Algorithm for recovering discontinuities of a function from its Radon transform (Q1195656)

In many applications of computer tomography it is not necessary to do a complete inversion of tomographic data, but only to locate discontinuities of the unknown piecewise smooth function. The present paper proposes a simple method for locating the discontinuities of a function \(f\) given the singularity curve \(p(\alpha)\) of its Radon transform \(Rf\). It is based on the fact that the singularities of \(Rf\) can be found at lines tangent to the discontinuity curves of \(f\). Problems of numerical implementation of the method are not discussed here.