Sound field reconstruction in rooms: inpainting meets superresolution

In this paper a deep-learning-based method for sound field reconstruction is proposed. It is shown the possibility to reconstruct the magnitude of the sound pressure in the frequency band 30-300 Hz for an entire room by using a very low number of irregularly distributed microphones arbitrarily arranged. In particular, the presented approach uses a limited number of arbitrary discrete measurements of the magnitude of the sound field pressure in order to extrapolate this field to a higher-resolution grid of discrete points in space with a low computational complexity. The method is based on a U-net-like neural network with partial convolutions trained solely on simulated data, i.e. the dataset is constructed from numerical simulations of the Green's function across thousands of common rectangular rooms. Although extensible to three dimensions, the method focuses on reconstructing a two-dimensional plane of the room from measurements of the three-dimensional sound field. Experiments using simulated data together with an experimental validation in a real listening room are shown. The results suggest a performance---in terms of mean squared error and structural similarity---which may exceed conventional reconstruction techniques for a low number of microphones and computational requirements.