Correlation imaging in inverse scattering is tomography on probability distributions. (4th December 2018)

• Record Type: Journal Article
• Authors: Caro, Pedro; Helin, Tapio; Kujanpää, Antti; Lassas, Matti
• Is Part Of: Inverse problems. Volume 35:Number 1(2019)
• Publication Date: 2018-12-04
• Subjects: inverse problems -- scattering -- random potential -- partial differential equations; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aaece1
• Languages: English
• ISSNs: 0266-5611

Abstract

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 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.