Joint Estimation of Room Geometry and Modes with Compressed Sensing

Acoustical behavior of a room for a given position of microphone and sound source is usually described using the room impulse response. If we rely on the standard uniform sampling, the estimation of room impulse response for arbitrary positions in the room requires a large number of measurements. In order to lower the required sampling rate, some solutions have emerged that exploit the sparse representation of the room wavefield in the terms of plane waves in the low-frequency domain. The plane wave representation has a simple form in rectangular rooms. In our solution, we observe the basic axial modes of the wave vector grid for extraction of the room geometry and then we propagate the knowledge to higher order modes out of the low-pass version of the measurements. Estimation of the approximate structure of the $k$-space should lead to the reduction in the terms of number of required measurements and in the increase of the speed of the reconstruction without great losses of quality.