The Calder\'on problem with corrupted data
Abstract
We consider the inverse Calder\'on problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, one usually assumes the data to be given by such map. This situation corresponds to having access to infinite-precision measurements, which is totally unrealistic. In this paper, we study the Calder\'on problem assuming the data to contain measurement errors and provide formulas to reconstruct the conductivity and its normal derivative on the surface. Additionally, we state the rate convergence of the method. Our approach is theoretical and has a stochastic flavour.
Keywords
Cite
@article{arxiv.1701.02244,
title = {The Calder\'on problem with corrupted data},
author = {Pedro Caro and Andoni Garcia},
journal= {arXiv preprint arXiv:1701.02244},
year = {2017}
}
Comments
15 pages; A longer discussion about the model for the measurement errors has been included; Minor changes recommended by referees