Independent component analysis for space-time and nonlinear mixtures
Vu A. Duong, Allen Roger Stubberud · 2004
Are we alone in the universe? This question has posed a great challenge to the human kind in the past, present and many years to come. One approach to answer this question would be to listen for possible signals from the intelligent life in outer space. However, detection and translation of outer space signals would be extremely difficult since we have no clue what these signals would be. In addition, if we could intercept an outer space signal then this signal would have propagated million-million miles before reaching the Earth, it may be more likely that the original signal would have been mixed with several other signal sources, noise or even with its own delayed versions due to reflection, diffraction and refraction in the space. The recovery of the original signal from a messy mixture would also be another great difficult task. Separation of predetermined source signals is often based on the principle of nonoverlapping or partially overlapping spectral characteristics of the signals. However, when the source signals are not known, the spectral method is not able to achieve the separation task. Independent component analysis (ICA) is an alternative method to overcome these challenges. ICA is a generalization of the second order correlation method, which explores the higher order dependencies in the observed signals. The first part of this dissertation is to extend an investigation of the ICA in space and time. The space-time ICA is a more realistic model for several real-world problems in communication, brain signal analysis, image processing and hopefully in detection and separation signals from outer space. It has been shown in this study that the complex model of space-time ICA can be separated into two consecutive processes: space process and followed by time process. In the space process, the observed signals are separated such that the resulting signals are independent in space. In the time process, the signals are deconvolved in order to remove any delayed version of the source signals to its original forms. The second part of this dissertation is the development of a new technique for nonlinear ICA mixtures. By combining the kurtosis for independent objective and polynomial series for nonlinear functions approximation, a new technique for nonlinear ICA is then developed. The simulation results using a variety of nonlinear functions to study the performance of the proposed nonlinear technique are reported.