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Licensed Unlicensed Requires Authentication Published by De Gruyter September 11, 2020

Solving a 1-D inverse medium scattering problem using a new multi-frequency globally strictly convex objective functional

  • Nguyen T. Thành ORCID logo EMAIL logo and Michael V. Klibanov ORCID logo

Abstract

We propose a new approach to constructing globally strictly convex objective functional in a 1-D inverse medium scattering problem using multi-frequency backscattering data. The global convexity of the proposed objective functional is proved. We also prove the global convergence of the gradient projection algorithm and derive an error estimate. Numerical examples are presented to illustrate the performance of the proposed algorithm.

MSC 2010: 35R30; 35J05; 78A46

Dedicated to to Professor Anatoly Yagola on his 75th birthday


Award Identifier / Grant number: W911NF-19-1-0044

Funding source: US Army Research Office

Award Identifier / Grant number: W911NF-19-1-0044

Funding statement: The work of Michael V. Klibanov was supported by US Army Research Laboratory and US Army Research Office grant W911NF-19-1-0044.

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Received: 2020-04-07
Accepted: 2020-08-24
Published Online: 2020-09-11
Published in Print: 2020-11-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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