  We find a new and simple inversion formula of the Radon transform RT with the
only use of the shearlet system and of well-known properties of RT. No
intertwining relation of differential operators in Euclidean space and Radon
domain is used. As a consequence, an additive noise is not incremented. Since
the continuum theory of shearlets has a straight translation to the discrete
theory, we find a fast, stable and computable algorithm that recovers a digital
image from noisy samples of the Radon transform preserving edges. In the
process, we find a more natural and easier-to-construct density-compensation
weight functions for the ShearLab toolbox.
