A method for derivation of inversion formulas for the Radon transform
of f(x) is given. This method allows one to construct functions psi(x)
which are easy to compute and which have the same wave fronts as f(x)
. This, in turn, allows one to calculate the singular support S of f(x
) by computing psi(x) given tomographic data. A simple geometrical rel
ation between the singular supports of f and (f) over cap, its Radon t
ransform, is formulated (the duality law).