Comparative studies of the globally convergent convexification algorithm with application to imaging of antipersonnel land mines

Abstract

A comparative study of various aspects on the globally convergent convexification algorithm for coefficient inverse problems is described. Numerical results of the algorithm with application to detection of antipersonnel land mines are presented. The aspects studied include initial guess and layer size for the layer stripping approach, dimensions of the basis for spatial and pseudo-frequency approximations, the lower limit of the integrals with respect to pseudo-frequency κ, the stopping criteria of steepest descent method in the least squares minimization, the tails to compensate the truncated integration with respect to κ, the parameter λ associated with the Carleman weight function, and adding different noise levels to the input data for the coefficient inverse problems. With our new implementation, the convexification algorithm is very efficient and feasible to be applied in real time to detect antipersonnel land mines in the field.

Keywords:

• Global convergence
• Convexification algorithm
• Coefficient inverse problems
• Tails
• Detection and imaging of land mines

Keywords:

• AMS Subject Classifications: 65N21
• 65D10
• 65F10

Acknowledgements

This research was supported by the US Army Research Laboratory and US Army Research Office under contract/grant number W911NF-05-1-0378.