Recovering dielectric constants of explosives via a globally strictly convex cost functional

Michael V. Klibanov, Nguyen Trung Th'anh

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

The inverse problem of estimating dielectric constants of explosives using boundary measurements of one component of the scattered electric field is addressed. It is formulated as a coefficient inverse problem for a hyperbolic differential equation. After applying the Laplace transform, a new cost functional is constructed and a variational problem is formulated. The key feature of this functional is the presence of the Carleman weight function for the Laplacian. The strict convexity of this functional on a bounded set in a Hilbert space of an arbitrary size is proven. This allows for establishing the global convergence of the gradient descent method. Some results of numerical experiments are presented.

Original languageEnglish (US)
Pages (from-to)518-537
Number of pages20
JournalSIAM Journal on Applied Mathematics
Volume75
Issue number2
DOIs
StatePublished - 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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