Efficient reconstruction algorithms for three-dimensional tomographic imaging

Helle Majander

Efficient reconstruction algorithms for three-dimensional tomographic imaging

Julkaisun otsikon käännös: Tehokkaita rekonstruktioalgoritmeja kolmiulotteiseen tomografiseen kuvantamiseen

Helle Majander

Tutkimustuotos: Doctoral Thesis › Collection of Articles

Abstrakti

Tässä väitöskirjassa käsitellään tomografisiin kuvantamismenetelmiin liittyviä epälineaarisia parametriestimointiongelmia, joiden taustalla on elliptinen osittaisdifferentiaaliyhtälö. Kyseessä on huonosti asetettu käänteisongelma, jonka ratkaisu vaatii regularisointia tai bayesiläisessä viitekehyksessä prioritietoa rekonstruoitavasta paikkariippuvasta parametrista. Jos erityisesti tiedetään, että parametri koostuu inkluusioista vakioarvoisessa taustassa, tämä tieto kvantifioidaan olettamalla, että diskretoinnin jälkeen parametri noudattaa reunoja korostavaa priorijakaumaa. Väitöskirjassa käsitellään myös erityyppisten mittaus- ja mallinnusvirheiden huomiointia, sillä huonosti asetettujen tomografisten kuvantamis-ongelmien tapauksessa pienetkin epätarkkuudet voivat pilata rekonstruktion. Tarkastellun inversio-ongelman ratkaisuna pidetään tässä työssä posteriorijakauman maksimikohtaa, joka voidaan löytää ratkaisemalla tietty minimointiongelma. Minimoijaa etsitään iteratiivisella algoritmilla, joka perustuu suoran mallin lineaarisoinnin, viivästetyn diffusiivisuusaskeleen ja pohjustetun Krylov-aliavaruusmenetelmän (LSQR) yhdistämiseen. Käsittelemällä impedanssitomografiaan (EIT), diffusiiviseen optiseen tomografiaan (DOT) ja kvantitatiiviseen fotoakustiseen tomografiaan (QPAT) liittyviä esimerkkejä osoitetaan, että esitelty algoritmi voidaan toteuttaa riittävän tehokkaasti suuren mittakaavan kolmiulotteisten ongelmien ratkaisemiseksi. Lisäksi erästä EIT:n täydellisen elektrodimallin konformi-invarianssitulosta käytetään geometristen mallinnusvirheiden kompensointiin.

Julkaisun otsikon käännös	Tehokkaita rekonstruktioalgoritmeja kolmiulotteiseen tomografiseen kuvantamiseen
Alkuperäiskieli	Englanti
Pätevyys	Tohtorintutkinto
Myöntävä instituutio	Aalto-yliopisto
Valvoja/neuvonantaja	Hyvönen, Nuutti, Vastuuprofessori Hyvönen, Nuutti, Ohjaaja
Kustantaja	Aalto University
Painoksen ISBN	978-952-60-7007-0
Sähköinen ISBN	978-952-60-7006-3
Tila	Julkaistu - 2016
OKM-julkaisutyyppi	G5 Artikkeliväitöskirja

Tutkimusalat

parametriestimointi
tomografinen kuvantaminen
reunoja korostava regularisointi
mallivirheet
pohjustaminen
impedanssitomografia
täydellinen elektrodimalli
diffusiivinen optinen tomografia
kvantitatiivinen fotoakustinen tomografia

Pääsy asiakirjaan

http://urn.fi/URN:ISBN:978-952-60-7006-3Lisenssi: Määrittelemätön

Siteeraa tätä

@phdthesis{189d1dd3c5c24630823772c137032b50,

title = "Efficient reconstruction algorithms for three-dimensional tomographic imaging",

abstract = "This thesis considers nonlinear parameter estimation problems arising from tomographic imaging modalities governed by elliptic partial differential equations. These are ill-posed inverse problems and hence their solution requires regularization or, in the Bayesian framework, incorporation of prior information about the to-be-reconstructed spatially varying parameter. In particular, if the parameter is known to have distinct inclusions in a constant background, we quantify such information by assuming that after discretization the parameter follows an edge-enhancing prior distribution. Moreover, we study how to recover from different kinds of errors in the data, since even small ones can be enough to ruin the reconstruction for an illposed tomographic imaging problem. We consider the solution of the investigated inverse problem to be the maximum a posteriori estimate for the parameter of interest, which can be found by solving a minimization problem. We propose to search for the minimizer by an iterative algorithm based on combining linearizations of the forward model, lagged diffusivity steps and a priorconditioned Krylov subspace method (LSQR). By presenting examples from electrical impedance tomography (EIT), diffuse optical tomography (DOT) and quantitative photoacoustic tomography (QPAT), we demonstrate that such a method can be implemented efficiently enough to be feasible for solving large-scale three-dimensional problems. In addition, we use a conformal invariance result for the complete electrode model (CEM) of EIT to compensate for geometric modeling errors.",

