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Solution of the inverse scattering problem from inhomogeneous media using affine invariant sampling

We pose a Bayesian formulation of the inverse problem associated to recovering both the support and the refractive index of a convex obstacle given measurements of near‐field scattered waves. Aiming at sampling efficiently from the arising posterior distribution using Markov Chain Monte Carlo, we construct a sampler (probability transition kernel) that is invariant under affine transformations of space. A point cloud method is used to approximate the scatterer support. We show that affine invariant sampling can successfully address the presence of multiple scales in inverse scattering in inhomogeneous media. Copyright © 2016 John Wiley & Sons, Ltd.