Room Reverberation Reconstruction: Interpolation of the Early Part Using Compressed Sensing

This paper deals with the interpolation of the Room Impulse Responses (RIRs) within a whole volume, from as few measurements as possible, and without the knowledge of the geometry of the room. We focus on the early reflections of the RIRs, that have the key property of being sparse in the time domain: this can be exploited in a framework of model-based Compressed Sensing. Starting from a set of RIRs randomly sampled in the spatial domain of interest by a 3D microphone array, we propose a modified Matching Pursuit algorithm to estimate the position of a small set of virtual sources. Then, the reconstruction of the RIRs at interpolated positions is performed using a projection onto a basis of monopoles, which correspond to the estimated virtual sources. An extension of the proposed algorithm allows the interpolation of the positions of both source and receiver, using the acquisition of four different source positions. This approach is validated both by numerical examples, and by experimental measurements using a 3D array with up to 120 microphones.