Low Frequency Interpolation of Room Impulse Responses Using Compressed Sensing

Measuring the Room Impulse Responses within a finite 3D spatial domain can require a very large number of measurements with standard uniform sampling. In this paper, we show that, at low frequencies, this sampling can be done with significantly less measurements, using some modal properties of the room. At a given temporal frequency, a plane wave approximation of the acoustic field leads to a sparse approximation, and therefore a compressed sensing framework can be used for its acquisition. This paper describes three different sparse models that can be constructed, and the corresponding estimation algorithms: two models that exploit the structured sparsity of the soundfield, with projections of the modes onto plane waves sharing the same wavenumber, and one that computes a sparse decomposition on a dictionary of independent plane waves with time / space variable separation. These models are compared numerically and experimentally, with an array of 120 microphones irregularly placed within a 2 ×2 ×2 m volume inside a room, with an approximate uniform distribution. One of the most challenging part is the design of estimation algorithms whose computational complexity remains tractable.