Spatial reconstruction of sound fields using local and data-driven functions.

Sound field analysis methods make it possible to characterize and reconstruct a sound field from a limited set of observations. Classical approaches rely on the use of analytical basis functions to model the sound field throughout the observed domain. When the complexity of the sound field is high, for example, in a room at mid and high frequencies, propagating wave representations can be suboptimal due to model discrepancy. We examine the use of local representations to alleviate this model discrepancy and explore data-driven approaches to obtain suitable models. Specifically, local representations are used to reconstruct the sound field over a large spatial aperture in a room. The performance of local models is compared against conventional plane wave reconstructions and the use of data-driven local functions is examined. Dictionary learning and principal component analysis are used to obtain functions from extensive spatial measurements in an empty room. The results indicate that local partitioning models conform to fields of high spatial complexity. Dictionary learning generalizes across different rooms and frequencies-conferring potential for modelling complex sound fields based on their local and statistical properties.