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Author:Seiskari, Otto
Title:Locating multiple inclusions from sweep data of electrical impedance tomography
Useiden inkluusioiden paikantaminen impedanssitomografian sweep-datasta
Publication type:Master's thesis
Publication year:2011
Pages:v + 83      Language:   eng
Department/School:Matematiikan ja systeemianalyysin laitos
Main subject:Matematiikka   (Mat-1)
Supervisor:Nevanlinna, Olavi
Instructor:Hyvönen, Nuutti
Electronic version URL: http://urn.fi/URN:NBN:fi:aalto-201207022737
OEVS:
Electronic archive copy is available via Aalto Thesis Database.
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Location:P1 Ark Aalto  74   | Archive
Keywords:electrical impedance tomography
inverse problems
layer potential
conductivity equation
Sobolev space
Laurent-Padé approximant
impedanssitomografia
inversio-ongelmat
layer-potentiaali
johtavuusyhtälö
Sobolev-avaruus
Laurent-Padé-approksimantti
Abstract (eng): Electrical impedance tomography (EIT) is the practice of estimating the position-dependent electrical properties of a body from current and voltage measurements on its boundary.
It has numerous present and prospective applications in, among others, medical imaging, geophysics and non-destructive material testing.

This thesis studies sweep data of EIT, which is a recent concept associated with a special two-electrode measurement introduced in [21] by Hyvönen, Harhanen and Hakula.
Based on the recent paper [16] by Hanke, where a similar analysis is carried out for a related novel EIT measurement, the backscatter data, a method for locating inclusions of different conductivities in an otherwise homogeneous disk-shaped object is devised.

The cornerstone of the analysis is a certain factorization of the difference Neumann-to-Dirichlet map, which is proven valid under somewhat weaker assumptions than in [16].
The factorization is subsequently used to construct an asymptotic small inclusion expansion and prove that sweep data can be interpreted as the boundary value of a complex analytic function.

As a new result, the method presented here has the capability of extracting information about the conductivities and sizes of the inclusions.
Even though inspired by the devised properties, the algorithm is not entirely backed by theory, but the numerical results strongly indicate that it works as desired.
Abstract (fin): Impedanssitomografiassa (EIT) kappaleen paikkariippuvia sähköisiä ominaisuuksia yritetään selvittää sen pinnalla mitattujen sähkövirtojen ja -jännitteiden perusteella.
Sillä on sovelluksia esimerkiksi lääketieteellisessä kuvantamisessa, geofysiikassa sekä materiaalien testauksessa.

Tässä diplomityössä tutkitaan impedanssitomografian sweep-dataa, joka on Hyvösen, Harhasen ja Hakulan artikkelissa [21] esitelty uusi, tiettyyn kahden elektrodin EIT -mittaukseen liittyvä käsite.
Diplomityössä esitellään menetelmä, jossa muuten homogeenisesta kiekkomaisesta kappaleesta paikannetaan sähkönjohtavuudeltaan poikkeavia inkluusioita.
Menetelmä pohjautuu Hanken artikkeliin [16], jossa analysoidaan vastaavalla tavalla EIT:n takaisinsirontadataa, joka on sweepdatan kaltainen ja tähän läheisesti liittyvä uusi käsite.

Työssä teoreettinen tarkastelu nojautuu tiettyyn Neumann-Dirichlet -erotuskuvauksen faktorointiin, jonka todistetaan pätevän heikommilla oletuksilla, kuin artikkelissa [16].
Faktoroinnin avulla muodostetaan asymptoottinen pieninkluusiokehitelmä ja todistetaan, että sweep-data voidaan tulkita kompleksianalyyttisen funktion reuna-arvona.

Uutena tuloksena esitetty menetelmä kykenee laskemaan inkluusioiden johtavuuksiin ja kokoihin liittyviä tietoja.
Vaikka algoritmi mukailee sweep-datan teoreettisia ominaisuuksia, eivät todistetut tulokset takaa sen toimivuutta.
Numeeriset esimerkit kuitenkin viittaavat vahvasti siihen, että menetelmä toimii halutulla tavalla.
ED:2011-12-21
INSSI record number: 43645
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