RIA: Multidimensional Bayesian Signal Reconstruction Motivated by X-ray Crystallography

这个提议的核心是非常困难的x射线晶体学重建问题——给定晶体电子密度的傅里叶变换的大小，重建电子密度，并因此确定要成像的分子原子的位置。主要的主题是一种基于马尔可夫随机场的新的统计方法，它承诺允许更容易和更有效地结合先验信息，如原子的可能位置，键的价结构，以及更一致地使用统计信息。在本研究过程中开发的方法将在模式识别和非凸优化等其他环境中有用。

At the heart of this proposal is the very difficult X-ray crystallography reconstruction problem - given the magnitude of the Fourier transform of the electron density of a crystal, reconstruct the electron density, and, hence, determine the locations of the atoms of the molecule to be imaged. The major theme is a new statistical approach based on Markov random fields which promises to permit easier and more effective incorporation of prior information such as the possible locations of the atoms, and on the valence structure of the bonds, and a more consistent use of statistical information. Methods which will be developed during the course of this investigation will be useful in other contexts such as pattern recognition and nonconvex optimization.