Bayesian reconstruction of surface shape from phaseless scattered acoustic data

The recovery of the properties or geometry of a rough surface from scattered sound is of interest in many applications, including medicine, water engineering, or structural health monitoring. Existing approaches to reconstruct the roughness profile of a scattering surface based on wave scattering have no intrinsic way of predicting the uncertainty of the reconstruction. In an attempt to recover this uncertainty, a Bayesian framework, and more explicitly, an adaptive Metropolis scheme, is used to infer the properties of a rough surface, parameterised as a superposition of sinusoidal components. The Kirchhoff approximation is used in the present work as the underlying model of wave scattering, and is constrained by the assumption of surface smoothness. This implies a validity region in the parameter space, which is incorporated in the Bayesian formulation, making the resulting method physics informed compared to data-based approaches. For a three-parameter sinusoidal surface and a rough surface with a random roughness profile, physical experiments were conducted to collect scattered field data. The models were then tested on the experimental data. The recovery offers insight of the Bayesian approach results expressed in terms of confidence intervals, and could be used as a method to identify uncertainty.