Abstract

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.

© 1981 Optical Society of America

Closed form bandlimited image extrapolation

David K. Smith and Robert J. Marks
Appl. Opt. 20(14) 2476-2483 (1981)

Digital restoration of incoherent bandlimited images

Junji Maeda and Kazumi Murata
Appl. Opt. 21(12) 2199-2204 (1982)

Tomographic image reconstruction from limited projections using iterative revisions in image and transform spaces

Takuso Sato, Stephen J. Norton, Melvin Linzer, Osamu Ikeda, and Makoto Hirama
Appl. Opt. 20(3) 395-399 (1981)

Gerchberg’s extrapolation algorithm in two dimensions

Robert J. Marks
Appl. Opt. 20(10) 1815-1820 (1981)

Restoration of arbitrary finite-energy optical objects from limited spatial and spectral information

H. Stark, D. Cahana, and H. Webb
J. Opt. Soc. Am. 71(6) 635-642 (1981)