In this paper, a new approach to the Filtered BackProjection (FBP) algorithm is presented. The method is based on the reconstruction stability in Sobolev spaces and B-spline functions which define a Pixel Intensity Distribution Model (PIDM-n) according to the spline degree n of the desired reconstruction. It is shown that PIDM-n reconstructions can be efficiently obtained. Angular sampling is studied and comparison with standard FBP shows the superiority of the algorithm presented. Moreover, simulation studies of noise degradation and blur in the projections show the algorithm to be superior to FBP in this more realistic case.