Subband decomposition independent component analysis and new performance criteria

We introduce a new extended model for independent component analysis (ICA) and/or blind source separation (BSS), in which the assumption of the standard ICA model that the source signals are mutually independent (or spatio-temporally uncorrelated) is relaxed. The source is presumed to be the sum of some independent and/or dependent subcomponents. We show a practical solution for this class of blind separation problem by using subband decomposition (SD) and the independence test by analyzing global mixing-demixing matrices obtained for various subbands or multi-bands. This is a very simple but efficient technique, and users just apply the proposed method to conventional ICA/BSS algorithms as pre- and post-processing. The proposed method has been tested for blind separation problems with partially dependent sources. The results indicate that the method is promising for the signal separation problem of speech, image, EEG data, etc.