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 language | English (US) |
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Pages (from-to) | 518-537 |
Number of pages | 20 |
Journal | SIAM Journal on Applied Mathematics |
Volume | 75 |
Issue number | 2 |
DOIs | |
State | Published - 2015 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Applied Mathematics