面向相干X射线成像的复杂度引导鲁棒相位恢复
Robust phase retrieval with complexity-guidance for coherent X-ray imaging
AI总结：
针对相干X射线成像中RAAR-ER相位恢复算法解复杂度偏高、存在伪影且需大量试解平均的问题，提出复杂度引导的CG-RAAR方法，可得到无伪影、分辨率匹配且减少试解需求的更可靠恢复结果。
摘要：
从相干X射线成像（CXI）实验中记录的含噪、不完整傅里叶强度数据中重建稳定可靠的解是一项具有挑战性的问题。以若干次误差减少（Error Reduction, ER）迭代收尾的松弛平均交替反射（Relaxed Averaged Alternating Reflections, RAAR）算法是常用的解决方案。RAAR-ER算法通常从独立随机猜测出发运行数百次，得到多个试解，随后对这些试解取平均以得到相位恢复传递函数（Phase Retrieval Transfer Function, PRTF）。本文从我们近期工作中提出的复杂度参数的角度，检验了采用RAAR-ER方法得到的相位恢复解。我们观察到，单次运行RAAR-ER算法得到的解的复杂度高于基于复杂度参数的预期值，这体现为解中存在虚假的高频颗粒状伪影，即便对多个试解取平均后，这些伪影似乎也无法完全消除。随后我们提出了CG-RAAR（复杂度引导RAAR）相位恢复方法，该方法可有效解决这一不一致问题，得到无伪影的解。我们首先用模拟的无遮挡含噪傅里叶强度数据验证了CG-RAAR方法，随后将其应用于可从CXIDB数据库获取的中心遮挡含噪蓝细菌数据。我们采用CG-RAAR得到的模拟和实验结果表明，相较于常用的RAAR-ER算法，该方法有两项重要改进：其一，经平均过程得到的CG-RAAR解更可靠，其包含的最小特征尺寸与PRTF曲线估计的分辨率一致；其二，由于单次运行CG-RAAR得到的解不存在颗粒状伪影，平均过程所需的试解数量得以减少。
英文摘要：
Reconstruction of a stable and reliable solution from noisy incomplete Fourier intensity data recorded in a coherent X-ray imaging (CXI) experiment is a challenging problem. The Relaxed Averaged Alternating Reflections (RAAR) algorithm that is concluded with a number of Error Reduction (ER) iterations is a popular choice. The RAAR-ER algorithm is usually employed for several hundreds of times starting with independent random guesses to obtain trial solutions that are then averaged to obtain the phase retrieval transfer function (PRTF). In this paper, we examine the phase retrieval solution obtained using the RAAR-ER methodology from perspective of the complexity parameter that was introduced by us in recent works. We observe that a single run of the RAAR-ER algorithm produces a solution with higher complexity compared to what is expected based on the complexity parameter as manifested by spurious high frequency grainy artifacts in the solution that do not seem to go away completely even after a number of trial solutions are averaged. We then describe a CG-RAAR (Complexity Guided RAAR) phase retrieval method that can effectively address this inconsistency problem and provides artifact-free solutions. The CG-RAAR methodology is first illustrated with simulated unblocked noisy Fourier intensity data and later applied to centrally-blocked noisy cyanobacterium data which is available from the CXIDB database. Our simulation and experimental results using CG-RAAR suggest two important improvements over the popular RAAR-ER algorithm. The CG-RAAR solutions after the averaging procedure is more reliable in the sense that it contains smallest features consistent with the resolution estimated by the PRTF curve. Secondly, since the single run of the CG-RAAR solution does not have grainy artifacts, the number of trial solutions needed for the averaging process is reduced.
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