Blind Source Separation: Fundamentals and Recent Advances (A Tutorial Overview Presented at SBrT-2001)

Blind source separation (BSS), i.e., the decoupling of unknown signals that have been mixed in an unknown way, has been a topic of great interest in the signal processing community for the last decade, covering a wide range of applications in such diverse fields as digital communications, pattern recognition, biomedical engineering, and financial data analysis, among others. This course aims at an introduction to the BSS problem via an exposition of well-known and established as well as some more recent approaches to its solution. A unified way is followed in presenting the various results so as to more easily bring out their similarities/differences and emphasize their relative advantages/disadvantages. Only a representative sample of the existing knowledge on BSS will be included in this course. The interested readers are encouraged to consult the list of bibliographical references for more details on this exciting and always active research topic.Comment: Tutorial overview of BSS (also presented at SBrT-2001), providing a complete account of the area in early 2000'

Transpose Properties in the Stability and Performance of the Classic Adaptive Algorithms for Blind Source Separation and Deconvolution

This paper presents a tutorial review of the problem of Blind Source Separation (BSS) and the properties of the classic adaptive algorithms when either the score function or a general (non-score) nonlinearity is employed in the algorithm. In new findings it is shown that the separating solution for both sub- and super-Gaussian signals can be stabilized by an algorithm employing any given nonlinearity. For these separating solutions the steady-state error levels are also given in terms of the nonlinearity and the pdf.s of the source signals. These results show that a transpose symmetry exists between the nonlinear algorithms for sub-and super-Gaussian signals. The behavior of the algorithm is then detailed when the ideal score-function nonlinearity is replaced by a general (hard saturation or u³) nonlinearity. The phases of convergence to decorrelated output signals and then to recovery of the source signals are explained. The results are then extended to single- and multi-channel..