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

TL;DR

This paper introduces a physics informed neural network to overcome nulls in spherical Bessel functions, enabling accurate sound field coefficient estimation for open sphere microphone arrays at problematic frequencies.

Contribution

It proposes a novel PINN-based method to predict sound fields and bypass Bessel nulls, improving sound field analysis with OSMA.

Findings

PINN effectively predicts sound fields at null frequencies.

Method outperforms rigid sphere approach in simulations.

Enables accurate sound coefficient estimation despite Bessel nulls.

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.