The Calderón problem with corrupted data

Abstract

We consider the inverse Calderón 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 Calderón 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.

15 pages; A longer discussion about the model for the measurement errors has been included; Minor changes recommended by referees

References in corpus (3)

• Global uniqueness for the Calderón problem with Lipschitz conductivities
• Uniqueness in Calderón's problem for conductivities with unbounded gradient
• Analysis of regularized inversion of data corrupted by white Gaussian noise

Cited by in corpus (4)

• Inverse problems for nonlinear magnetic Schrödinger equations on conformally transversally anisotropic manifolds
• Direct regularized reconstruction for the three-dimensional Calderón problem
• Reconstruction in the Calderón problem on conformally transversally anisotropic manifolds
• The observational limit of wave packets with noisy measurements