#### Abstract

In Ref. [I] a signal reconstruction problem motivated by x-ray crystallography was solved using a Bayesian statistical approach. The signal is zero-one, 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. In Ref, [2] a detailed parameterization of the a priori model appropriate for crystallography was proposed and symmetry-breaking parameters in the riolution were usecl to perform data-dependent adaptation of the estimator. The adaptation attempts to minimize the effects of the spherical model approximation used in the solution. In this paper these ideas are extended to signals that obey a space group syrrlmetry, which is a crucial extension for the x-ray crystallography application. Performance statistics for reconstruction in the presence of a space group symmetry based on simulated data are presented. [I.] Peter C. Doerschuk. Bayesian Signal Reconstruction, Markov Random Fields, and X-Ray Crystallography." Journal of the Optical Society of America A, 8(8):1207-1221, 1991. [2] Peter C. Doerschuk. "Adaptive Bayesian Signal Reconstruction with A. Priori Model Implementation 'and Synthetic Examples for X-ray Crystallography." Jounal of the Optical Society of America A, 8(8):1222-1232,1991.

#### Date of this Version

April 1992