Gridless three-dimensional acoustic imaging based on the concept of sonons: Reconstruction of source directivity and equivalent spatial distribution

Abstract

Three-dimensional acoustic imaging with microphone arrays is a challenging task due to the numerous degrees of freedom of the physical processes at stake. Instead of meshing a region of space to identify acoustic source distributions, the aim of this work is to propose a novel gridless method to reconstruct the sound field by an equivalent set of point sources with unrestricted coordinates, named “acoustic sonons”. Their radiation is expected to reproduce the same acoustic properties as the measured acoustic field, such as its pressure level, directivity and spatial coherence by recovering phase information. It is found that the proposed concept of sonons, while being very flexible, effectively provides equivalent representations for a variety of source distributions. The simulation results show that the method can be adapted to diverse acoustic field situations, whether they are composed of elementary sources or intricate volumetric source densities. The problem is formulated within a probabilistic framework, through a hierarchical Bayesian model inferred by a dedicated Markov chain Monte Carlo algorithm. The performance of the method is evaluated on analytical radiation problems and its ability to reconstruct the directivity is tested for two far-field radiation cases.