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IEEE Transactions on Antennas and Propagation
Volume 48 Number 10, October 2000

Table of Contents for this issue

Complete paper in PDF format

Linear Inverse Problems in Wave Motion: Nonsymmetric First-Kind Integral Equations

Donald G. Dudley, Fellow, IEEE Tarek M. Habashy and Emil Wolf

Page 1607.

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 nonuniquenes 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.

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