A Bayesian approach for the spatial reconstruction of the sound field in a room

It is essential for various applications in sound field analysis and sound field control to characterize the spatial properties of a sound field in a room. Standard sampling techniques require an extensive number of measurement points in order to accurately capture the sound field within an extended region of the room. In order to reduce the experimental effort, it is the objective to reconstruct the sound field based on only a limited number of measurements. This contribution presents a probabilistic Bayesian approach for the spatial reconstruction of the sound field for small and medium-sized rooms in the modal frequency range, since the Bayesian approach is well suited to handle a lack of experimental observations. A plane wave expansion model is used to decompose the sound field in the reconstruction domain and the posterior distributions of the plane wave amplitudes are inferred through Bayesian inference. The proposed method is able to accurately reconstruct the reference sound field and it additionally results in a probability distribution of the sound pressure at each reconstruction point. This additional information enables to quantify the uncertainty of the reconstruction and provides insights into its robustness, which is the main benefit over conventional deterministic reconstruction methods.