We consider the problem of blind multi-channel speech dereverberation without the knowledge of room acoustics. The dereverberated speech component is estimated by subtracting the undesired component, estimated using multi-channel linear prediction (MCLP), from the reference microphone signal. In this paper we present a framework for MCLP-based speech dereverberation by exploiting sparsity in the time-frequency domain. The presented framework uses a wideband or a narrowband signal model and a sparse analysis or synthesis model for the desired speech component. The proposed problems involving a reweighted $\ell_1$-norm, are solved in a flexible optimization framework. The obtained results are comparable to the state of the art, motivating further extensions exploiting sparsity and speech structure.
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