A framework for evaluating ICA methods for the extraction of the red-shifted 21cm hydrogen line

Abstract

This dissertation is concerned with the problem of Blind Source Separation in 21 cm cosmology. Independent Component Analysis is a powerful technique for source separation, and we focus on evaluating the performance of two ICA algorithms, FastICA [19] and EL-ICA [26], in order to determine whether they can extract the 21 cm signal from the mixture of signals observed by ground-based radio telescopes, where the signal is contaminated by galactic and extra-galactic foregrounds. Also, since statistical independence of the source signals is a crucial requirement for ICA to be successful, and mathematical definitions of independence are based on signals with an infinite number of samples, we develop an algorithm which is capable of determining whether two signals are statistically independent or not, when only a finite number of samples are available. In order to determine whether FastICA and EL-ICA are candidate algorithms for the extraction of the red-shifted hydrogen line, we build a simulation and evaluation framework for ICA of temporal and spatial signals, and then use this framework to carry out blind source separation on simulated astronomical data cubes. We perform various runs of the algorithms to cater for the stochastic component, since both start with an un-mixing matrix initialised to a random set of weights. We also vary the main parameters used by the algorithms, and test the viability of two hypotheses for signal convolution, in order to determine which parameters and hypothesis give the best results. After performing several tests on both the FastICA and EL-ICA algorithms, we demonstrate that neither one is, in fact, capable of extracting the cosmological 21 cm signal, because it is too weak when compared to the other contaminating signals, although we conclude that FastICA, in general, performs much better than EL-I CA.