  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.
