Singularities of the Radon transform of a class of piecewise smooth functions in \(R^{2}\) (Q2431044)

The paper is concerned with the recovery of edge information from the Radon transform. More precisely, let \(f \in C^{\infty}(\mathbb{R}^2 \setminus \Gamma)\), where \(\Gamma\) is the finite union of smooth curves. Denote the Radon transform of \(f\) by \(Rf (p,\omega)\), with \(p \in \mathbb{R}\) and \(\omega \in \mathbb{S}^1\). The chief result of the paper relates the points of lower regularity of \(Rf\) to tangent vectors of \(\Gamma\). The final section explains how to explicitly recover \(\Gamma\) from the singularities of \(Rf\) using the Legendre transform.