An algorithm for two-dimensional reconstruction of a discontinuous density from its Radon transform

X-ray tomography is an important way of finding the density of objects in medical imaging evaluation. In many applications of computer tomography, one can be interested not in the complete inverse of tomography data but only in determining discontinuities of the unknown piecewise continuous 2D density, from its Radon transform. In this paper, we propose a new computational filtered backprojection algorithm for the solution of this problem. A function f_M is defined and computed from the Radon transform of the density function f; one can recover the locations and values of jumps in the original density f from those in f_M