Spatial reconstruction of the sound field in a room in the modal frequency range using Bayesian inference

Abstract

Spatial characterization of the sound field in a room is a challenging task, as it usually requires a large number of measurement points. This paper presents a probabilistic approach for sound field reconstruction in the modal frequency range for small and medium-sized rooms based on Bayesian inference. A plane wave expansion model is used to decompose the sound field in the examined domain. The posterior distribution for the amplitude of each plane wave is inferred based on a uniform prior distribution with limits based on the maximum sound pressure observed in the measurements. Two different application cases are studied, namely a numerically computed sound field in a non-rectangular two-dimensional (2D) domain and a measured sound field in a horizontal evaluation area of a lightly damped room. The proposed reconstruction method provides an accurate reconstruction for both examined cases. Further, the results of Bayesian inference are compared to the reconstruction with a deterministic compressive sensing framework. The most significant advantage of the Bayesian method over deterministic reconstruction approaches is that it provides a probability distribution of the sound pressure at every reconstruction point, and thus, allows quantifying the uncertainty of the recovered sound field.

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

“…Acoustic fields in a room are usually intricate due to the boundaries and elements in the room that introduce scattering and diffraction effects. In the literature, various approaches can be found that characterise the sound field in a room, including plane wave expansions [8], modal expansions [9], sparse reconstruction reconstruction [10,11], Bayesian inference [12,13], kernel regression [14], deep-learning techniques [15,16], and others.…”