Inverse scattering problem for a two dimensional random potential
The setup of the stochastic scattering problem consists in the two-dimensional Schrödinger equation with outgoing radiation condition, where the potential is assumed to be a random generalized function supported in a bounded and simply connected domain in the plane. It is assumed also that its covariance operator is a classical pseudodifferential operator. It is proved that the backscattered field, obtained from a single realization of the potential \(q\), determines uniquely the principal symbol of the covariance operator of \(q\). The main tools used to this end are a combination of harmonic and microlocal analysis with stochastic methods.
scientific article; zbMATH DE number 5279030
scientific article