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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Finding discontinuities from tomographic data


Author: A. G. Ramm
Journal: Proc. Amer. Math. Soc. 123 (1995), 2499-2505
MSC: Primary 44A12
MathSciNet review: 1273517
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Abstract: A method for derivation of inversion formulas for the Radon transform of $ f(x)$ is given. This method allows one to construct functions $ \psi (x)$ which are easy to compute and which have the same wave fronts as $ f(x)$. This, in turn, allows one to calculate the singular support S of $ f(x)$ by computing $ \psi (x)$ given tomographic data. A simple geometrical relation between the singular supports of f and $ \hat f$, its Radon transform, is formulated (the duality law).


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DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1273517-6
PII: S 0002-9939(1995)1273517-6
Article copyright: © Copyright 1995 American Mathematical Society