ITR: Phase Retrieval Algorithms

ITR：相位检索算法

• 批准号: 0081775
• 负责人: Veit Elser
• 金额: $ 23.43万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-01 至 2003-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0081775&HistoricalAwards=false
• 关键词: ITR; Phase; Retrieval; Algorithms

X-ray crystallography is a fundamental technique for determining the structure of proteins. However, the physics of this process means that information about the relative phases of the thousands of x-ray beams used in the process is lost. The recovery of phases is referred to as "phase retrieval." Essentially all modern algorithms for phase retrieval are iterative, including the well-known "Shake and Bake" algorithm. However, a general problem with iterative approaches is that the iterates are drawn to attractors that are not true solutions. This project will investigate a significantly different, non-iterative approach that does not share this drawback. If successful, the result will be a computing environment that will benefit a variety of disciplines that engage in phase retrieval.The new algorithm exploits techniques in optimization theory that have never been used in phase retrieval before. One key idea is to use a different objective function from past approaches: the zero-frequency component, or "charge" Q. A key property of Q is linearity, which avoids the many local minima that stagnate iterative methods for other objective functions. In the language of optimization theory, the objective function Q permits a direct translation of the phase retrieval problem into a mixed-integer program (MIP). Decades of research on solving MIPs can thus be applied to solve difficult instances of phase retrieval encountered in crystallography.

X射线晶体学是确定蛋白质结构的基本技术。然而，这一过程的物理学意味着，有关该过程中使用的数千个X射线束的相对相位的信息丢失了。相位的恢复被称为“相位恢复”。基本上，所有用于相位恢复的现代算法都是迭代的，包括众所周知的“Shake and Bake”算法。然而，迭代方法的一个普遍问题是迭代被吸引到不是真解的吸引子。这个项目将研究一个显著不同的，非迭代的方法，不共享这个缺点。如果成功的话，结果将是一个计算环境，将有利于各种学科从事相位retrieval.The新的算法利用优化理论中的技术，从来没有被用于相位retrieval.The的新算法。一个关键的想法是使用与过去方法不同的目标函数：零频率分量，或“电荷”Q。Q的一个关键属性是线性，它避免了许多局部最小值，这些局部最小值会使其他目标函数的迭代方法停滞。在优化理论的语言中，目标函数Q允许将相位恢复问题直接转化为混合整数规划（MIP）。因此，数十年来对解决MIP的研究可以应用于解决晶体学中遇到的相恢复的困难情况。