Blind channel identification for speech dereverberation using l ₁-norm sparse learning

Speech dereverberation remains an open problem after more than three decades of research. The most challenging step in speech dereverberation is blind channel identification (BCI). Although many BCI approaches have been developed, their performance is still far from satisfactory for practical applications. The main difficulty in BCI lies in finding an appropriate acoustic model, which not only can effectively resolve solution degeneracies due to the lack of knowledge of the source, but also robustly models real acoustic environments. This paper proposes a sparse acoustic room impulse response (RIR) model for BCI, that is, an acoustic RIR can be modeled by a sparse FIR filter. Under this model, we show how to formulate the BCI of a single-input multiple-output (SIMO) system into a l₁- norm regularized least squares (LS) problem, which is convex and can be solved efficiently with guaranteed global convergence. The sparseness of solutions is controlled by l₁-norm regularization parameters. We propose a sparse learning scheme that infers the optimal l₁-norm regularization parameters directly from microphone observations under a Bayesian framework. Our results show that the proposed approach is effective and robust, and it yields source estimates in real acoustic environments with high fidelity to anechoic chamber measurements.