In this paper, formulas relating the Radon transform and Radon transform inversion to various wavelet and multiscale transformations, including the continuous wavelet transform, the semi-continuous wavelet transform of Mallat, steerable multiscale filters of Freeman and Adelson, and separable orthogonal and nonorthogonal wavelet bases, are given. The use of wavelets as a valuable tool in the local inversion of the Radon transform in even dimensions is justified, and explicit estimates on the decay of ramp-filtered wavelets is given.