  We consider a particular approach to the regularization of the inverse
problem of computerized tomography. This approach is based on notions
pertaining to Fourier synthesis. It refines previous contributions, in which
the preprocessing of the data was performed according to the Fourier slice
theorem. Since real models must account for the geometrical system response and
possibly Compton scattering and attenuation, the Fourier slice theorem does not
apply, yielding redefinition of the preprocessing. In general, the latter is
not explicit, and must be performed numerically. The most natural choice of
preprocessing involves the computation of unstable solutions. A proximal
strategy is proposed for this step, which allows for accurate computations and
preserves global stability of the reconstruction process.
