Comparison of processing methods for rigid spherical microphone arrays in spatial and spherical-harmonic domains for soundfield reconstruction

Rigid Spherical Microphone Arrays (SMAs), such as commercially available Eigenmikes, are widely used for capturing 3-D sound fields. Various array processing methods have been developed to enhance the spatial extent and accuracy of soundfield reconstructions, particularly for virtual navigation applications. The traditional approach employs spherical-harmonic basis functions to decompose array measurements into the Higher-Order Ambisonics (HOAs) format, enabling soundfield reconstruction within the constraints of truncation order. Alternatively, measurements can be directly decomposed using spatial basis functions of plane-wave sources, point-sources, or mixed-wave sources via inverse filtering and compressive sensing techniques, exploiting the diversity introduced by the scattering properties of rigid SMAs. Hybrid methods also enable spatial basis decomposition from HOAs. Recently, physics-guided machine-learning models, such as the point-neuron framework, have emerged to ensure strict adherence of the equivalent source decompositions to the physical laws governed by the fundamental wave equation. While these methods have demonstrated success in specific scenarios, a unified evaluation is needed to compare their performance comprehensively. This paper examines their efficacy in terms of reconstruction accuracy, computational efficiency, and robustness to measurement noise and reverberation, highlighting trade-offs to guide practical applications in soundfield navigation.