Abstract

A new Markov random field based algorithm is proposed for signal reconstruction from Fourier transform magnitude motivated by the data reduction calculations of x-ray crystallography. The purpose of an x-ray crystallography experiment is to determine the position in three dimensional space of each atom in a molecule. The measured data are the magnitudes squared of the Fourier transform of the electron density function of a crystal of the molecule of interest and possibly also of chemical derivatives. The data reduction calculations are a signal reconstruction problem for the three dimensional electron density. In the so-called “direct” methods of interest here, the reconstruction is based on a noisy measurement of the magnitude squared of the Fourier transform of the electron density of a single crystal, that is, no chemical derivatives of the molecule are studied.

© 1992 Optical Society of America