Reconstruction of a stable and good quality solution from noisy single-shot Fourier intensity data is a challenging problem for phase retrieval algorithms. We examine behavior of the solution provided by the hybrid input–output (HIO) algorithm for noisy data, from the perspective of the complexity guidance methodology that was introduced by us in an earlier paper [J. Opt. Soc. Am. A 36, 202 (2019) [CrossRef] ]. We find that for noisy data, the complexity of the solution outside the support keeps increasing as the HIO iterations progress. Based on this observation, a strategy for controlling the solution complexity within and outside the support during the HIO iterations is proposed and tested. In particular, we actively track and control the growth of complexity of the solution outside the support region with iterations. This in turn provides us with guidance regarding the level to which the complexity of the solution within the support region needs to be adjusted, such that the total solution complexity is equal to that estimated from raw Fourier intensity data. In our studies, Poisson noise with mean photon counts per pixel in the Fourier intensity data ranges over four orders of magnitude. We observe that the performance of the proposed strategy is noise robust in the sense that with increasing noise, the quality of the phase solution degrades gradually. For higher noise levels, the solution loses textural details while retaining the main object features. Our numerical experiments show that the proposed strategy can uniformly handle pure phase objects, mixed amplitude-phase objects, and the case of dc blocked Fourier intensity data. The results may find a number of applications where single-shot Fourier phase retrieval is critical to the success of corresponding applications.

中文翻译：

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从噪声数据中进行复杂度指导的傅立叶相位检索

从嘈杂的单次傅立叶强度数据重建稳定和高质量的解决方案对于相位检索算法而言是一个具有挑战性的问题。从我们在较早的论文中介绍的复杂性指导方法的角度，我们研究了混合输入输出（HIO）算法为嘈杂数据提供的解决方案的行为[J. 选择。Soc。是。甲36，202（2019）[交叉引用] ]。我们发现，对于嘈杂的数据，随着HIO迭代的进行，支持之外的解决方案的复杂性不断增加。基于此观察结果，提出并测试了在HIO迭代过程中控制支撑内外支撑解决方案复杂性的策略。特别是，我们通过迭代主动跟踪和控制解决方案在支持区域之外的复杂性的增长。反过来，这为我们提供了有关需要将支撑区域内的解决方案的复杂度调整到何种程度的指导，以使总解决方案的复杂度等于根据原始傅立叶强度数据估算的复杂度。在我们的研究中，傅立叶强度数据中每个像素的平均光子计数的泊松噪声范围超过四个数量级。我们观察到，所提出的策略的性能具有一定的噪声鲁棒性，即随着噪声的增加，相位解决方案的质量会逐渐降低。对于更高的噪声水平，解决方案会丢失纹理细节，同时保留主要对象特征。我们的数值实验表明，所提出的策略可以均匀地处理纯相位对象，混合幅度相位对象以及直流阻塞傅立叶强度数据的情况。结果可能会发现许多应用，其中单次傅里叶相位检索对于相应应用的成功至关重要。我们的数值实验表明，所提出的策略可以均匀地处理纯相位对象，混合幅度相位对象以及直流阻塞傅立叶强度数据的情况。结果可能会发现许多应用，其中单次傅里叶相位检索对于相应应用的成功至关重要。我们的数值实验表明，所提出的策略可以均匀地处理纯相位对象，混合幅度相位对象以及直流阻塞傅立叶强度数据的情况。结果可能会发现许多应用，其中单次傅里叶相位检索对于相应应用的成功至关重要。