ISBN 9783843941693

978-3-8439-4169-3, Reihe Mathematik

Max Nimmer
Spectral Imaging Based on 2D Diffraction Patterns and Robust Principal Component Analysis

183 Seiten, Dissertation Technische Universität Kaiserslautern (2019), Softcover, A5

Zusammenfassung / Abstract

In spectral imaging, the acquisition and analysis of spectral data involve interesting mathematical problems. In this thesis we deal with both aspects. For a novel snapshot spectral imaging device we develop a model and an optimization algorithm for the reconstruction of spectral data from 2D diffraction patterns. In respect to the analysis of such data, we investigate an optimization algorithm for a particular robust version of principal component analysis. Here, we pay special attention to underlying spaces, namely the Stiefel and the Grassmannian manifolds.