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arXiv · 1112.0654

Application of a nudging technique to thermoacoustic tomography

Xavier Bonnefond·Sébastien Marinesque
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Abstract

ThermoAcoustic Tomography (TAT) is a promising, non invasive, medical imaging technique whose inverse problem can be formulated as an initial condition reconstruction. In this paper, we introduce a new algorithm originally designed to correct the state of an evolution model, the \emph{back and forth nudging} (BFN), for the TAT inverse problem. We show that the flexibility of this algorithm enables to consider a quite general framework for TAT. The backward nudging algorithm is studied and a proof of the geometrical convergence rate of the BFN is given. A method based on Conjugate Gradient (CG) is also introduced. Finally, numerical experiments validate the theoretical results with a better BFN convergence rate for more realistic setups and a comparison is established between BFN, CG and a usual inversion method.

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Xavier Bonnefond, Sébastien Marinesque. 2011-12-03. Application of a nudging technique to thermoacoustic tomography. https://arxiv.org/abs/1112.0654

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