Room Impulse Response Reconstruction from Distributed Microphone Arrays using Kernel Ridge Regression

The use of Bayesian Inference and probabilistic models is an increasingly important topic in the field of sound field analysis. Kernel functions, widely utilised in a Gaussian Processes, enable us to describe a sound field in terms of its spatial covariance. In this study, we explore the use of kernel functions to reconstruct the late part of the room impulse response, based on measurements from a set of distributed spherical microphone arrays. As the density of reflections increases quadratically with time, and the spatial statistics of reverberant fields are well described, we are able to express the spatial covariance of the field as a closed-form function. This phenomenon allows us to make use of the so-called kernel trick, which significantly improves the computational efficiency when compared to conventional Bayesian Inference. The experimental results of this study show a successful reconstruction of the room impulse response as well as a fair extrapolation of the sound field far from the measurement aperture. The results also indicate an improvement in the computational burden, and a good generalisability across different rooms.