Blind Decorrelation and SOS for Robust Blind Identification
Andrzej S Cichocki, Шун-ичи Амари · 2002
Temporal, spatial and spatio-temporal decorrelations play important roles in signal processing. These techniques are based only on second order statistics (SOS). They are the basis for modern subspace methods of spectrum analysis and array processing and often used in a preprocessing stage in order to improve convergence properties of adaptive systems, to eliminate redundancy or to reduce noise. Spatial decorrelation or prewhitening is often considered as a necessary (but not sufficient) condition for the stronger stochastic independence criteria. After prewhitening, the BSS or ICA tasks usually become somewhat easier and well-posed (less ill-conditioned), because the subsequent separating (unmixing) system is described by an orthogonal matrix for real-valued signals and a unitary matrix for complex-valued signals and weights. Furthermore, spatio-temporal and time-delayed decorrelation can be used to identify the mixing matrix and perform blind source separation of colored sources. In this chapter, we discuss and analyze a number of efficient and robust adaptive and batch algorithms for spatial whitening, orthogonalization, spatio-temporal and time-delayed blind decorrelation. Moreover, we discuss several promising robust algorithms for blind identification and blind source separation of non-stationary and/or colored sources.