Inverse Problems for Wave Equation and Imaging

Abstract

In this talk, the problem of reconstruction of sound speed and attenuation in the wave equation will be discussed. In an overdetermined statement, the speaker uses some versions of the boundary control method for solving this problem. The solution is reduced to the precision of moments.

Another problem to be discussed in this talk is the imaging in ultrasound medicine tomography. An example of the acoustical model would be the fat and granular tissues with known velocities and several unknown small and weak inclusions. The speaker and his group use a method based on the reverse time migration to first determine the unknown boundary between fat and boundary tissues and then the image of inclusions.

About the speaker

Prof. Leonid Pestov received his two doctoral degrees in Mathematics from the Computing Centre of Siberian Branch of USSR Academy of Sciences in 1979 and from the Sobolev Institute of Mathematics of Russia in 2004. He is currently a Professor of Mathematics and the Head of the Laboratory at the Institute of Applied Informatics and Mathematical Geophysics of the Immanuel Kant Baltic Federal University.

Prof. Pestov’s research interests include inverse problems of mathematical physics, inverse problems of geometry, numerical solving of inverse problems and imaging. He authored two books on tomography problems.

About the program

For more information, please refer to the program website at http://iasprogram.ust.hk/inverseproblems.