Cahana D, Stark H
Appl Opt. 1981 Aug 15;20(16):2780-6. doi: 10.1364/AO.20.002780.
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.
格奇伯格 - 帕普利斯（GP）算法在与带限或空间受限图像外推相关的文献中已被广泛讨论。尽管与早期的超分辨率方案相比，它似乎具有更优越的抗噪性能，但GP算法通常收敛速度非常慢，因此起始点的选择至关重要。我们讨论了如何将额外的先验信息，如图像的低通投影（LPI），纳入算法中，以减少递归起始点与真实信号之间的初始误差。我们还研究了如何通过以下方式提高收敛速度：（1）在每次迭代中使用LPI以实现每周期双校正，以及（2）应用自适应阈值处理。有点令人惊讶的是，发现使用LPI对收敛速度的影响很小。另一方面，当与自适应阈值处理相结合时，LPI的使用既显著降低了起始点误差，又提高了收敛速度。
