An efficient time-frequency approach to blind source separation based on wavelets

Abstract

Time-frequency representations based on wavelets, such as the discrete wavelet (DWT) and wavelet packet (WPT) transforms, offer an efficient means of analysing, de-noising and filtering non-stationary signals. They furthermore provide a rich description of time-varying frequency content of a signal, that is useful for the problem of blind source separation (BSS). We present and explore a multispectral decorrelation approach, whereby linear mixtures of sources with unique time-frequency signatures are separated, without pre-whitening, through joint diagonalisation of wavelet sub-band covariance matrices. Compared with BSS algorithms using temporal decorrelation only, wavelet BSS works well for stationary and non-stationary synthetic mixtures, with stable performance as the number of sources increases. Combined with conventional wavelet analysis and filtering techniques, wavelet BSS offers an integrated, versatile and efficient framework for analysing non-stationary multichannel signals in general, with promising results when applied to multichannel electroencephalographic (EEG) data. © Springer-Verlag 2004.