Image reconstruction by OPED algorithm with averaging

OPED is a new image reconstruction algorithm based on orthogonal polynomial expansion on the disk. We show that the integral of the approximation function in OPED can be given explicitly and evaluated efficiently. As a consequence, the reconstructed image over a pixel can be effectively represented by its average over the pixel, instead of by its value at a single point in the pixel, which can help to reduce the aliasing caused by under sampling. Numerical examples are presented to show that the averaging process indeed improves the quality of the reconstructed images.