Circumvent spherical Bessel function nulls for open sphere microphone arrays with physics informed neural network

Abstract: Open sphere microphone arrays (OSMAs) are simple to design and do not introduce scattering fields, and thus can be advantageous than other arrays for implementing spatial acoustic algorithms under spherical model decomposition. However, an OSMA suffers from spherical Bessel function nulls which make it hard to obtain some sound field coefficients at certain frequencies. This paper proposes to assist an OSMA for sound field analysis with physics informed neural network (PINN). A PINN models the measurement of an OSMA and predicts the sound field on another sphere whose radius is different from that of the OSMA. Thanks to the fact that spherical Bessel function nulls vary with radius, the sound field coefficients which are hard to obtain based on the OSMA measurement directly can be obtained based on the prediction. Simulations confirm the effectiveness of this approach and compare it with the rigid sphere approach.