keywords = "parameter estimation problem, tomographic imaging, edge-enhancing regularization, modeling errors, priorconditioning, LSQR, electrical impedance tomography, complete electrode model, diffuse optical tomography, quantitative photoacoustic tomography, parametriestimointi, tomografinen kuvantaminen, reunoja korostava regularisointi, mallivirheet, pohjustaminen, impedanssitomografia, t{\"a}ydellinen elektrodimalli, diffusiivinen optinen tomografia, kvantitatiivinen fotoakustinen tomografia, parameter estimation problem, tomographic imaging, edge-enhancing regularization, modeling errors, priorconditioning, LSQR, electrical impedance tomography, complete electrode model, diffuse optical tomography, quantitative photoacoustic tomography",

author = "Helle Majander",

year = "2016",

language = "English",

isbn = "978-952-60-7007-0",

series = "Aalto University publication series DOCTORAL DISSERTATIONS",

publisher = "Aalto University",

number = "181",

address = "Finland",

school = "Aalto University",

}

TY - BOOK

T1 - Efficient reconstruction algorithms for three-dimensional tomographic imaging

AU - Majander, Helle

PY - 2016

Y1 - 2016

N2 - This thesis considers nonlinear parameter estimation problems arising from tomographic imaging modalities governed by elliptic partial differential equations. These are ill-posed inverse problems and hence their solution requires regularization or, in the Bayesian framework, incorporation of prior information about the to-be-reconstructed spatially varying parameter. In particular, if the parameter is known to have distinct inclusions in a constant background, we quantify such information by assuming that after discretization the parameter follows an edge-enhancing prior distribution. Moreover, we study how to recover from different kinds of errors in the data, since even small ones can be enough to ruin the reconstruction for an illposed tomographic imaging problem. We consider the solution of the investigated inverse problem to be the maximum a posteriori estimate for the parameter of interest, which can be found by solving a minimization problem. We propose to search for the minimizer by an iterative algorithm based on combining linearizations of the forward model, lagged diffusivity steps and a priorconditioned Krylov subspace method (LSQR). By presenting examples from electrical impedance tomography (EIT), diffuse optical tomography (DOT) and quantitative photoacoustic tomography (QPAT), we demonstrate that such a method can be implemented efficiently enough to be feasible for solving large-scale three-dimensional problems. In addition, we use a conformal invariance result for the complete electrode model (CEM) of EIT to compensate for geometric modeling errors.

AB - This thesis considers nonlinear parameter estimation problems arising from tomographic imaging modalities governed by elliptic partial differential equations. These are ill-posed inverse problems and hence their solution requires regularization or, in the Bayesian framework, incorporation of prior information about the to-be-reconstructed spatially varying parameter. In particular, if the parameter is known to have distinct inclusions in a constant background, we quantify such information by assuming that after discretization the parameter follows an edge-enhancing prior distribution. Moreover, we study how to recover from different kinds of errors in the data, since even small ones can be enough to ruin the reconstruction for an illposed tomographic imaging problem. We consider the solution of the investigated inverse problem to be the maximum a posteriori estimate for the parameter of interest, which can be found by solving a minimization problem. We propose to search for the minimizer by an iterative algorithm based on combining linearizations of the forward model, lagged diffusivity steps and a priorconditioned Krylov subspace method (LSQR). By presenting examples from electrical impedance tomography (EIT), diffuse optical tomography (DOT) and quantitative photoacoustic tomography (QPAT), we demonstrate that such a method can be implemented efficiently enough to be feasible for solving large-scale three-dimensional problems. In addition, we use a conformal invariance result for the complete electrode model (CEM) of EIT to compensate for geometric modeling errors.

KW - parameter estimation problem

KW - tomographic imaging

KW - edge-enhancing regularization

KW - modeling errors

KW - priorconditioning

KW - LSQR

KW - electrical impedance tomography

KW - complete electrode model

KW - diffuse optical tomography

KW - quantitative photoacoustic tomography

KW - parametriestimointi

KW - tomografinen kuvantaminen

KW - reunoja korostava regularisointi

KW - mallivirheet

KW - pohjustaminen

KW - impedanssitomografia

KW - täydellinen elektrodimalli

KW - diffusiivinen optinen tomografia

KW - kvantitatiivinen fotoakustinen tomografia

KW - parameter estimation problem

KW - tomographic imaging

KW - edge-enhancing regularization

KW - modeling errors

KW - priorconditioning

KW - LSQR

KW - electrical impedance tomography

KW - complete electrode model

KW - diffuse optical tomography

KW - quantitative photoacoustic tomography

M3 - Doctoral Thesis

SN - 978-952-60-7007-0

T3 - Aalto University publication series DOCTORAL DISSERTATIONS

PB - Aalto University

ER -

Efficient reconstruction algorithms for three-dimensional tomographic imaging

Abstrakti

Tutkimusalat

Pääsy asiakirjaan

Sormenjälki

Siteeraa tätä