Computer Science
Scientific paper
Nov 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993spie.2029...94t&link_type=abstract
Proc. SPIE Vol. 2029, p. 94-104, Digital Image Recovery and Synthesis II, Paul S. Idell; Ed.
Computer Science
Scientific paper
The crystallographic X-ray diffraction experiment gives the amplitudes of the Fourier series expansion of the electron density distribution within the crystal. The 'phase problem' in crystallography is the determination of the phase angles of the Fourier coefficients required to calculate the Fourier synthesis and reveal the molecular structure. The magnitude of this task varies enormously as the size of the structures ranges from a few atoms to thousands of atoms, and the number of Fourier coefficients ranges from hundreds to hundreds of thousands. The issue is further complicated for large structures by limited resolution. This problem is solved for 'small' molecules (up to 200 atoms and a few thousand Fourier coefficients) by methods based on probabilistic models which depend on atomic resolution. These methods generally fail for larger structures such as proteins. The phase problem for protein molecules is generally solved either by laborious experimental methods or by exploiting known similarities to solved structures. Various direct methods have been attempted for very large structures over the past 15 years, with gradually improving results -- but so far no complete success. This paper reviews the features of the crystallographic image reconstruction problem which render it recalcitrant, and describes recent encouraging progress in the application of maximum entropy methods to this problem.
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