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

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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.