The aim of this article is to provide and compare several numerical methods for the tomographic reconstruction of blurred and noised binary images, based on one single snapshot taken from an axially symmetric 3D object. This problem is motivated by a physical experiment of the CEA, where a single radiography is taken during the implosion process of some dense such object and is strongly blurred and noised. In a previous article [3] we have provided a refined functional analysis of the Radon operator restricted to axisymmetric functions and proved that it enjoys strong regularity properties in fractional order Hilbert spaces. Based on that theoretical study, we provide here the details of the numerical solving of a minimization problem settled in suitable fractional order Hilbert spaces, using a numerical approximation of the fractional Laplacian and some adapted Newton-like methods. The resulting procedure happens to be very efficient, both for the execution time and for the quality of the reconstruction. We compare this approach with two other numerical approaches: the first one uses the Fourier transform, and the second uses a wavelet reconstruction sofware.