Correlation imaging in inverse scattering is tomography on probability distributions

Abstract

Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments of the field to be recovered from correlations between amplitude measurements of the leading singularities, detected in the exterior of a region where the potential is almost surely supported. The result is then applied to show that if two sufficiently regular random fields yield the same data, they have identical laws as function-valued random variables.

Determination of two unknowns for a stochastic plate equation

“…We refer to [46] for inverse problems for a stochastic transport equation. For inverse scattering problems for stochastic systems, we can refer to [3,4,5,6,11,10,22,29,30,31,33,34,36,32,35]. To the best of our knowledge, there is no paper considering the inverse problem for stochastic plate equations to determine u 0 and g. For the observability problems for some stochastic partial differential equations, we refer to [8,17,38,39,44,53].…”