Bayesian Optimal Experimental Design in Imaging

Juha-Pekka Puska

Bayesian Optimal Experimental Design in Imaging

Julkaisun otsikon käännös: Bayesiläinen optimaalinen koesuunnittelu kuvantamisessa

Juha-Pekka Puska

Matematiikan ja systeemianalyysin laitos

Tutkimustuotos: Doctoral Thesis › Collection of Articles

Abstrakti

Inversio-ongelma määritellään ongelmana, joka rikkoo yhtä hyvin asetetun ongelman klassisista kriteereistä: ongelmalla on ratkaisu, joka on yksikäsitteinen ja jatkuva datan suhteen jossain järkevässä topologiassa. Ongelman, joka ei ole hyvin asetettu, sanotaan olevan huonosti asetettu, ja huonosti asetettujen ongelmien ratkaisemiseen soveltuvien työkalujen kehitys on inversio-ongelmien tutkimusalan tavoite. Kuvantamisessa tuntemattoman muuttujan korkea dimensio verrattuna mittausdatan dimensioon johtaa usein siihen, että ongelma on huonosti asetettu. Kuvantamisongelmassa yritetään rekonstruoida kohteena olevan kappaleen kaksi- tai kolmiulotteinen rakenne, minkä seurauksena tuntemattomien parametrien määrä voi olla satojatuhansia, tai jopa ylikin. Mittausdatan dimension sen sijaan määrittää sensorien lukumäärä, joten fyysisten rajoitteiden seurauksena se on yleensä vähintään kertaluokkaa matalampi. Toinen seuraus ongelman korkeasta dimensiosta on ratkaisemisen laskennallinen vaativuus. Kuvantamisongelmassa datan keräämisestä seuraa myös kustannuksia, joten luonnollisena tavoitteena on minimoida tarvitun datan määrä. Yksi työkalu tähän on optimaalinen koesuunnittelu, jossa yritetään suorittaa koe niin, että saadun datan arvo olisi mahdollisimman suuri. Haasteena tässä on, että optimaalisen koeasetelman etsiminen johtaa yleensä laskennallisesti haastavaan ongelmaan, jonka koko riippuu sekä datan että tuntemattoman dimensiosta. Tämän haasteen ratkaiseminen on tämän väitöskirjan pääasiallinen tavoite. Ongelmaa voidaan lähestyä käyttämällä gaussisia approksimaatioita ongelman asettelussa, mikä johtaa käytännöllisiin ratkaisukaavoihin kohdemuuttujille. Tässä väitöskirjassa kehitetään työkaluja, jotka mahdollistavat mittausasetelmien odotusarvoisten hyötyjen tehokkaan laskennan, erityisesti sekventiaalisille kuvantamisongelmille ja ei-gaussisille priorimalleille. Lisäksi näitä työkaluja sovelletaan sekä lääketieteelliseen kuvantamiseen että tähtitieteeseen.

Julkaisun otsikon käännös	Bayesiläinen optimaalinen koesuunnittelu kuvantamisessa
Alkuperäiskieli	Englanti
Pätevyys	Tohtorintutkinto
Myöntävä instituutio	Aalto-yliopisto
Valvoja/neuvonantaja	Hyvönen, Nuutti, Vastuuprofessori Hyvönen, Nuutti, Ohjaaja
Kustantaja	Aalto University
Painoksen ISBN	978-952-64-1608-3
Sähköinen ISBN	978-952-64-1609-0
Tila	Julkaistu - 2023
OKM-julkaisutyyppi	G5 Artikkeliväitöskirja

Tutkimusalat

inversio-ongelma
bayesiläinen mallinnus
optimaalinen koesuunnittelu
tomografiakuvantaminen
tietokonetomografia
magnetorelaxometriakuvantaminen
adaptiivinen optiikka

Pääsy asiakirjaan

http://urn.fi/URN:ISBN:978-952-64-1609-0

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@phdthesis{8f0e907400d444908118513c5ff3644f,

title = "Bayesian Optimal Experimental Design in Imaging",

abstract = "An inverse problem is defined as a problem that violates one of the classical criteria of a well posed problem: a solution exists, is unique, and is continuous with respect to the data in some reasonable topology. A problem that is not well posed is called illposed, and the development of tools to tackle illposed problems is the goal of the field of inverse problems research. In imaging, illposedness is often an inevitable consequence of the high dimension of the unknown, compared with the measurement data. In an imaging problem, one aims to reconstruct the spatial two- or three-dimensional structure of an object of interest, leading to unknown parameters in the hundreds of thousands or beyond, while the dimension of the measurement data is determined by the number of sensors, and thus limited by physical constraints to values often at least an order of magnitude lower. Another consequence of the high dimensionality of the problem is the computational cost involved in the computations. In imaging problems, there is also usually a cost involved in acquiring data, and thus one would naturally want to minimize the amount of data collection required. One tool for this is optimal experimental design, where one aims to perform the experiment in a way as to maximize the value of the data obtained. The challenge of this however, is that the search for this optimal design usually leads to a computationally challenging problem, whose size is dependent on the dimension of both the data and the unknown. Overcoming this difficulty is the main objective of this thesis. The problem can be tackled by using Gaussian approximations in the formulation of the imaging problem, which leads to practical solution formulas for the quantities of interest. In this thesis, tools are developed to enable the efficient computation of expected utilities for certain measurement designs, particularily in sequential imaging problems and for non-Gaussian prior models. Additionally, these tools are applied to medical imaging and astronomy.",

