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Time harmonic inverse scattering using accurate forward models is oftencomputationally expensive. On the other hand, the use of computationallyefficient solvers, such as the Born approximation, may fail if the targets donot satisfy the assumptions of the simplified model. In the Bayesian frameworkfor inverse problems, one can construct a statistical model for the errors thatare induced when approximate solvers are used, and hence increase the domain ofapplicability of the approximate model. In this paper, we investigate the errorstructure that is induced by the Born approximation and show that the Bayesianapproximation error approach can be used to partially recover from theseerrors. In particular, we study the model problem of reconstruction of theindex of refraction of a penetrable medium from measurements of the far fieldpattern of the scattered wave.

A Bayesian approach to improving the Born approximation for inverse scattering with high contrast materials