Joint Acoustic Localization and Dereverberation Through Plane Wave Decomposition and Sparse Regularization

Acoustic source localization and dereverberation are formulated jointly as an inverse problem. The inverse problem consists of the approximation of the sound field measured by a set of microphones. The recorded sound pressure is matched with that of a particular acoustic model based on a collection of plane waves arriving from different directions at the microphone positions. In order to achieve meaningful results, spatial and spatio-spectral sparsity can be promoted in the weight signals controlling the plane waves. The large-scale optimization problem resulting from the inverse problem formulation is solved using a first order optimization algorithm combined with a weighted overlap-add procedure. It is shown that once the weight signals capable of effectively approximating the sound field are obtained, they can be readily used to localize a moving sound source in terms of direction of arrival (DOA) and to perform dereverberation in a highly reverberant environment. Results from simulation experiments and from real measurements show that the proposed algorithm is robust against both localized and diffuse noise exhibiting a noise reduction in the dereverberated signals.