In SPECT, both the noise affecting the data and the discretization of the inverse Radon transform are responsible for the ill-posed nature of the reconstruction. To constrain the problem, we propose a regularized backprojection method (RBP) which takes advantage of the relationships existing between the continuity properties of the projections and those of the reconstructed object. The RBP method involves two stages: first, a statistical model (the fixed-effect model) is used to estimate the noise-free part of the projections. Then, the filtered projections are reconstructed using a backprojection algorithm (spline filtered backprojection) which ensures that the reconstructed object belongs to a space consistent with that containing the projections. The method is illustrated using analytical simulations, and the RBP approach is compared to the conventional filtered backprojection. The effect on the reconstructed slices of the parameters involved in RBP is studied in terms of spatial resolution, homogeneity in uniform regions and quantification. It is shown that appropriate combinations of these parameters yield a better compromise between homogeneity and spatial resolution than conventional FBP, with similar quantification performances.