American Institute of Mathematical Sciences

November  2013, 7(4): 1235-1250. doi: 10.3934/ipi.2013.7.1235

Multi-wave imaging in attenuating media

 1 Department of Mathematics, Purdue University, West Lafayette, IN 47906, United States

Received  January 2013 Revised  August 2013 Published  November 2013

We consider a mathematical model of thermoacoustic tomography and other multi-wave imaging techniques with variable sound speed and attenuation. We find that a Neumann series reconstruction algorithm, previously studied under the assumption of zero attenuation, still converges if attenuation is sufficiently small. With complete boundary data, we show the inverse problem has a unique solution, and modified time reversal provides a stable reconstruction. We also consider partial boundary data, and in this case study those singularities that can be stably recovered.
Citation: Andrew Homan. Multi-wave imaging in attenuating media. Inverse Problems & Imaging, 2013, 7 (4) : 1235-1250. doi: 10.3934/ipi.2013.7.1235
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