Simultaneous recovery of attenuation and source density in SPECT

Sean Holman; Philip Richardson

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arXiv · 2206.10208

Simultaneous recovery of attenuation and source density in SPECT

Sean Holman·Philip Richardson

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Abstract

We show that under a certain non-cancellation condition the attenuated Radon transform uniquely determines piecewise constant attenuation $a$ and piecewise $C^2$ source density $f$ with jumps over real analytic boundaries possibly having corners. We also look at numerical examples in which the non-cancellation condition fails and show that unique reconstruction of multi-bang $a$ and $f$ is still appears to be possible although not yet explained by theoretical results.

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Sean Holman, Philip Richardson. 2022-06-21. Simultaneous recovery of attenuation and source density in SPECT. https://arxiv.org/abs/2206.10208

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