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

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.