Thermoacoustic tomography with variable sound speed

By Plamen Stefanov, Gunther Uhlmann. 2009

295 citations recorded by the source corpus.

We study the mathematical model of thermoacoustic tomography in media with a variable speed for a fixed time interval [0, T] so that all signals issued from the domain leave it after time T. In the case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann series expansion. We give almost necessary and sufficient conditions for uniqueness and stability when the measurements are taken on a part of the boundary.

Subfields: Biomedical Engineering, Mathematical Physics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/c47fa413cf5ed3baba1a4004a925b86081aa97ff

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In Biomedical Engineering

In Mathematical Physics

In Mechanics of Materials

Citations in the corpus

Inverse diffusion theory of photoacoustics (2009, background): “ energy is therefore quite accurate Inverse Diﬀusion Theory of Photoacoustics 2 in many practical settings. For references on the practical and theoretical aspects of PAT, we refer the reader to e.g. [1, 5, 6, 7, 9, 8, 10, 12, 13, 14, 15, 16, 17, 20, 21]. Once the amount of deposited energy has been”
Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems (2012, background): “[142] P. Stefanov and G. Uhlmann, Thermoacoustic tomography with variable sound speed, Inverse Problems, 25, 075011, 2009.”
Reconstruction of Coefficients in Scalar Second‐Order Elliptic Equations from Knowledge of Their Solutions (2011, background): “This first step of QPAT provides access to the following internal functionals [5, 6, 7, 19]”