  We prove that the unitary affine Radon transform intertwines the
quasi-regular representation of a class of semidirect products, built by
shearlet dilation groups and translations, and the tensor product of a standard
wavelet representation with a wavelet-like representation. This yields a
formula for shearlet coefficients that involves only integral transforms
applied to the affine Radon transform of the signal, thereby opening new
perspectives in the inversion of the Radon transform.
