Discretization and Bayesian modeling in inverse problems and imaging

Tapio Helin

Discretization and Bayesian modeling in inverse problems and imaging

Julkaisun otsikon käännös: Discretization and Bayesian modeling in inverse problems and imaging

Tapio Helin

Matematiikan ja systeemianalyysin laitos

Tutkimustuotos: Doctoral Thesis › Collection of Articles

Abstrakti

In this thesis the Bayesian modeling and discretization are studied in inverse problems related to imaging. The treatise consists of four articles which focus on the phenomena that appear when more detailed data or a priori information become available. Novel Bayesian methods for solving ill-posed signal processing problems in edge-preserving manner are introduced and analysed. Furthermore, modeling photographs in image processing problems is studied and a novel model is presented.

Julkaisun otsikon käännös	Discretization and Bayesian modeling in inverse problems and imaging
Alkuperäiskieli	Englanti
Pätevyys	Tohtorintutkinto
Myöntävä instituutio	Aalto-yliopisto
Valvoja/neuvonantaja	Nevanlinna, Olavi, Vastuuprofessori
Kustantaja	Aalto-yliopiston teknillinen korkeakoulu
Painoksen ISBN	978-952-60-3040-1
Sähköinen ISBN	978-952-60-3041-8
Tila	Julkaistu - 2010
OKM-julkaisutyyppi	G5 Artikkeliväitöskirja

Pääsy asiakirjaan

http://urn.fi/URN:ISBN:978-952-60-3041-8

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title = "Discretization and Bayesian modeling in inverse problems and imaging",

abstract = "In this thesis the Bayesian modeling and discretization are studied in inverse problems related to imaging. The treatise consists of four articles which focus on the phenomena that appear when more detailed data or a priori information become available. Novel Bayesian methods for solving ill-posed signal processing problems in edge-preserving manner are introduced and analysed. Furthermore, modeling photographs in image processing problems is studied and a novel model is presented.",

keywords = "inverse problems, Mumford-Shah functional, Bayesian inversion, hierarchical modeling, discretization invariance, image model, Borel measure, metric space, inverse problems, Mumford-Shah functional, Bayesian inversion, hierarchical modeling, discretization invariance, image model, Borel measure, metric space",

author = "Tapio Helin",

year = "2010",

language = "English",

isbn = "978-952-60-3040-1",

series = " Research reports / Helsinki University of Technology, Institute of Mathematics, A",

publisher = "Aalto-yliopiston teknillinen korkeakoulu",

number = "584",

address = "Finland",

school = "Aalto University",

}

TY - BOOK

T1 - Discretization and Bayesian modeling in inverse problems and imaging

AU - Helin, Tapio

PY - 2010

Y1 - 2010

N2 - In this thesis the Bayesian modeling and discretization are studied in inverse problems related to imaging. The treatise consists of four articles which focus on the phenomena that appear when more detailed data or a priori information become available. Novel Bayesian methods for solving ill-posed signal processing problems in edge-preserving manner are introduced and analysed. Furthermore, modeling photographs in image processing problems is studied and a novel model is presented.

AB - In this thesis the Bayesian modeling and discretization are studied in inverse problems related to imaging. The treatise consists of four articles which focus on the phenomena that appear when more detailed data or a priori information become available. Novel Bayesian methods for solving ill-posed signal processing problems in edge-preserving manner are introduced and analysed. Furthermore, modeling photographs in image processing problems is studied and a novel model is presented.

KW - inverse problems

KW - Mumford-Shah functional

KW - Bayesian inversion

KW - hierarchical modeling

KW - discretization invariance

KW - image model

KW - Borel measure

KW - metric space

KW - inverse problems

KW - Mumford-Shah functional

KW - Bayesian inversion

KW - hierarchical modeling

KW - discretization invariance

KW - image model

KW - Borel measure

KW - metric space

M3 - Doctoral Thesis

SN - 978-952-60-3040-1

T3 - Research reports / Helsinki University of Technology, Institute of Mathematics, A

PB - Aalto-yliopiston teknillinen korkeakoulu

ER -

Discretization and Bayesian modeling in inverse problems and imaging

Abstrakti

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