Point cloud-based scatterer approximation and affine invariant sampling in the inverse scattering problem

We study the problem of recovering a scatterer object boundary by measuring the acoustic far field using Bayesian inference. This is the inverse acoustic scattering problem, and Bayesian inference is used to quantify the uncertainty on the unknowns (e.g., boundary shape and position). Aiming at sampling efficiently from the arising posterior probability distribution, we introduce a probability transition kernel (sampler) that is invariant under affine transformations of space. The sampling is carried out over a cloud of control points used to interpolate candidate boundary solutions. We demonstrate the performance of our method through a classical problem. Copyright (C) 2016 John Wiley & Sons, Ltd.