Article Contents

2013, Volume 7, Issue 4: 1235-1250. Doi: 10.3934/ipi.2013.7.1235

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Multi-wave imaging in attenuating media

Andrew Homan^1,

1.
Department of Mathematics, Purdue University, West Lafayette, IN 47906

Received: January 2013

Revised: August 2013

Published: November 2013

Abstract / Introduction Related Papers Cited by

Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 35R30; Secondary: 35A27, 92C55.

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