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Singularities of the Radon transform

Alexander G. Ramm·Alexander I. Zaslavsky
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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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BibTeXRIS

Alexander G. Ramm, Alexander I. Zaslavsky. 1993-01-01. Singularities of the Radon transform. https://arxiv.org/abs/math/9301215

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