@article {Akduman:2002:0266-5611:1659, author = "Akduman I.", author = "Kress R.", title = "Electrostatic imaging via conformal mapping", journal = "Inverse Problems", volume = "18", year = "2002", 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.48703-18). We establish a convergence result for the iteration procedure and through numerical examples we illustrate the feasibility of the method.
", pages = "1659-1672(14)", url = "http://www.ingentaconnect.com/content/iop/ip/2002/00000018/00000006/art00315" }