  We study the effect of additive noise to the inversion of FIOs associated to
a diffeomorphic canonical relation. We use the microlocal defect measures to
measure the power spectrum of the noise and analyze how that power spectrum is
transformed under the inversion. In particular, we compute the standard
deviation of the noise added to the inversion as a function of the standard
deviation of the noise added to the data. As an example, we study the Radon
transform in the plane in parallel and fan-beam coordinates, and present
numerical examples.
