Blind Source Separation Based On Wavelet Signal Representation

Most of the proposed techniques for solving the Blind Source Separation problem (BSS) or Independent Component Analysis (ICA) rely on independence or at least uncorrelation assumption of source signals. This paper introduces a technique for cases that source signals present only different time-scale localization properties. We present a new BSS algorithm for the static mixing problem that exploits the advantages of wavelet transform and we propose a representation called Spatial Time Scale Distributions (STSD) to characterize energy and interference of the observed data. The most striking result is the possibility to perform separation from a smaller number of STSD matrices. We also discuss the possibility and the suitability of the STSD matrices to a joint diagonalisation criterion because of the different time-scale property assumption. A variety of simulations, for synthetic signals and real audio recordings, assess the accuracy of the proposed technique to restore statistical independence, and compare their performances over those of the JADE algorithm in noisy environment.