Marks Ii R J
Appl Opt. 1981 May 15;20(10):1815-20. doi: 10.1364/AO.20.001815.
Gerchberg's 1-D iterative extrapolation algorithm for bandlimited signals is generalized to two dimensions in two distinct ways. One generalization requires knowledge of the entire spectral pupil of the bandlimited image. The second requires only knowledge of two 1-D intervals formed by the vertical and horizontal projections of the pupil. For real bandlimited images of the low-pass type, this corresponds to knowing only the maximum x and y spatial frequencies of the image. The utilization of information of the known portion of the image in the extrapolation process is discussed for both algorithms. The second algorithm, reformulated discretely, is placed in closed form.
格奇伯格用于带限信号的一维迭代外推算法被以两种不同方式推广到二维。一种推广需要知道带限图像的整个频谱光瞳。第二种只需要知道由光瞳的垂直和水平投影形成的两个一维区间。对于低通型的实带限图像，这只相当于知道图像的最大x和y空间频率。针对这两种算法，讨论了在外推过程中利用图像已知部分信息的情况。重新离散化表述的第二种算法以封闭形式给出。
