The detection of weak signals in noisy data is a problem which occurs across various disciplines. Here, the signal of interest is the spectral signature of the electron magnetic chiral dichroism (EMCD) effect. In principle, EMCD allows for the measurement of local magnetic structures in the electron microscope, its spatial resolution, versatility and low hardware requirements giving it an eminent position among competing measurement techniques. However, experimental shortcomings as well as intrinsically low signal to noise ratio render its measurement challenging to the present day.   

This thesis explores how posterior data processing may aid the analysis of various data from the electron microscope. Following a brief introduction to different signals arising in the microscope and a yet briefer survey of the state of the art of EMCD measurements, noise removal strategies are presented. Afterwards, gears are shifted to discuss the separation of mixed signals into their physically meaningful source components based on their assumed mathematical characteristics, so called blind source separation (BSS).    

A data processing workflow for detecting weak signals in noisy spectra is derived from these considerations, ultimately culminating in several demonstrations of the extraction of EMCD signals. While the focus of the thesis does lie on data processing strategies for EMCD detection, the approaches presented here are similarly applicable in other situations. Related topics such as the general analysis of hyperspectral images using BSS methods or the fast analysis of large data sets are also discussed.