Abstract
Since all attenuation models for dissipative media that come into question for thermoacoustic tomography (TAT) violate causality, a causal attenuation model for TAT is proposed. A goal of this article is to discuss causality in the context of dissipative wave propagation and TAT. In the process we shortly discuss the frequency power law, a causal attenuation model (with a constant wave front speed which can be adjusted via an additional parameter) and the respective wave equation. Afterwards an integral equation model for estimating the unattenuated pressure data of TAT from the attenuated pressure data of TAT is presented and discussed. Our numerical results show a fast decrease of resolution of TAT for increasing distance of the object of interest from the pressure detector.
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Kowar, R. (2012). On Causality of Thermoacoustic Tomography of Dissipative Tissue. In: Günther, M., Bartel, A., Brunk, M., Schöps, S., Striebel, M. (eds) Progress in Industrial Mathematics at ECMI 2010. Mathematics in Industry(), vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25100-9_59
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DOI: https://doi.org/10.1007/978-3-642-25100-9_59
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