Finding discontinuities from tomographic data

Ramm, A. G.

doi:10.1090/S0002-9939-1995-1273517-6

Finding discontinuities from tomographic data
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Proc. Amer. Math. Soc. 123 (1995), 2499-2505 Request permission

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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Finding jumps of a function using local tomography

Radon transform and some of its applications