In this work, the solution of inverse scattering by ensemble approaches is studied. We first present a direct ensemble approach, which calculates the coefficients of an ensemble of solutions to forward scattering problems to match a given measured far field pattern. We will show that the resulting scattered field provides an approximation to the true scattered field in the exterior of the union of scatterers under consideration. In a second and third step, we study ensemble approaches which take their motivation from a Bayesian perspective on the inverse problem as taken by Somersalo and Kaipio 2005 or Nakamura and Potthast 2015. The second approach determines real positive coefficients based on the far-field equation. The third approach calculates such coefficients by a Bayesian weighting based on the difference of the ensemble far field pattern to the measurements.
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