A globally convergent numerical method for an inverse elliptic problem of optical tomography

Abstract

A new globally convergent numerical method is developed for an inverse problem for the elliptic equation with the unknown potential. The boundary data simulating measurements in optical tomography are generated by the running source. Global convergence analysis is presented along with numerical experiments.

Keywords:

• globally convergent method
• inverse problems
• diffuse optical tomography

AMS Subject Classifications:

• 65N21
• 65D10
• 65F10

Acknowledgements

The work of all authors was supported by the National Institutes of Health grant number 1R21NS052850-01A1. The work of MK was also supported by the U.S. Army Research Laboratory and U.S. Army Research Office under contracts/grant number W911NF-08-1-0470.