Butola Mansi, Rajora Sunaina, Khare Kedar
J Opt Soc Am A Opt Image Sci Vis. 2019 Feb 1;36(2):202-211. doi: 10.1364/JOSAA.36.000202.
Iterative phase retrieval methods based on the Gerchberg-Saxton (GS) or Fienup algorithm typically show stagnation artifacts even after a large number of iterations. We introduce a complexity parameter that can be computed directly from the Fourier magnitude data and provides a measure of fluctuations in the desired phase retrieval solution. It is observed that when initiated with a constant or a uniformly random phase map, the complexity of the Fienup solution containing stagnation artifacts stabilizes at a numerical value that is higher than . We propose a modified Fienup algorithm that uses a controlled sparsity-enhancing step such that in every iteration the complexity of the resulting guess solution is explicitly made close to . This approach, which we refer to as complexity-guided phase retrieval, is seen to provide an artifact-free phase retrieval solution within a few hundred iterations. Numerical illustrations are provided for both amplitude as well as phase objects with and without Poisson noise introduced in the Fourier intensity data. The complexity-guidance concept may potentially be combined with a variety of phase retrieval algorithms and can enable several practical applications.
基于格尔奇伯格 - 萨克斯顿（GS）或菲纽普算法的迭代相位恢复方法通常即使在大量迭代之后仍会出现停滞伪影。我们引入一个复杂度参数，它可以直接从傅里叶幅度数据计算得出，并提供了一种对所需相位恢复解中的波动的度量。据观察，当用常数或均匀随机相位图初始化时，包含停滞伪影的菲纽普解的复杂度会稳定在一个高于该参数数值的值。我们提出一种改进的菲纽普算法，该算法使用一个可控的稀疏增强步骤，使得在每次迭代中，所得猜测解的复杂度明确地接近该参数值。这种方法，我们称之为复杂度引导的相位恢复，被发现能在几百次迭代内提供无伪影的相位恢复解。针对在傅里叶强度数据中引入和未引入泊松噪声的幅度和相位物体都给出了数值示例。复杂度引导概念可能潜在地与多种相位恢复算法相结合，并能实现若干实际应用。
