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Singularities of the Radon transform


Authors: A. G. Ramm and A. I. Zaslavsky
Journal: Bull. Amer. Math. Soc. 28 (1993), 109-115
MSC: Primary 44A12; Secondary 53C65, 92C55
DOI: https://doi.org/10.1090/S0273-0979-1993-00350-1
MathSciNet review: 1168516
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Abstract: Singularities of the Radon transform of a piecewise smooth function $ f(x)$, $ x \in {R^n}$, $ n \geq 2$, are calculated. If the singularities of the Radon transform are known, then the equations of the surfaces of discontinuity of $ f(x)$ are calculated by applying the Legendre transform to the functions, which appear in the equations of the discontinuity surfaces of the Radon transform of $ f(x)$; examples are given. Numerical aspects of the problem of finding discontinuities of $ f(x)$, given the discontinuities of its Radon transform, are discussed.


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DOI: https://doi.org/10.1090/S0273-0979-1993-00350-1
Article copyright: © Copyright 1993 American Mathematical Society

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