PROPAGATION AND RECOVERY OF SINGULARITIES IN THE INVERSE CONDUCTIVITY PROBLEM

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Greenleaf , A , Lassas , M , Santacesaria , M , Siltanen , S & Uhlmann , G 2018 , ' PROPAGATION AND RECOVERY OF SINGULARITIES IN THE INVERSE CONDUCTIVITY PROBLEM ' , Analysis & PDE , vol. 11 , no. 8 , pp. 1901-1943 . https://doi.org/10.2140/apde.2018.11.1901

Title: PROPAGATION AND RECOVERY OF SINGULARITIES IN THE INVERSE CONDUCTIVITY PROBLEM
Author: Greenleaf, Allan; Lassas, Matti; Santacesaria, Matteo; Siltanen, Samuli; Uhlmann, Gunther
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Politecnico di Milano
University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, University of Washington
Date: 2018
Language: eng
Number of pages: 43
Belongs to series: Analysis & PDE
ISSN: 1948-206X
URI: http://hdl.handle.net/10138/307030
Abstract: The ill-posedness of Calderon's inverse conductivity problem, responsible for the poor spatial resolution of electrical impedance tomography (EIT), has been an impetus for the development of hybrid imaging techniques, which compensate for this lack of resolution by coupling with a second type of physical wave, typically modeled by a hyperbolic PDE. We show in two dimensions how, using EIT data alone, to use propagation of singularities for complex principal-type PDEs to efficiently detect interior jumps and other singularities of the conductivity. Analysis of variants of the CGO solutions of Astala and Paivarinta (Ann. Math. (2) 163: 1 (2006), 265-299) allows us to exploit a complex principal-type geometry underlying the problem and show that the leading term in a Born series is an invertible nonlinear generalized Radon transform of the conductivity. The wave front set of all higher-order terms can be characterized, and, under a prior, some refined descriptions are possible. We present numerics to show that this approach is effective for detecting inclusions within inclusions.
Subject: electrical impedance tomography
propagation of singularities
Calderon's problem
tomography
Radon transform
ELECTRICAL-IMPEDANCE TOMOGRAPHY
D-BAR METHOD
FOURIER INTEGRAL-OPERATORS
BOUNDARY-VALUE PROBLEM
GLOBAL UNIQUENESS
LEVEL SET
DISCONTINUOUS CONDUCTIVITIES
NONSMOOTH CONDUCTIVITIES
FACTORIZATION METHOD
NUMERICAL-SOLUTION
111 Mathematics
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