A feasible set approach to the crystallographic phase problem

Laurence Marks*, W. Sinkler, E. Landree

*Corresponding author for this work

Research output: Contribution to journalArticle

45 Scopus citations


The connection between the crystallographic phase problem and the feasible set approach is explored. It is argued that solving the crystallographic phase problem is formally equivalent to a feasible set problem using a statistical operator interpretable via a log-likelihood functional, projection onto the non-convex set of experimental structure factors coupled with a phase-extension constraint and mapping onto atomic positions. In no way does this disagree with or dispute any of the existing statistical relationships available in the literature; instead it expands understanding of how the algorithms work. Making this connection opens the door to the application of a number of well developed mathematical tools in functional analysis. Furthermore, a number of known results in image recovery can be exploited both to optimize existing algorithms and to develop new and improved algorithms.

Original languageEnglish (US)
Pages (from-to)601-612
Number of pages12
JournalActa Crystallographica Section A: Foundations of Crystallography
Issue number4
StatePublished - Jan 1 1999

ASJC Scopus subject areas

  • Structural Biology

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