keywords = "inverse problem, Bayesian modeling, optimal experimental design, computed tomography, magnetorelaxometry imaging, adaptive optics, inversio-ongelma, bayesil{\"a}inen mallinnus, optimaalinen koesuunnittelu, tomografiakuvantaminen, tietokonetomografia, magnetorelaxometriakuvantaminen, adaptiivinen optiikka, inverse problem, Bayesian modeling, optimal experimental design, computed tomography, magnetorelaxometry imaging, adaptive optics",

author = "Juha-Pekka Puska",

year = "2023",

language = "English",

isbn = "978-952-64-1608-3",

series = "Aalto University publication series DOCTORAL THESES",

publisher = "Aalto University",

number = "230",

address = "Finland",

school = "Aalto University",

}

TY - BOOK

T1 - Bayesian Optimal Experimental Design in Imaging

AU - Puska, Juha-Pekka

PY - 2023

Y1 - 2023

N2 - An inverse problem is defined as a problem that violates one of the classical criteria of a well posed problem: a solution exists, is unique, and is continuous with respect to the data in some reasonable topology. A problem that is not well posed is called illposed, and the development of tools to tackle illposed problems is the goal of the field of inverse problems research. In imaging, illposedness is often an inevitable consequence of the high dimension of the unknown, compared with the measurement data. In an imaging problem, one aims to reconstruct the spatial two- or three-dimensional structure of an object of interest, leading to unknown parameters in the hundreds of thousands or beyond, while the dimension of the measurement data is determined by the number of sensors, and thus limited by physical constraints to values often at least an order of magnitude lower. Another consequence of the high dimensionality of the problem is the computational cost involved in the computations. In imaging problems, there is also usually a cost involved in acquiring data, and thus one would naturally want to minimize the amount of data collection required. One tool for this is optimal experimental design, where one aims to perform the experiment in a way as to maximize the value of the data obtained. The challenge of this however, is that the search for this optimal design usually leads to a computationally challenging problem, whose size is dependent on the dimension of both the data and the unknown. Overcoming this difficulty is the main objective of this thesis. The problem can be tackled by using Gaussian approximations in the formulation of the imaging problem, which leads to practical solution formulas for the quantities of interest. In this thesis, tools are developed to enable the efficient computation of expected utilities for certain measurement designs, particularily in sequential imaging problems and for non-Gaussian prior models. Additionally, these tools are applied to medical imaging and astronomy.

AB - An inverse problem is defined as a problem that violates one of the classical criteria of a well posed problem: a solution exists, is unique, and is continuous with respect to the data in some reasonable topology. A problem that is not well posed is called illposed, and the development of tools to tackle illposed problems is the goal of the field of inverse problems research. In imaging, illposedness is often an inevitable consequence of the high dimension of the unknown, compared with the measurement data. In an imaging problem, one aims to reconstruct the spatial two- or three-dimensional structure of an object of interest, leading to unknown parameters in the hundreds of thousands or beyond, while the dimension of the measurement data is determined by the number of sensors, and thus limited by physical constraints to values often at least an order of magnitude lower. Another consequence of the high dimensionality of the problem is the computational cost involved in the computations. In imaging problems, there is also usually a cost involved in acquiring data, and thus one would naturally want to minimize the amount of data collection required. One tool for this is optimal experimental design, where one aims to perform the experiment in a way as to maximize the value of the data obtained. The challenge of this however, is that the search for this optimal design usually leads to a computationally challenging problem, whose size is dependent on the dimension of both the data and the unknown. Overcoming this difficulty is the main objective of this thesis. The problem can be tackled by using Gaussian approximations in the formulation of the imaging problem, which leads to practical solution formulas for the quantities of interest. In this thesis, tools are developed to enable the efficient computation of expected utilities for certain measurement designs, particularily in sequential imaging problems and for non-Gaussian prior models. Additionally, these tools are applied to medical imaging and astronomy.

KW - inverse problem

KW - Bayesian modeling

KW - optimal experimental design

KW - computed tomography

KW - magnetorelaxometry imaging

KW - adaptive optics

KW - inversio-ongelma

KW - bayesiläinen mallinnus

KW - optimaalinen koesuunnittelu

KW - tomografiakuvantaminen

KW - tietokonetomografia

KW - magnetorelaxometriakuvantaminen

KW - adaptiivinen optiikka

KW - inverse problem

KW - Bayesian modeling

KW - optimal experimental design

KW - computed tomography

KW - magnetorelaxometry imaging

KW - adaptive optics

M3 - Doctoral Thesis

SN - 978-952-64-1608-3

T3 - Aalto University publication series DOCTORAL THESES

PB - Aalto University

ER -

Bayesian Optimal Experimental Design in Imaging

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