Bayesian Image Reconstruction in X-ray Fiber Diffraction

Abstract

The structure completion problem in x-ray fiber diffraction analysis, a crystallographic method for studying polymer structures, involves reconstructing an incomplete image from a known part and experimental data in the form of the squared amplitudes of the Fourier coefficients. Formulating this as a Bayesian estimation problem allows explicit expressions for MMSE and MAP estimates to be obtained. Calculations using simulated fiber diffraction data show that the MMSE estimate out- performs current methods that correspond to certain MAP estimates.