Bayesian Sound Field Reconstruction Using Partial Boundary Information

The problem of reconstructing a spatial sound field from microphone signals and a coarse, partial, and/or uncertain point cloud representation of the boundaries of the room is considered. This problem has downstream applications within sound field control for which precise reconstruction is essential. Typical for these applications is that only microphone measurements are considered, resulting in poor reconstruction in a large spatial region and at high frequencies when few microphones are available. In contrast, in an idealistic setting, where boundary geometry and acoustic properties are known, the sound field can be simulated as a forward problem. However, since the acquisition of such information can be costly and time-consuming, we consider the intermediate setting where partial information of the boundary geometry is available. We formulate the problem in a Bayesian setting, where the boundary information is used to form a prior distribution on the sound field. The paper extends our preliminary work in [1] by allowing for multiple impedance boundary conditions and by introducing a weighting of the boundary points. A scheme for finding an optimal weighting is introduced to reduce the influence of points far from the region of interest or points not consistent with the microphone measurements. Finally, extensive numerical simulation experiments are performed to understand the properties of the boundary-informed regularizer. To further validate the performance and robustness on real data in relation to commonly used regularizers, we release the Field LAser-calibrated Impulse Response (FLAIR) dataset. This dataset consists of 135 microphone measurements along with a laser calibrated, millimeter accurate point cloud of the room geometry and microphone positions that is aimed at stimulating further research in this domain.