Global convergence for a 1-D inverse problem with application to imaging of land mines

Abstract

A new globally convergent numerical method is developed for a 1-D coefficient inverse problem for a hyperbolic partial differential equation (PDE). The back reflected data are used. A version of the quasi-reversibility method is proposed. A global convergence theorem is proven via a Carleman estimate. The results of numerical experiments are presented.

Keywords:

• inverse problems
• globally convergent method
• quasi-reversibility method
• Carleman estimate

AMS Subject Classifications::

• 15A15
• 15A09
• 15A23

Acknowledgements

This work was supported by the US Army Research Laboratory and US Army Research Office under grant number W911NF-05-1-0378. The authors are grateful to Professor Paul Sacks (Iowa State University) for kindly providing his data for blind testing.