STATISTICAL ESTIMATIONS IN INVERSE SCATTERING PROBLEMS

Methods of statistically estimating the characteristics of scatterers from noisy data are proposed. The first approach is based on the Lippm an-Schwinger (LS) equations. The estimator based on the method of maxi mum posterior probability minimizes the appropriate non-quadratic func tional. The latter includes the quadratic form of the discrepancy betw een the estimated fields and experimental data, constraints imposed on the inner fields, and apriori statistical information on the scattere r. The second approach uses the Marchenko Newton-Rose (MNR) equation t o estimate the inner field and the correlation function of reconstruct ion errors. This equation implies the pulse regime. Now the estimate m ay be obtained either directly from the LS equation or from the wave e quation. The ''miracle'' phenomenon is analyzed: the scatterer estimat e is independent of the inner field parameters-the position of the poi nt source and the time of observation-which are chosen after solving t he MNR equation. With this approach, the ''miracle'' takes place only within the correlation domain of the errors in reconstructing the inne r field.