Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data

Abstract

It is shown that the contraction mapping principle with the involvement of a Carleman Weight Function works for a Coefficient Inverse Problem for a 1D hyperbolic equation. Using a Carleman estimate, the global convergence of the corresponding numerical method is established. Numerical studies for both computationally simulated and experimentally collected data are presented. The experimental part is concerned with the problem of computing dielectric constants of explosive-like targets in the standoff mode using severely underdetermined data.

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Cited by in corpus (3)

• Numerical viscosity solutions to Hamilton-Jacobi equations via a Carleman estimate and the convexification method
• The Carleman convexification method for Hamilton-Jacobi equations on the whole space
• The Carleman contraction mapping method for quasilinear elliptic equations with over-determined boundary data