On singularities and instability of reconstruction in thermoacoustic tomography

Details On singularities and instability of reconstruction in thermoacoustic tomography On singularities and instability of reconstruction in thermoacoustic tomography

2009-11-29

arxiv.org/abs/0911.5521v2

Mathematics

Analysis of PDEs

Scientific paper

We consider the problem of thermoacoustic tomography (TAT), in which one
needs to reconstruct the initial value of a solution of the wave equation from
its value on an observation surface. We show that if some geometric rays for
the equation do not intersect the observation surface, the reconstruction in
TAT is not H\"{o}lder stable.

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