Simultaneous recovery of attenuation and source density in SPECT

Sean Holman; Philip Richardson

Simultaneous recovery of attenuation and source density in SPECT

Sean Holman, Philip Richardson

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that under a certain non-cancellation condition the attenuated Radon transform uniquely determines piecewise constant attenuation a and piecewise C²
source density ƒ 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 ƒ still appears to be possible although not yet explained by theoretical results.

Original language	English
Journal	Inverse Problems and Imaging
Publication status	Accepted/In press - 24 Jan 2023

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Licence: CC BY
Embargo ends: 1/01/30

Cite this

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title = "Simultaneous recovery of attenuation and source density in SPECT",

abstract = "We show that under a certain non-cancellation condition the attenuated Radon transform uniquely determines piecewise constant attenuation a and piecewise C2source density ƒ 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 ƒ still appears to be possible although not yet explained by theoretical results.",

author = "Sean Holman and Philip Richardson",

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AU - Richardson, Philip

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N2 - We show that under a certain non-cancellation condition the attenuated Radon transform uniquely determines piecewise constant attenuation a and piecewise C2source density ƒ 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 ƒ still appears to be possible although not yet explained by theoretical results.

AB - We show that under a certain non-cancellation condition the attenuated Radon transform uniquely determines piecewise constant attenuation a and piecewise C2source density ƒ 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 ƒ still appears to be possible although not yet explained by theoretical results.

M3 - Article

JO - Inverse Problems and Imaging

JF - Inverse Problems and Imaging

SN - 1930-8337

ER -

Simultaneous recovery of attenuation and source density in SPECT

Abstract

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