29 December 1992 Bayesian signal reconstruction from Fourier-transform magnitude and x-ray crystallography
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Abstract
A Bayesian binary signal reconstruction problem which includes noisy magnitude of Fourier transform measurements and a Markov random field a priori model was solved. The solution is analytical and is based on the spherical model and small noise asymptotic approximations. Parameters in the solution are used for data adaptation. The work is motivated by the phase retrieval problem in x-ray crystallography where the signal is the periodic electron density in the crystal. In crystallography, the signal is known to be invariant under the actions of some space group symmetry (e.g., division of the repeat unit of the crystal into two halves with one half the mirror image of the other half). The cited references have been extended in three different ways to incorporate this additional information. In addition, a numerical optimization in the cited references has been improved by the use of analytical gradients which can be rapidly computed using FFT based formulae.
© (1992) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Peter C. Doerschuk "Bayesian signal reconstruction from Fourier-transform magnitude and x-ray crystallography", Proc. SPIE 1767, Inverse Problems in Scattering and Imaging, (29 December 1992); doi: 10.1117/12.139036; https://doi.org/10.1117/12.139036
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