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Correlation imaging in inverse scattering is tomography on probability distributions. (English) Zbl 1412.94006

Summary: 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 empirical 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 correlations, they have identical laws as function-valued random variables.

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
35L15 Initial value problems for second-order hyperbolic equations
35P25 Scattering theory for PDEs
35R30 Inverse problems for PDEs
44A12 Radon transform
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
92C55 Biomedical imaging and signal processing
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