Analysis of a sound field in a room using dictionary learning

The sound field in a room is often modeled as a superposition of elementary waves, such as plane or spherical waves. These wave expansions provide a powerful means to interpolate or extrapolate the sound field within (and outside) the measurement domain. However, projecting the sound field of a large domain in a room on a planar or spherical wave base yields a high number of very elemental components. We examine the use of dictionary learning to find a set of alternative basis functions that are suitable to represent the sound field enclosed in a room. The resulting dictionary is able to capture the dominant features of the sound field, and represent it using only a sparse set of functions, the dictionary atoms. In this study, high resolution measurements of the sound pressure in a room are simulated and used as a training set to learn a dictionary. We analyze the spatial properties of the learned dictionary, and compare it to simple elementary basis functions such as plane and spherical waves.