Wavelet packets approach to blind separation of statistically dependent sources

Sub-band decomposition independent component analysis (SDICA) assumes that wide-band source signals can be dependent but some of their sub-components are independent. Thus, it extends applicability of standard independent component analysis (ICA) through the relaxation of the independence assumption. In this paper, firstly, we introduce novel wavelet packets (WPs) based approach to SDICA obtaining adaptive sub-band decomposition of the wideband signals. Secondly, we introduce small cumulant based approximation of the mutual information (MI) as a criterion for the selection of the sub-band with the least-dependent components. Although MI is estimated for measured signals only, we have provided a proof that shows that index of the sub-band with least dependent components of the measured signals will correspond with the index of the sub-band with least dependent components of the sources. Unlike in the case of the competing methods, we demonstrate consistent performance in terms of accuracy and robustness as well as computational efficiency of WP SDICA algorithm.