For protein crystals in which more than two thirds of the volume is occupied by solvent, the featureless nature of the solvent region often generates a constraint that is powerful enough to allow direct phasing of X-ray diffraction data. Practical implementation relies on the use of iterative projection algorithms with good global convergence properties to solve the difficult nonconvex phase-retrieval problem. In this paper, some aspects of phase retrieval using iterative projection algorithms are systematically explored, where the diffraction data and density-value distributions in the protein and solvent regions provide the sole constraints. The analysis is based on the addition of random error to the phases of previously determined protein crystal structures, followed by evaluation of the ability to recover the correct phase set as the distance from the solution increases. The properties of the difference-map (DM), relaxed-reflect-reflect (RRR) and relaxed averaged alternating reflectors (RAAR) algorithms are compared. All of these algorithms prove to be effective for crystallographic phase retrieval, and the useful ranges of the adjustable parameter which controls their behavior are established. When these algorithms converge to the solution, the algorithm trajectory becomes stationary; however, the density function continues to fluctuate significantly around its mean position. It is shown that averaging over the algorithm trajectory in the stationary region, following convergence, improves the density estimate, with this procedure outperforming previous approaches for phase or density refinement.

中文翻译：

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使用迭代投影算法分析晶体相检索。


对于超过三分之二体积被溶剂占据的蛋白质晶体，溶剂区域的无特征性质通常会产生一个足够强大的约束，以允许 X 射线衍射数据的直接定相。实际实现依赖于使用具有良好全局收敛特性的迭代投影算法来解决困难的非凸相位恢复问题。在本文中，系统地探讨了使用迭代投影算法进行相恢复的某些方面，其中蛋白质和溶剂区域的衍射数据和密度值分布提供了唯一的约束。该分析基于向先前确定的蛋白质晶体结构的相添加随机误差，然后评估随着与溶液距离的增加而恢复正确相集的能力。比较了差值图 （DM） 、松弛反射 （RRR） 和松弛平均交替反射器 （RAAR） 算法的特性。所有这些算法都被证明对晶体学相检索是有效的，并且建立了控制其行为的可调参数的有用范围。当这些算法收敛到解时，算法轨迹变为平稳;然而，密度函数继续在其平均位置附近大幅波动。结果表明，在收敛之后，在静止区域中对算法轨迹进行平均可以提高密度估计，该程序的性能优于以前的相位或密度细化方法。