Tomographic acquisition uses projection angles evenly distributed around 2π. The Mojette transform and the discrete Finite Radon Transform (FRT) both use discrete geometry to overcome the ill-posedeness of the inverse Radon transform. This paper focuses on the transformation of acquired tomographic projections into suitable discrete projection forms. Discrete Mojette and FRT algorithms can then be used for image reconstruction. The impact of physical acquisition parameters (which produce uncertainties in the detected projection data) is also analysed to determine the possible useful interpolations according to the choice of angle acquisitions and the null space of the transform. The mean square error (MSE) reconstruction results obtained for data from analytical phantoms consistently shows the superiority of these discrete approaches when compared to the classical "continuous space" FBP reconstruction.