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Convex Obstacles from Travelling Times

Author

Listed:
  • Lyle Noakes

    (Department of Mathematics and Statistics, The University of Western Australia, Crawley 6009, Australia
    These authors contributed equally to this work.)

  • Luchezar Stoyanov

    (Department of Mathematics and Statistics, The University of Western Australia, Crawley 6009, Australia
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Lyle Noakes & Luchezar Stoyanov, 2021. "Convex Obstacles from Travelling Times," Mathematics, MDPI, vol. 9(19), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2434-:d:647537
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