Bandlimited and Haar filtered back-projection reconstructions

A new way to discretize the filtered back-projection (FBP) algorithm is presented. The function basis is the Haar system (2D product of rectangular windows). This scheme allows one to derive the optimal shape of the apodisation window, which is angle varying, and the oversampling ratio between the pixel and the projection cell size. The discrete equivalent filter is also derived. The comparison of standard radial band-limited and separable Haar reconstructions shows that improvements, in terms of linearity, shift-invariance and aliasing, can be obtained even for the case of a limited number of views. Considerations of projection degradations are then analyzed according to a specific imaging device to derive the optimum oversampling ratio.