Room impulse response interpolation using a sparse spatio-temporal representation of the sound field

Room Impulse Responses (RIRs) are typically measured using a set of microphones and a loudspeaker. When RIRs spanning a large volume are needed, many microphone measurements must be used to spatially sample the sound field. In order to reduce the number of microphone measurements, RIRs can be spatially interpolated. In the present study, RIR interpolation is formulated as an inverse problem. This inverse problem relies on a particular acoustic model capable of representing the measurements. Two different acoustic models are compared: the plane wave decomposition model and a novel time-domain model that consists of a collection of equivalent sources creating spherical waves. These acoustic models can both approximate any reverberant sound field created by a far field sound source. In order to produce an accurate RIR interpolation, sparsity regularization is employed when solving the inverse problem. In particular, by combining different acoustic models with different sparsity promoting regularizations, spatial sparsity, spatio-spectral sparsity and spatio-temporal sparsity are compared. The inverse problem is solved using a matrix-free large scale optimization algorithm. Simulations show that the best RIR interpolation is obtained when combining the novel time-domain acoustic model with the spatio-temporal sparsity regularization, outperforming the results of the plane wave decomposition model even when far fewer microphone measurements are available