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Abstract
This work presents a new constructive uniqueness proof for Calderón's inverse problem of electrical impedance tomography, subject to local Cauchy data, for a large class of piecewise constant conductivities that we call "piecewise constant layered conductivities" (PCLC). The resulting reconstruction method only relies on the physically intuitive monotonicity principles of the local NeumanntoDirichlet map, and therefore the method lends itself well to efficient numerical implementation and generalization to electrode models. Several direct reconstruction methods exist for the related problem of inclusion detection, however they share the property that "holes in inclusions" or "inclusionswithininclusions" cannot be determined. One such method is the monotonicity method of Harrach, Seo, and Ullrich, and in fact the method presented here is a modified variant of the monotonicity method which overcomes this problem. More precisely, the presented method abuses that a PCLC type conductivity can be decomposed into nested layers of positive and/or negative perturbations that, layerbylayer, can be determined via the monotonicity method. The conductivity values on each layer are found via basic onedimensional optimization problems constrained by monotonicity relations.
Original language  English 

Publisher  arXiv.org 
Number of pages  10 
Publication status  Published  2019 
Keywords
 electrical impedance tomography
 partial data reconstruction
 piecewise constant coefficient
 monotonicity principle
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Dive into the research topics of 'Reconstruction of piecewise constant layered conductivities in electrical impedance tomography'. Together they form a unique fingerprint.Activities
 1 Visiting another research institution

Aalto University
Henrik Garde (Visiting researcher)
1 Feb 2019 → 31 Dec 2019Activity: Visiting another research institution