Sparse representation of the sound field in a room with dictionary learning

Phased array measurements of the sound pressure in a room enable to reconstruct the sound field, i.e., to estimate pressure, velocity and sound intensity in positions that have not been measured. Typically, analytical wave functions are used to expand the measured data and interpolate the wave field. However, these bases are often redundant and lead to non-sparse solutions, as multiple basis functions are required to represent the measured data. In this study, we examine the use of dictionary learning to obtain a sparse representation of the sound field in a room, using atoms learned from experimental data. The aim is to obtain a model of reduced dimensionality that can represent optimally the spatial properties of the sound field in a room. We analyse the properties of the extracted dictionaries, their ability to reconstruct the sound field, and their generality. A broader question is the suitability of a given dictionary, which has been extracted from a particular room, to represent the sound field in another room.