This study examines the use of Gaussian process (GP) regression for sound field reconstruction. GPs enable the reconstruction of a sound field from a limited set of observations based on the use of a covariance function (a kernel) that models the spatial correlation between points in the sound field. Significantly, the approach makes it possible to quantify the uncertainty on the reconstruction in a closed form. In this study, the relation between reconstruction based on GPs and classical reconstruction methods based on linear regression is examined from an acoustical perspective. Several kernels are analyzed for their potential in sound field reconstruction, and a hierarchical Bayesian parameterization is introduced, which enables the construction of a plane wave kernel of variable sparsity. The performance of the kernels is numerically studied and compared to classical reconstruction methods based on linear regression. The results demonstrate the benefits of using GPs in sound field analysis. The hierarchical parameterization shows the overall best performance, adequately reconstructing fundamentally different sound fields. The approach appears to be particularly powerful when prior knowledge of the sound field would not be available.
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