Spatio-temporal Gaussian process regression for room impulse response interpolation with acoustically informed priors

The reconstruction of sound fields in a room from a limited set of measurements is a central problem in acoustics, with relevant applications in e.g. acoustic analysis, audio, or sound field control. Conventional approaches rely on measuring the room impulse response (RIR) at several locations in the room, and fitting a wave model that enables to estimate the field at other locations—via solving an inverse problem. Previous studies have shown that the reconstruction of RIRs strongly depends on the regularization method used to solve the problem, and that enforcing sparsity is beneficial for the reconstruction of the early part of the RIR. This work studies Gaussian processes with time-dependent regularization in order to exploit the temporal properties of RIRs. The inverse problem is solved in the time domain, where hierarchical Bayes is applied in order to explicitly promote solutions where waves are more likely to propagate as time evolves. The model aims at reconstructing both the early part, and the late part of the RIRs. The performance of the proposed model is studied with experimental measurements, and compared to classical reconstruction methods with l1 and l2-norm regularization schemes