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A model based approach to multi-channel blind source separation for blind dereverberation of speech is proposed. The models considered are chosen to avoid source-channel ambiguities by removing strong assumptions about signal characteristics. The method, however, necessitates the source to be nonstationary, and the channel to be stationary. Estimation theory is used to obtain channel estimates, and inverse filtering dereverberates the speech. A weakness of previous model based approaches is their inability to deal with complicated acoustic environments: ones that can be modelled by hundreds of parameters. This, primarily, is due to their attempt to simultaneously model the full channel spectrum, leading to a non-parsimonious representation, a high computational load, and a lack of scalability for higher dimensional problems. In this paper, a subband channel model is proposed, with the aim of tackling real room acoustics. Although the emphasis of the proposal is the scalability of the model, preliminary results are presented for the case when real speech is passed through a synthetic channel.