REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM

被引：117

作者：

Knudsen, Kim ^{[1
]}

Lassas, Matti ^{[2
]}

Mueller, Jennifer L. ^{[3
,4
]}

Siltanen, Samuli ^{[2
]}

机构：

[1] Tech Univ Denmark, Dept Math, Lyngby, Denmark

[2] Univ Helsinki, Dept Math & Stat, FIN-00014 Helsinki, Finland

[3] Colorado State Univ, Dept Math, Ft Collins, CO 80523 USA

[4] Colorado State Univ, Sch Biomed Engn, Ft Collins, CO 80523 USA

来源：

INVERSE PROBLEMS AND IMAGING | 2009年 / 3卷 / 04期

基金：

美国国家科学基金会;

关键词：

inverse problem; ill-posed problem; electrical impedance tomography; inverse conductivity problem; regularization; ELECTRICAL-IMPEDANCE TOMOGRAPHY; ILL-POSED PROBLEMS; NONLINEAR TIKHONOV REGULARIZATION; GLOBAL UNIQUENESS; RECONSTRUCTION ALGORITHM; NUMERICAL-SOLUTION; CALDERON PROBLEM; BANACH-SPACES; CONVERGENCE; EQUATION;

D O I：

10.3934/ipi.2009.3.599

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A strategy for regularizing the inversion procedure for the two-dimensional D-bar reconstruction algorithm based on the global uniqueness proof of Nachman [Ann. Math. 143 (1996)] for the ill-posed inverse conductivity problem is presented. The strategy utilizes truncation of the boundary integral equation and the scattering transform. It is shown that this leads to a bound on the error in the scattering transform and a stable reconstruction of the conductivity; an explicit rate of convergence in appropriate Banach spaces is derived as well. Numerical results are also included, demonstrating the convergence of the reconstructed conductivity to the true conductivity as the noise level tends to zero. The results provide a link between two traditions of inverse problems research: theory of regularization and inversion methods based on complex geometrical optics. Also, the procedure is a novel regularized imaging method for electrical impedance tomography.

引用

页码：599 / 624

页数：26

共 93 条

[41] Numerical solution of the Cauchy problem for the stationary Schrodinger equation using Faddeev's Green function [J].