The symmetries of image formation by scattering. I. Theoretical framework

Dimitrios Giannakis, Peter Schwander, Abbas Ourmazd

Research output: Contribution to journalArticlepeer-review


We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe. Here, we present an approach to image formation based on the symmetry properties of operations in three-dimensional space. Augmented with graph-theoretic means, this approach can recover the three-dimensional structure of objects from random snapshots of unknown orientation at four orders of magnitude higher complexity than previously demonstrated. This is critical for the burgeoning field of structure recovery by X-ray Free Electron Lasers, as well as the more established electron microscopic techniques, including cryo-electron microscopy of biological systems. In a subsequent paper, we demonstrate the recovery of structure and dynamics from experimental, ultralow-signal random sightings of systems with X-rays, electrons, and photons, with no orientational or timing information.

Original languageEnglish (US)
Pages (from-to)12799-12826
Number of pages28
JournalOptics Express
Issue number12
StatePublished - Jun 4 2012

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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