Blind Separation of Sources with Dependent Frequency Sub-Components

When exploiting independent component analysis (ICA) to perform blind source separation (BSS), it is assumed that sources are mutually independent. However, in practice, the latent sources are usually dependent to some extent. Subband decomposition ICA (SDICA) is an extension of ICA to admit source dependence. It assumes that each source is represented as the sum of some independent sub-components and dependent sub-components, which have different frequency bands. In this paper we aim at developing approaches to find the optimal filter which enhances independence between such sources and allows successful BSS by ICA. We first investigate the feasibility of separating the SDICA mixture in an adaptive manner. Second, by minimizing the mutual information between outputs, we develop an adaptive method for SDICA, namely band selective ICA (BSICA), which finds both the mixing matrix and the estimate of the source independent sub-components. We also consider the case where sources are the same type of natural signals and some sources are available, and the known sources help to estimate the filter more reliably. Third, we investigate the overcomplete ICA problems with sources having specific frequency characteristics, which BS-ICA can also be used to solve. Experimental results illustrate the success of the proposed approach for solving both SDICA and the overcomplete ICA problems. Index Terms — Subband decomposition ICA, Frequency representation, Adaptive, Mutual information, Overcomplete ICA Note: for reference, please refer to the following papers: 1. Kun Zhang and Lai-Wan Chan, ”An Adaptive Method for Subband Decompostion ICA ”, Neural Computation, 18(1), 2006, pp. 191–223 2. Kun Zhang and Lai-Wan Chan, ”Enhancement of Source Independence for Blind Source Separation”, In 6th International Conference on Independent Component Analysis and Blind Signal Separation (ICA 2006), LNCS 3889, Charleston, SC, USA, Mar., 2006, pp. 731–738