Bayesian Recovery of Sinusoidal Rough Surface from Scattered Acoustic Pressure on a Linear Microphone Array

The recovery of the properties or geometry of a rough surface from scattered sound is of interest in many applications including medicine and river flow or structural health monitoring. Both classical inversion algorithms and more recent data-driven machine learning techniques have shown great potential but are often sensitive to uncertainties. In addition, the information about the confidence in the prediction is often limited. Aiming to further the developments of the inverse techniques and account for uncertainties, a Bayesian framework is used in the present work to infer the properties of a rough surface, parameterised as a superposition of sinusoidal components. The forward model used for the inversion relies on the Kirchhoff approximation of the scattered sound above the surface of interest. The Kirchhoff approximation implies a validity region in the parameter space which is incorporated in the Bayesian formulation. This accelerates convergence while yielding solutions that have physical meaning. An implementation based on the Metropolis-Hastings algorithm is tested on both synthetic surface realisations and experimental samples produced in a laboratory setting. The robustness of the estimation in the presence of noise is evaluated.