Multiresolution Parameter Choice Method With Total Variation Based Regularization In Image Denoising

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http://urn.fi/URN:NBN:fi:hulib-202002041273
Title: Multiresolution Parameter Choice Method With Total Variation Based Regularization In Image Denoising
Author: Pohjola, Ilmari
Contributor: University of Helsinki, Faculty of Science
Publisher: Helsingin yliopisto
Date: 2020
Language: eng
URI: http://urn.fi/URN:NBN:fi:hulib-202002041273
http://hdl.handle.net/10138/311027
Thesis level: master's thesis
Discipline: Soveltava matematiikka
Abstract: This thesis will present a basic total variation based image denoising method which in applied mathematics is a specic case of a large group of problems called inverse problems. This study will specically concentrate on choosing a suitable regularization parameter and aims to investigate whether it could be automatically done by a method which was introduced in a paper called "Multiresolution Parameter Choice Method for Total Variation Regularized Tomography" (Kati Niinimäki, Lassas, Keijo Hämäläinen, Aki Kallonen, Ville Kolehmainen, Esa Niemi, and Samuli Siltanen. SIAM J. IMAGING SCIENCES 2016). I will go through the theoretical basic concepts regarding total variation based regularization and inverse problems in general. Finally I will introduce a new automatic parameter choice method candidate proposed by my supervisor, Samuli Siltanen, and gather some results how well it performs with the given task in practice.


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