Dependent component analysis

Editorial Source separation is not a new problem. We, human beings, as well as many other species, do it unconsciously at every instant of our lives. Our organisms receive a multitude of signals mixed together from the environment, and we are constantly uncovering the relevant ones in order to derive vital information to continue our lives. Other than the biological signals that are occurring at the cell or organ level, there are also various source separation tasks that we consciously do daily. In a crowded underground, room or office, we try to extract what our friend or colleague is telling us among all other speech or audial signals arriving at our ears. Although the source separation problem is handled rather seamlessly by our brains, its implementation in computers has required the development of mathematical models and algorithms. Starting in the 1980s, the problem has been addressed firstly in the context of the cocktail party problem: how to separate a number of speech signals from multichannel mixtures of them. Originally, a simple model of linear mixing was adopted. A solution has been provided to this simplified problem by the independent component analysis algorithm. Later, several other applications have been considered with source separation problems ranging from financial time series analysis to functional magnetic resonance imaging, and from cosmological image separation to music signal separation. The model has been extended to convolutive mixtures and to non-linear mixtures, and variations of the independent component analysis (ICA) algorithm have been utilised. The essence behind independent component analysis is the assumption of statistical independence of the sources. Since the problem is a blind one, that is, we do not know the channel (mixing) characteristics, the mixture model alone represents an ill-posed problem, and we need additional information to resolve the unmixing. The independence assumption provides this additional