Independent component analysis (ICA) is a recently introduced signal processing technique to solve the blind source separation (BSS) problem in a clear data-driven approach. BSS consists of finding underlying source signals from their observed linear mixtures. This is very difficult since both the mixing and sources are unknown. The solution of the BSS problem has useful applications in many research fields, including biomedical systems, telecommunication and finance. With ICA the problem is solved by assuming that the source signals are statistically independent, which has proven to be quite a natural assumption in many cases. ICA has been used to, for example, identify interesting signals, remove artifacts and reduce noise. ICA can also be used in feature extraction, having applications in, for example, natural image processing and human vision.
One very promising area for ICA is functional brain imaging. Using methods like functional magnetic resonance imaging (fMRI), it is possible to record signals related to the neural activity of the human brain. However, the complex and unpredictable nature of such data make it difficult to analyze using classical signal processing methods, for example, based on modeling the signals. ICA has been recently used with great success in several fMRI studies and may offer the possibility to conduct more advanced studies than before.
Yet, some problems remain in the wide adoption of ICA. One concern is the fact that the solutions found can change slightly each time ICA is applied, naturally causing one to question the reliability of the method. This differing nature of the solutions can be caused by many factors. For example, the strict assumption of statistical independence may not hold for the data, or the estimation process in the ICA algorithm may be inherently stochastic. Also, additive noise can make even the most robust algorithm find varying solutions. Thus, it is difficult to know how stable and reliable the estimated solutions are.
Usually ICA solutions have been compared to those obtained with other methods, or an expert has estimated their feasibility under current knowledge. Needless to say, this effectively cancels the benefits attainable with strictly data-driven analysis. Moreover, such an expert might not even exist. On the other hand, bootstrapping has been successful in identifying consistent solutions. Bootstrapping means controlled resampling of the data and, essentially, allows the statistical analysis of the behavior of an algorithm. It has even been used to group consistently appearing solutions. However, the potential of bootstrapping and analyzing the consistency has not yet been fully exploited.
Increased interest on the matter has convinced that it is important to develop an efficient and usable method to better analyze the consistency of the solutions and characterize the affecting phenomena.
The purpose was to develop an efficient method to exploit the variability of independent components based on existing tools and earlier experiments of the research group (most recently in Ylipaavalniemi and Vigário, 2004) as an improved alternative to other methods recently developed.
The method is based on running ICA multiple times in a bootstrapping manner and then clustering the solutions. Moreover, the method actually exploits the inherent stochastic variability to improve the solutions and to gain further information, which helps to properly interpret the solutions, even without an expert.
The usefulness was tested with real functional magnetic resonance imaging (fMRI) data, which uses a speech stimulus. There the method reveals interesting components with consistent stimulus-related activation patterns. Additionally, the results include other interesting components, whose time-courses are only mildly related to the stimulus, hence difficult to detect with traditional methods. Moreover, the experiments reveal also less consistent, yet interesting phenomena, which are hard to interpret using other methods.
An additional goal was to develop the needed tools to process and visualize fMRI data. The visualization tools are important during the interpretation of the results, and may eventually be published as an easy to use toolbox.
The thesis begins by introducing the basics of functional brain imaging in Chapter 2 and also briefly explaining the traditional analysis method. Chapter 3 is an introduction to independent component analysis and the chosen algorithm implementation. It also explains the theoretical and algorithmic problems in utilizing such an algorithm. Finally, it describes how ICA can be applied to fMRI data.
Chapter 4 considers the actual variability of independent components and presents the method to exploit it in analysis. After that, Chapter 5 explains how the analysis results can be visualized to allow easy and correct interpretation.
The experiments to test the method are described in Chapter 6 and the results are presented in Chapter 7. Finally, Chapter 8 gives the conclusions drawn from the work.
The thesis ends with Appendix A giving further information on the key mathematical concepts and Appendix B showing the complete results of the experiments.