Singular Values of the Attenuated Photoacoustic Imaging Operator
Functional Analysis
2016-11-18 v1 Analysis of PDEs
Spectral Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1611.05807,
title = {Singular Values of the Attenuated Photoacoustic Imaging Operator},
author = {Peter Elbau and Otmar Scherzer and Cong Shi},
journal= {arXiv preprint arXiv:1611.05807},
year = {2016}
}