Narrowband source localization gets extremely challenging in strong reverberation. When the room is perfectly known, some dictionary-based methods have recently been proposed, allowing source localization with few measurements. In this paper, we first show that, for these methods, the choice of frequencies is important as they fail to localize sources that emit at a frequency near the modal frequencies of the room. A more difficult case, but also important in practice, is when the room geometry and boundary conditions are unknown. In this setup, we introduce a new model for the acoustic soundfield, based on the Vekua theory, that allows a separation of the field into its reverberant and direct source contributions, at the cost of more measurements. This can be used for the design of a dereverberation pre-processing step, suitable for a large variety of standard source localization techniques. We discuss the spatial sampling strategies for the sound field, in order to successfully recover acoustic sources, and the influence of parameters such as number of measurements and model order. This is validated in numerical and experimental tests, that show that this method significantly improves localization in strong reverberant conditions.

Strong reverberation is a challenge for narrowband source localization, as most of the existing methods are based on times-of-arrival measurements, that is affected by boundaries. Amongst the methods that explicitly take into account the reverberation, wavefield separation projector processing (WSPP) splits the acoustic wave field into the direct path of the sources and the reverberation. However, WSPP requires a very large number of microphones, making this method impractical. This article studies three ways of alleviating this constraint, extending WSPP by adding different prior information on the wavefield. The first method is based on using the knowledge of the critical distance of the room to decrease the selectivity of the field separation. The second method adds constraints called "virtual measurements" when the room geometry is partially known. Finally, the last method requires a simple calibration step to estimate the Green's functions between each pair of microphones; this also extends the model to weakly inhomogeneous propagation media. It is shown numerically and experimentally that these methods allow a precise source localization, with a reduced number of microphones.