This paper describes a procedure proposed for the quantitative evaluation of the influence of the scattering noise on the reconstructed PET images. Applying the same experimental procedure used to evaluate the Scatter Fraction (SF) on the sinograms obtained measuring line sources within a uniform scattering medium, the method here proposed permits the computation, after reconstruction, of a derived index of the SF i.e. the Reconstructed Scatter Fraction (RSF). This offers the advantage of providing an estimate of the scatter noise directly on the images obtained in the same processing conditions as during the in vivo human studies. Comparative data of SF and RSF are reported as well as the effect of varying the filter function and of the measured attenuation correction on the RSF. The preliminary results obtained show that the values of the reconstructed scatter fraction are closer to the SF ones when this last is computed only in the cylinder region and the RSF is computed on images reconstructed with a ramp filter.