  A generalized cross-validation approach to estimate the reconstruction filter
bandwidth in two-dimensional Filtered Backprojection is presented. The method
writes the reconstruction equation in equivalent backprojected filtering form,
derives results on eigendecomposition of symmetric two-dimensional circulant
matrices and applies them to make bandwidth estimation a computationally
efficient operation within the context of standard backprojected filtering
reconstruction. Performance evaluations on a wide range of simulated emission
tomography experiments give promising results. The superior performance holds
at both low and high total expected counts, pointing to the method's
applicability even in weaker signal-noise situations. The approach also applies
to the more general class of elliptically symmetric filters, with
reconstruction performance often better than even that obtained with the true
optimal radially symmetric filter.
