ABSTRACT
This chapter proposes an idea for finding discontinuity curve of the original function from its tomographic data. It derives a subset of the tomographic data which is in a one-to-one correspondence with the discontinuity surfaces of the density function. The chapter briefly recalls the main facts which are needed for constructing the algorithm for geometrical tomography. It provides a description of the algorithm and different numerical experiments. Two-dimensional tomographic data is considered, and different methods are developed for numerical finding of the density function. The chapter derives a set of noisy values of the Radon transform based on independent and identically distributed random variables with finite first and second moments. At present, geometrical tomography does not allow one to compute values of jumps and, moreover, its numerical realization is much less stable with respect to noise in the data than local tomography or pseudolocal tomography.
