Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 263, Issue 9, Pages 5330-5376Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1007/BF01456804
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Funding
- Doctoral Program Dissipation and Dispersion in Nonlinear PDEs [FWF W1245]
- FWF-project Interdisciplinary Coupled Physics Imaging [FWF P26687]
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We analyse the ill-posedness of the photoacoustic imaging problem in the case of an attenuating medium. To this end, we introduce an attenuated photoacoustic operator and determine the asymptotic behaviour of its singular values. Dividing the known attenuation models into strong and weak attenuation classes, we show that for strong attenuation, the singular values of the attenuated photoacoustic operator decay exponentially, and in the weak attenuation case the singular values of the attenuated photoacoustic operator decay with the same rate as the singular values of the non-attenuated photoacoustic operator. (C) 2017 Elsevier Inc. All rights reserved.
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