Using the time-frequency (or -scale) diversity of the source processes allows the blind source separation problem to be tackled within Gaussian models. In this work, we show that this approach amounts to minimizing a certain sparseness criterion for the energy distribution of the source over the time-frequency (or -scale) plane. We also explore the link between independence and sparsity and shows that other sparsity criteria (some examples of which are provided) can be used. Further, we introduce an adaptive method which tries to find the best sparse representation of the source energy in order to exploit the sparsity in a most efficient way. An algorithm, adapted from that of Coifman and Wickerhauser has been developed for this end. Finally a simulation example has been given.