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We consider an inverse shape problem coming from electrical impedancetomography with a Robin transmission condition. In general, a boundarycondition of Robin type models corrosion. In this paper, we study two methodsfor recovering an interior corroded region from electrostatic data. We considerthe case where we have small volume and extended regions. For the case wherethe region has small volume, we will derive an asymptotic expansion of thecurrent gap operator and prove that a MUSIC-type algorithm can be used torecover the region. In the case where one has an extended region, we will showthat the regularized factorization method can be used to recover said region.Numerical examples will be presented for both cases in two dimensions in theunit circle.

Reconstruction of small and extended regions in EIT with a Robin transmission condition