Electrostatic imaging via conformal mapping


Akduman I., KRESS R.

INVERSE PROBLEMS, vol.18, no.6, pp.1659-1672, 2002 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 6
  • Publication Date: 2002
  • Doi Number: 10.1088/0266-5611/18/6/315
  • Journal Name: INVERSE PROBLEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1659-1672
  • Istanbul Technical University Affiliated: No

Abstract

We present the solution of an inverse boundary value problem for harmonic functions arising in electrostatic imaging through conformal mapping techniques. The numerical method consists of two parts. In a first step, by successive approximations a nonlinear equation is solved to determine the boundary values of a holomorphic function on the outer boundary circle of an annulus. Then in a second step an ill-posed Cauchy problem is solved to determine the holomorphic function in the annulus. The method extends and modifies an earlier analysis of Idemen and Akduman (Idemen M and Akduman I 1988 SIAM J. Appl. Math. 48 703-18). We establish a convergence result for the iteration procedure and through numerical examples we illustrate the feasibility of the method.