Workshop on Bioimaging I, Fri, 16 Nov, 2007
Speaker: Michael Klibanov
Abstract
The development of numerical methods for multidimensional coefficient inverse problems is a quite challenging task. Two phenomenon cause major difficulties in achieving this task: nonlinearity and ill-posedness. Our strategic goal is to develop globally convergent numerical methods, whose convergence will be rigorously guaranteed and numerical performance will be verified for at least some applications. We will present one of such methods, the so-called "convexification" algorithm (Klibanov and Timonov, 2003-06), as well as its modifications (Klibanov and Xin; Klibanov and Kuhjuget; Klibanov, Shan, Su and Liu). We will also present a new numerical method for thermoacoustic tomography (Clason and Klibanov). These results are actually based on the theory of Carleman estimates, and corresponding theorems will also be presented.
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
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