Physics-informed neural network assisted spherical microphone array signal processing

Thanks to their rotational symmetry that facilitates three-dimensional signal processing, spherical microphone arrays are the common array apertures used for spatial audio and acoustic applications. However, practical implementations of spherical microphone arrays suffer from two issues. First, at high frequency range, a large number of sensors are needed to accurately capture a sound field. Second, the accompanying signal processing algorithm, i.e., the spherical harmonic decomposition method, requires a variable radius array or a rigid surface array to circumvent the spherical Bessel function nulls. Such arrays are hard to design and introduce a scattering field. To address these issues, this paper proposes to assist a spherical microphone array with a physics-informed neural network (PINN) for three-dimensional signal processing. The PINN models the sound field around the array based on the sensor measurements and the acoustic wave equation, augmenting the sound field information captured by the array through prediction. This makes it possible to analyze a high frequency sound field with a reduced number of sensors and avoid the spherical Bessel function nulls with a simple single radius open-sphere microphone array.