Boundary-Informed Sound Field Reconstruction

We consider the problem of reconstructing the sound field in a room using prior information of the boundary geometry, represented as a point cloud. In general, when no boundary information is available, an accurate sound field reconstruction over a large spatial region and at high frequencies requires numerous microphone measurements. On the other hand, if all geometrical and acoustical aspects of the boundaries are known, the sound field could, in theory, be simulated without any measurements. In this work, we address the intermediate case, where only partial or uncertain boundary information is available. This setting is similar to one studied in virtual reality applications, where the goal is to create a perceptually convincing audio experience. In this work, we focus on spatial sound control applications, which in contrast require an accurate sound field reconstruction. Therefore, we formulate the problem within a linear Bayesian framework, incorporating a boundary-informed prior derived from impedance boundary conditions. The formulation allows for joint optimization of the unknown hyperparameters, including the noise and signal variances and the impedance boundary conditions. Using numerical experiments, we show that incorporating the boundary-informed prior significantly enhances the reconstruction, notably even when only a few hundreds of boundary points are available or when the boundary positions are calibrated with an uncertainty up to 1 dm.