A simple artificial illustration of blind source separation is given in Figures 5-7. In this illustration, deterministic signals were used for purposes of illustration. However, the spectral properties of the signals are not used in the ICA framework, and thus the results would remain unchanged if the signals were simply (non-Gaussian) white noise.
In [140,141,101], results on applying ICA for blind separation of electroencephalographic (EEG) and magnetoencephalographic (MEG) data were reported. The EEG data consisted of recordings of brain activity obtained using electrodes attached to the scalp. Thus a 23-dimensional signal vector was observed. The MEG data was obtained with a more sophisticated measuring method, giving rise to a 122-dimensional signal vector. The ICA algorithms succeeded in separating certain source signals that were so-called artifacts, or noise sources not corresponding to brain activity [140,141]. Canceling these noise sources is a central, and as yet unsolved problem in EEG and MEG signal processing. ICA offers a very promising method. Similarly, ICA can be used for decomposition of evoked field potentials measured by EEG or MEG [142,143], which is an application of considerable interest in the neurosciences. Application on further brain imaging data, this time obtained by functional magnetic resonance imaging (fMRI), is reported in .
Another application area is on economic time series. Some work is reported in . Very recently, applications on telecommunications have also been published .
Since most of the research on ICA has been done with the application of source separation in mind, many authors treating the ICA problem do not use the term ICA, but speak simply of blind source separation (BSS). We make, however, a clear distinction between ICA, which is a theoretical problem or data model with different applications, and blind source separation, which is an application that can be solved using various theoretical approaches, including but not limited to ICA. In fact, the blind source separation problem can be solved using methods very different from ICA. In particular, methods using frequency information, or spectral properties, are prominent (see [16,18,136,147,135,105]). These methods can be used for time-correlated signals, which is of course the usual case in blind source separation, but not in many other applications of ICA (see below). Using such frequency methods, it is also possible to separate Gaussian source signals.