arXiv:0911.5521 Abstract | arXiv Analytics

arXiv:0911.5521 [math.AP]Abstract References Reviews Resources

On singularities and instability of reconstruction in thermoacoustic tomography

Published 2009-11-29, updated 2009-12-15Version 2

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.

Categories: math.AP

Subjects: 35R30, 92C55

Keywords: thermoacoustic tomography, reconstruction, singularities, observation surface, instability

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