Abstract

A signal-reconstruction problem motivated by x-ray crystallography [ J. Opt. Soc. Am. A 8, 1207 ( 1991)] is (approximately) solved in a Bayesian statistical approach. The signal is 0–1 and periodic, and substantial statistical a priori information is known, which is modeled with a Markov random field. The data are inaccurate magnitudes of the Fourier coefficients of the signal. The solution is explicit, and the computational burden is independent of the signal dimension. I propose a detailed parameterization of the a priori model appropriate for crystallography and use symmetry-breaking parameters in the solution to perform a data-dependent adaptation of the estimator. With this adaptation I attempt to minimize the effects of the spherical model approximation used in the solution. Several examples in one and two dimensions based on simulated data are presented.

© 1991 Optical Society of America

Bayesian signal reconstruction, Markov random fields, and x-ray crystallography

Peter C. Doerschuk
J. Opt. Soc. Am. A 8(8) 1207-1221 (1991)

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Reconstructing symmetric images from their undersampled Fourier intensities

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Sinogram recovery with the method of convex projections for limited-data reconstruction in computed tomography

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