Obstacle Detection using Wave Scattering with a T-Matrix Model and Bayesian Inference

We consider the inverse problem of determining the locations of one or more scatterers with known geometries and boundary properties. We assume noisy far-field data for a known incident wave and we use Bayesian inference, where the outcome is a posterior probability distribution for the possible locations. In practice, to obtain the posterior requires the simulation of scattering for a significant number of multiple scattering configurations. We achieve this in feasible time using a wave-scattering native reduced order model based on the T-matrix. The T-matrix of a scatterer for acoustic wave scattering was first developed by Waterman [Waterman, P. C. (1969). “New Formulation of Acoustic Scattering”, J. Acou. Soc. of Amer. 45, 6, 1417-1429]. It fully describes a scatterer’s wave scattering properties. Wave solutions of the Helmholtz equation are expressible as series expansions and the coefficients of any incident wave, and its associated scattered wave are connected by the T-matrix. This characterization is particularly efficient in problems of one or more scatterers that require changes in orientation and/or translations with respect to the incident wave. For this application we developed a high-performance C++ implementation of the TMATROM3 package [Ganesh, M. and Hawkins, S.C. (2022). “A numerically stable T-matrix method for acoustic scattering by nonspherical particles with large aspect ratios and size parameters”, J. Acou. Soc. of Amer. 151, 3, 1978-1988] that provides a flexible and fast platform for multiple scattering simulations.