Joint source localization and dereverberation by sound field interpolation using sparse regularization

In this paper, source localization and dereverberation are formulated jointly as an inverse problem. The inverse problem consists in the interpolation of the sound field measured by a set of microphones by matching the recorded sound pressure with that of a particular acoustic model. This model is based on a collection of equivalent sources creating either spherical or plane waves. In order to achieve meaningful results, spatial, spatio-temporal and spatio-spectral sparsity can be promoted in the signals originating from the equivalent sources. The inverse problem consists of a large-scale optimization problem that is solved using a first order matrix-free optimization algorithm. It is shown that once the equivalent source signals capable of effectively interpolating the sound field are obtained, they can be readily used to localize a speech sound source in terms of Direction of Arrival (DOA) and to perform dereverberation in a highly reverberant environment