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Abstrakt
The monotonicitybased approach has become one of the fundamental methods for reconstructing inclusions in the inverse problem of electrical impedance tomography. Thus far the method has not been proven to be able to handle extreme inclusions that correspond to some parts of the studied domain becoming either perfectly conducting or perfectly insulating. The main obstacle has arguably been establishing suitable monotonicity principles for the corresponding NeumanntoDirichlet boundary maps. In this work, we tackle this shortcoming by first giving a convergence result in the operator norm for the NeumanntoDirichlet map when the conductivity coefficient decays to zero and/or grows to infinity in some given parts of the domain. This allows passing the necessary monotonicity principles to the limiting case. Subsequently, we show how the monotonicity method generalizes to the definite case of reconstructing either perfectly conducting or perfectly insulating inclusions, as well as to the indefinite case where the perturbed conductivity can take any values between, and including, zero and infinity.
Originalsprog  Engelsk 

Udgiver  arXiv.org 
Antal sider  19 
Status  Udgivet  2019 
Fingeraftryk
Dyk ned i forskningsemnerne om 'Monotonicitybased reconstruction of extreme inclusions in electrical impedance tomography'. Sammen danner de et unikt fingeraftryk.Aktiviteter
 1 Gæsteophold ved andre institutioner

Aalto University
Henrik Garde (Gæsteforsker)
1 feb. 2019 → 31 dec. 2019Aktivitet: Gæsteophold ved andre institutioner