Bandlimited image extrapolation with faster convergence.

The Gerchberg-Papoulis (GP) algorithm has been widely discussed in the literature in connection with band-limited or space-limited image extrapolation. Despite its seemingly superior noise-resistant properties over earlier superresolution schemes, the GP algorithm generally exhibits very slow convergence thereby making the choice of starting point critical. We discuss how additional a priori information, such as the low-pass projection of the image (LPI), can be incorporated in the algorithm to decrease the initial error between the starting point of the recursion and the true signal. We also investigate how convergence rates might be improved by (1) using the LPI in each iteration to achieve a double per cycle correction, and (2) applying adaptive thresholding. Somewhat surprisingly, it was found that using the LPI had only a minor effect on the rate of convergence. On the other hand, when combined with adaptive thresholding the use of the LPI both significantly reduced the starting point error and improved the rate of convergence.