The Calderón problem with corrupted data. (6th June 2017)

• Record Type: Journal Article
• Authors: Caro, Pedro; Garcia, Andoni
• Is Part Of: Inverse problems. Volume 33:Number 8(2017:Aug.)
• Publication Date: 2017-06-06
• Subjects: inverse boundary value problems -- inverse Calderón problem -- noisy data -- reconstruction; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa7425
• Languages: English
• ISSNs: 0266-5611

Abstract

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 a 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.