Compressed sensing for acoustic response reconstruction: Interpolation of the early part

The goal of this paper is to interpolate Room Impulse Responses (RIRs) within a whole volume, from a few measurements. We here focus on the early reflections, 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 space by a 3D microphone array, we use 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. This approach is validated both by numerical and experimental measurements using a 120-microphone 3D array.