind integral equations

Author

Dudley, Donald G. ; Habashy, Tarek M. ; Wolf, Emil

Author_Institution

Dept. of Electr. & Comput. Eng., Arizona Univ., Tucson, AZ, USA

Volume

48

Issue

10

fYear

2000

fDate

10/1/2000 12:00:00 AM

Firstpage

1607

Lastpage

1617

Abstract

We present a general framework to study the solution of first-kind integral equations. The integral operator is assumed to be compact and nonself-adjoint and the integral equation can possess a nonempty null space. An approach is presented for adding contributions from the null space to the minimum-energy solution of the integral equation through the introduction of weighted Hilbert spaces. Stability, accuracy, and nonuniqueness of the solution are discussed through the use of model resolution, data fit, and model covariance operators. The application of this study is to inverse problems that exhibit nonuniqueness

Keywords

Fredholm integral equations; Hilbert spaces; electromagnetic wave polarisation; inverse problems; mathematical operators; singular value decomposition; SVD; compact integral operator; data fit operator; eigenfunctions; first-kind Fredholm integral equations; linear inverse problems; minimum-energy solution; model covariance operator; model resolution; nonempty null space; nonself-adjoint integral operator; nonsymmetric first-kind integral equations; singular-value decomposition; solution accuracy; solution nonuniqueness; stability; wave motion; weighted Hilbert spaces; Computed tomography; Eigenvalues and eigenfunctions; Hilbert space; Integral equations; Inverse problems; Mathematical model; Null space; Packaging; Physics; Stability;

fLanguage

English

Journal_Title

Antennas and Propagation, IEEE Transactions on

Publisher

ieee

ISSN

0018-926X

Type

jour

DOI

10.1109/8.899677

Filename

899677