We present a formal inversion of the multiscale discrete Radon trasform, valid both for 2D and
3D. With the transformed data from just one of the four quadrants of the direct 2D Radon
transform, or one of the twelve dodecants, in case of 3D Radon transform, we can invert exactly and directly, with no iterations, the whole domain. The computational complexity of the
proposed algorithms will be O(N log N). With N the total size of the problem, either square or
cubic. But this inverse transforms are extremely ill conditioned, so the presence of noise in the
transformed domain turns them useless. Still we present both algorithms, and characterize its
weakness against noise.
