Browsing by Author "Pohjola, Ilmari"

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.