Boundary shape analysis of electrical impedance tomography with applications

Stratos Staboulis

Boundary shape analysis of electrical impedance tomography with applications

Julkaisun otsikon käännös: Reunanmuotoanalyysin sovelluksia impedanssitomografiaan

Stratos Staboulis

Tutkimustuotos: Doctoral Thesis › Collection of Articles

Abstrakti

Impedanssitomografiassa (EIT) kappaleen reunanmuodon ja elektrodien sijaintienepätarkka mallinnus pilaa tavallisesti johtavuuden rekonstruktion. Väitöskirjassa esitelläänuusi (reunan)muotoanalyysiin perustuva menetelmä, joka mahdollistaa mittausgeometrianreaaliaikaisen sovittamisen dataan. Työssä osoitetaan, että EIT:n täydellisen elektrodimallin (CEM) suoran ongelman ratkaisuon Fréchet-derivoituva sekä kappaleen reunanmuodon että elektrodien sijaintien suhteen.Johtavuusjakauma ja mittausgeometria rekonstruoidaan yhtäaikaisesti Newton-tyyppiselläneliösumman minimointialgoritmilla. Tarvittavat gradientit voidaan laskea tehokkaastiduaalitekniikan avulla. Muotoanalyyttisiä menetelmiä sovelletaan myös optimaalisen EIT-mittauksen suunnitteluun, missä elektrodien sijainnit optimoidaan numeerisestiposteriorikovarianssiin liittyvien Bayesiläisten kriteerien mukaisesti. Erityistä huomiota kiinnitetään CEM:n Sobolev-säännöllisyysominaisuuksiin, jotka ovatolennaisia työssä sovelletun muotoanalyysin kannalta. Sobolev-avaruuksien väliselläinterpolaatiolla osoitetaan, että CEM on perturboitu versio eräästä ideaalisestaelektrodimallista (shunt-malli). Tästä tuloksesta voidaan päätellä muotoderivaattojennumeerisen approksimoinnin epästabiilius, mikäli kontaktiresistanssit ovat pieniä.

Julkaisun otsikon käännös	Reunanmuotoanalyysin sovelluksia impedanssitomografiaan
Alkuperäiskieli	Englanti
Pätevyys	Tohtorintutkinto
Myöntävä instituutio	Aalto-yliopisto
Valvoja/neuvonantaja	Hyvönen, Nuutti, Vastuuprofessori Hyvönen, Nuutti, Ohjaaja
Kustantaja	Aalto University
Painoksen ISBN	978-952-60-5862-7
Sähköinen ISBN	978-952-60-5863-4
Tila	Julkaistu - 2014
OKM-julkaisutyyppi	G5 Artikkeliväitöskirja

Tutkimusalat

inversio-ongelmat
impedanssitomografia
täydellinen elektrodimalli
muotoanalyysi
optimaalinen kokeiden suunnittelu
Bayesiläinen inversio
elliptiset reuna-arvo-ongelmat
sekareunaehdot

Pääsy asiakirjaan

http://urn.fi/URN:ISBN:978-952-60-5863-4Lisenssi: Määrittelemätön

Siteeraa tätä

@phdthesis{57ea535a9fa948e9b5d05410fa2241e2,

title = "Boundary shape analysis of electrical impedance tomography with applications",

abstract = "A typical electrical impedance tomography (EIT) reconstruction is ruined if the shape of theimaged body or the electrode locations are not accurately known. In this dissertation, a newapproach based on (boundary) shape analysis is presented for online adaptation of themeasurement geometry model. It is shown that the forward operator of the complete electrode model (CEM) of EIT is Fr{\'e}chet differentiable with respect to both the outer boundary shape of the object and the electrodelocations. A dual technique allows feasible computation of the gradients in a Newton-type'output least squares' algorithm for the simultaneous reconstruction of the conductivity andthe measurement geometry. Shape calculus techniques are also applied to optimal experimentdesign for EIT. To be more precise, numerical optimization of the electrode positions is carriedout with respect to posterior covariance related criteria derived from the Bayesian inversionparadigm. Special attention is paid to the Sobolev regularity properties of the CEM essential for the shape analysis. By interpolation of Sobolev spaces it is proven that the CEM is a perturbation of the less regular shunt model of EIT. Consequently, instability in the computation of the numerical shape derivative can be expected if the contact resistances are small.",

