Derivation and implementation of spatio-temporal plane-wave and boostlet kernels for sound field reconstruction with Gaussian processes

Type of seminar: MWL Seminars

Participating: Awen Callo (Le Mans University, France)

Abstract: Sound field reconstruction methods are essential in spatial audio rendering, virtual acoustics, and noise control applications. Recently, data-driven approaches have been considered using Gaussian processes (GPs), which are attractive for their capacity to reconstruct sound fields from a limited number of observation points, thanks to the support of Gaussian processes on a covariance function as a kernel. Newly introduced in scientific literature, the continuous boostlet transform offers a representation system for acoustic waves in space-time. It considers various natural acoustic field features and decomposes spatiotemporal waves into frequency bands and phase velocities. This work aims first to implement spatio-temporal plane wave kernels to reconstruct sound fields using GPs. In fact, current GP kernels exploit spatial correlations to reconstruct the sound field at a fixed time, particularly for isotropic and anisotropic plane wave kernels. Then, the diffeomorphism between wavenumber-frequency and boostlet domains is introduced in the plane wave kernels, which are subsequently expanded into boostlet kernels with their corresponding hyperparameters. In the long run, the hypothesis is that boostlet kernels will increase the predictive performance of Gaussian processes applied to sparse measurements in space-time.