Variationell Regularisering av Inversproblem med Till¨ampning inom Skiktr¨ontgen

Abstract

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.