TY - RPRT

T1 - Towards a d-bar reconstruction method for three-dimensional EIT

AU - Cornean, Horia Decebal

AU - Knudsen, Kim

PY - 2004

Y1 - 2004

N2 - Three-dimensional electrical impedance tomography (EIT) is considered. Both uniqueness proofs and theoretical reconstruction algorithms available for this problem rely on the use of exponentially growing solutions to the governing conductivity equation. The study of those solutions is continued here. It is shown that exponentially growing solutions exist for low complex frequencies without imposing any regularity assumption on the conductivity. Further, a reconstruction method for conductivities close to a constant is given. In this method the complex frequency is taken to zero instead of infinity. Since this approach involves only moderately oscillatory boundary data, it enables a new class of three-dimensional EIT algorithms, free from the usual high frequency instabilities.

AB - Three-dimensional electrical impedance tomography (EIT) is considered. Both uniqueness proofs and theoretical reconstruction algorithms available for this problem rely on the use of exponentially growing solutions to the governing conductivity equation. The study of those solutions is continued here. It is shown that exponentially growing solutions exist for low complex frequencies without imposing any regularity assumption on the conductivity. Further, a reconstruction method for conductivities close to a constant is given. In this method the complex frequency is taken to zero instead of infinity. Since this approach involves only moderately oscillatory boundary data, it enables a new class of three-dimensional EIT algorithms, free from the usual high frequency instabilities.

M3 - Report

T3 - Research Report Series

BT - Towards a d-bar reconstruction method for three-dimensional EIT

PB - Department of Mathematical Sciences, Aalborg University

CY - Aalborg

ER -