Bayesian reconstruction of signals invariant under a space-group symmetry from Fourier transform magnitudes

摘要

A Bayesian signal reconstruction problem, motivated by X-ray crystallography, which includes magnitude of Fourier transform measurements and a Markov random field a priori model was approximately solved by Doerschuk (see J. Opt. Soc. Amer. A, vol.8, no.8, p.1222-1232 and p.1207-1221, 1991). These ideas are extended to signals that obey a space-group symmetry, which is a crucial extension for X-ray crystallography application. Performance statistics based on simulated data are presented.