Convex Obstacles from Travelling Times

Lyle Noakes and Luchezar Stoyanov
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Lyle Noakes: Department of Mathematics and Statistics, The University of Western Australia, Crawley 6009, Australia
Luchezar Stoyanov: Department of Mathematics and Statistics, The University of Western Australia, Crawley 6009, Australia

Mathematics, 2021, vol. 9, issue 19, 1-14

Abstract: We consider situations where rays are reflected according to geometrical optics by a set of unknown obstacles. The aim is to recover information about the obstacles from the travelling-time data of the reflected rays using geometrical methods and observations of singularities. Suppose that, for a disjoint union of finitely many strictly convex smooth obstacles in the Euclidean plane, no Euclidean line meets more than two of them. We then give a construction for complete recovery of the obstacles from the travelling times of reflected rays.

Keywords: inverse scattering; planar obstacles; strictly convex; no-eclipse; singularity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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