Variationell Regularisering av Inversproblem med Till¨ampning inom Skiktr¨ontgen
Typ
Examensarbete för kandidatexamen
Program
Publicerad
2022
Författare
Christensen, Louise
Nilsson, Sara
Pauli, Oskar
Svensson, Gustav
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
The aim of this study was to solve ill-posed inverse problems when reconstructing data by
using variational regularization theory. This problem was solved using MATLAB. Data was
simulated from MATLAB’s 256×256 Shepp-Logan phantom, which also acted as our reference
image. This phantom was reconstructed using Tikhonov regularization and total variation
regularization, both with and without a non-negativity constraint. The regularization methods
rely on a regularization parameter λ for which we used L-curves and testing to find appropriate
values. Results was presented in the form of the reconstructions together with their respective
values of the regularization parameter and compared against each other. There were clear
differences between Tikhonov regularization and total variation regularization, mainly in how
they handled noise. Further development was discussed.