Multigrid reconstruction of sound fields using moving microphones

A multi-resolution technique is presented for sound field recovery based on measurements of one or multiple moving microphones. The interpolation of the spatial samples enables us to set up a system of linear equations that recovers room impulse responses on a virtual uniform grid in space. The spacing of the virtual grid must be very small when directly recovering for the entire bandwidth, thus, the system to be solved requires a large number of measurement positions. In this work, we propose two recovery schemes based on multiple virtual grids that represent distinct sub-bands of the spatiotemporal sound field. This allows for faster reconstruction of low frequencies at minor computational cost and improves the recovery quality when measurement noise is present.