keywords = "inverse problems, electrical impedance tomography, complete electrode model, shape analysis, optimal experimental design, Bayesian inversion, elliptic boundary value problems, mixed boundary conditions, inversio-ongelmat, impedanssitomografia, t{\"a}ydellinen elektrodimalli, muotoanalyysi, optimaalinen kokeiden suunnittelu, Bayesil{\"a}inen inversio, elliptiset reuna-arvo-ongelmat, sekareunaehdot, inverse problems, electrical impedance tomography, complete electrode model, shape analysis, optimal experimental design, Bayesian inversion, elliptic boundary value problems, mixed boundary conditions",

author = "Stratos Staboulis",

year = "2014",

language = "English",

isbn = "978-952-60-5862-7",

series = "Aalto University publication series DOCTORAL DISSERTATIONS",

publisher = "Aalto University",

number = "141",

address = "Finland",

school = "Aalto University",

}

TY - BOOK

T1 - Boundary shape analysis of electrical impedance tomography with applications

AU - Staboulis, Stratos

PY - 2014

Y1 - 2014

N2 - A typical electrical impedance tomography (EIT) reconstruction is ruined if the shape of theimaged body or the electrode locations are not accurately known. In this dissertation, a newapproach based on (boundary) shape analysis is presented for online adaptation of themeasurement geometry model. It is shown that the forward operator of the complete electrode model (CEM) of EIT is Fréchet differentiable with respect to both the outer boundary shape of the object and the electrodelocations. A dual technique allows feasible computation of the gradients in a Newton-type'output least squares' algorithm for the simultaneous reconstruction of the conductivity andthe measurement geometry. Shape calculus techniques are also applied to optimal experimentdesign for EIT. To be more precise, numerical optimization of the electrode positions is carriedout with respect to posterior covariance related criteria derived from the Bayesian inversionparadigm. Special attention is paid to the Sobolev regularity properties of the CEM essential for the shape analysis. By interpolation of Sobolev spaces it is proven that the CEM is a perturbation of the less regular shunt model of EIT. Consequently, instability in the computation of the numerical shape derivative can be expected if the contact resistances are small.

AB - A typical electrical impedance tomography (EIT) reconstruction is ruined if the shape of theimaged body or the electrode locations are not accurately known. In this dissertation, a newapproach based on (boundary) shape analysis is presented for online adaptation of themeasurement geometry model. It is shown that the forward operator of the complete electrode model (CEM) of EIT is Fréchet differentiable with respect to both the outer boundary shape of the object and the electrodelocations. A dual technique allows feasible computation of the gradients in a Newton-type'output least squares' algorithm for the simultaneous reconstruction of the conductivity andthe measurement geometry. Shape calculus techniques are also applied to optimal experimentdesign for EIT. To be more precise, numerical optimization of the electrode positions is carriedout with respect to posterior covariance related criteria derived from the Bayesian inversionparadigm. Special attention is paid to the Sobolev regularity properties of the CEM essential for the shape analysis. By interpolation of Sobolev spaces it is proven that the CEM is a perturbation of the less regular shunt model of EIT. Consequently, instability in the computation of the numerical shape derivative can be expected if the contact resistances are small.

KW - inverse problems

KW - electrical impedance tomography

KW - complete electrode model

KW - shape analysis

KW - optimal experimental design

KW - Bayesian inversion

KW - elliptic boundary value problems

KW - mixed boundary conditions

KW - inversio-ongelmat

KW - impedanssitomografia

KW - täydellinen elektrodimalli

KW - muotoanalyysi

KW - optimaalinen kokeiden suunnittelu

KW - Bayesiläinen inversio

KW - elliptiset reuna-arvo-ongelmat

KW - sekareunaehdot

KW - inverse problems

KW - electrical impedance tomography

KW - complete electrode model

KW - shape analysis

KW - optimal experimental design

KW - Bayesian inversion

KW - elliptic boundary value problems

KW - mixed boundary conditions

M3 - Doctoral Thesis

SN - 978-952-60-5862-7

T3 - Aalto University publication series DOCTORAL DISSERTATIONS

PB - Aalto University

ER -

Boundary shape analysis of electrical impedance tomography with applications

Abstrakti

Tutkimusalat

Pääsy asiakirjaan

Sormenjälki

Siteeraa tätä