Blind source separation (BSS) has found wide use in many disciplines including signal processing as it starts from a simple generative model minimizing assumptions on the data generation mechanism and achieves useful decompositions of the observed data. In particular, independent component analysis (ICA) has been the most commonly used approach to achieve BSS since statistical independence of the underlying components is plausible in many applications. Besides independence, sample correlation is another inherent property of many signals of interest. Traditionally, these two properties are addressed separately when developing methods for source separation. Entropy rate, on the other hand, is a natural cost that allows one to account for independence and sample correlation jointly, and hence promises to result in a new class of powerful solutions with wide applicability. In addition, it enables one to easily incorporate model selection---another key problem complementing the power of BSS---into the problem through the use of information theoretic criteria.
The focus of this research is the development of a class of powerful methods for source separation and model selection using entropy rate so that one can take both the higher-order-statistical information and sample correlation into account to achieve significant performance gains in more challenging problems. The main application domain is one that can truly take advantage of this fully combined approach: the analysis of functional magnetic resonance (fMRI) data and the rejection of gradient and pulse artifacts in electroencephalography (EEG) in concurrent EEG-fMRI data. Both are applications that have proven challenging for the traditional model-based approach due to the unique nature of the noise and artifacts in these problems. Hence, they provide a unique testbed for the performance evaluation of the new class of methods developed under this study. Since independence and sample correlation are intrinsic properties of many other types of data, the new set of methods will be attractive solutions for many other problems as well.