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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the injectivity of the attenuated Radon transform


Author: Alexander Hertle
Journal: Proc. Amer. Math. Soc. 92 (1984), 201-205
MSC: Primary 44A15; Secondary 65R10, 92A07
DOI: https://doi.org/10.1090/S0002-9939-1984-0754703-0
MathSciNet review: 754703
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Abstract: We show that the attenuated (exponential) Radon transform $ {R_\mu }$, where $ \mu $ is assumed to be linear in the space variable, is injective on compactly supported distributions. Moreover, a limited angle reconstruction is possible and a hole theorem holds. We review the well-known special case of constant attenuation.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0754703-0
Keywords: Attenuated Radon transform, generalized Radon transform, Fourier transform
Article copyright: © Copyright 1984 American Mathematical Society