Interpolation of room impulse responses in 3d using compressed sensing

In a room, the acoustic transfer between a source and a receiver is described by the so-called “Room Impulse Response”, which depends on both positions and the room characteristics. According to the sampling theorem, directly measuring the full set of acoustic impulse responses within a 3D-space domain would require an unreasonably large number of measurements. Nevertheless, considering that the acoustic wavefield is sparse in some dictionaries, the Compressed Sensing framework allows the recovery of the full wavefield with a reduced set of measurements (microphones), but raises challenging computational and memory issues. In this paper, we exhibit two sparsity assumptions of the wavefield and we derive two practical algorithms for the wavefield estimation. The first one takes advantage of the Modal Theory for the sampling of the Room Impulse Responses in low frequencies (sparsity in frequency), and the second one exploits the Image Source Method for the interpolation of the early reflections (sparsity in time). These two complementary approaches are validated both by numerical and experimental measurements using a 120-microphone 3D array, and results are given as a function of the number of microphones.