A new version of the quasi-reversibility method for the thermoacoustic tomography and a coefficient inverse problem

Abstract

An inverse problem of the determination of an initial condition in a hyperbolic equation from the lateral Cauchy data is considered. This problem has applications to the thermoacoustic tomography, as well as to linearized coefficient inverse problems of acoustics and electromagnetics. A new version of the quasi-reversibility method is described. This version requires a new Lipschitz stability estimate, which is obtained via the Carleman estimate. Numerical results are presented.

Keywords:

• quasi-reversibility method
• Carleman estimate
• numerical results
• imaging of sharp peaks

AMS Subject Classifications: :

• 65N21
• 65D10
• 65F10

Acknowledgements

The research of M.V. Klibanov and A.V. Kuzhuget was supported by the U.S. Army Research Laboratory and U.S. Army Research Office under contract/grant number W911NF-05-1-0378. M.V. Klibanov has performed a part of this work during the Special Semester on Quantative Biology Analyzed by Mathematical Methods, 1 October 2007 to 27 January 2008, organized by RICAM, Austrian Academy of Sciences.