Fixed Angle Inverse Scattering for Almost Symmetric or Controlled Perturbations
Rakesh, Salo, Mikko. (2020). Fixed Angle Inverse Scattering for Almost Symmetric or Controlled Perturbations. SIAM Journal on Mathematical Analysis, 52(6), 5467-5499. https://doi.org/10.1137/20M1319309
Published inSIAM Journal on Mathematical Analysis
DisciplineInversio-ongelmien huippuyksikköMatematiikkaCentre of Excellence in Inverse ProblemsMathematics
© 2020 Society for Industrial & Applied Mathematics (SIAM)
We consider the fixed angle inverse scattering problem and show that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. We also show that almost symmetric or horizontally controlled potentials are uniquely determined by their fixed angle scattering data. This is done by establishing an equivalence between the frequency domain and the time domain formulations of the problem, and by solving the time domain problem by extending the methods of [Rakesh and M. Salo, Inverse Problems, 36 (2020), 035005] which adapts the ideas introduced in [A. Bukhgeim and M. Klibanov, Soviet Math. Dokl., 24 (1981), pp. 244--247] and [O. Imanuvilov and M. Yamamoto, Comm. Partial Differential Equations, 26 (2001), pp. 1409--1425] on the use of Carleman estimates for inverse problems.
PublisherSociety for Industrial & Applied Mathematics (SIAM)
Publication in research information system
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Related funder(s)European Commission; Academy of Finland
Funding program(s)Academy Project, AoF; Centre of Excellence, AoF
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingThe work of the first author was supported by the National Science Foundation grant DMS-1615616. The work of the second author was supported by the Academy of Finland grants 284715, 309963 and the European Research Council under Horizon 2020 grant ERC CoG 770924.
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