The symmetries of image formation by scattering. II. Applications

Peter Schwander, Dimitrios Giannakis, Chun Hong Yoon, Abbas Ourmazd

Research output: Contribution to journalArticlepeer-review


We show that the symmetries of image formation by scattering enable graph-theoretic manifold-embedding techniques to extract structural and timing information from simulated and experimental snapshots at extremely low signal. The approach constitutes a physically-based, computationally efficient, and noise-robust route to analyzing the large and varied datasets generated by existing and emerging methods for studying structure and dynamics by scattering. We demonstrate three-dimensional structure recovery from X-ray diffraction and cryo-electron microscope image snapshots of unknown orientation, the latter at 12 times lower dose than currently in use. We also show that ultra-low-signal, random sightings of dynamically evolving systems can be sequenced into high quality movies to reveal their evolution. Our approach offers a route to recovering timing information in time-resolved experiments, and extracting 3D movies from two-dimensional random sightings of dynamic systems.

Original languageEnglish (US)
Pages (from-to)12827-12849
Number of pages23
JournalOptics Express
Issue number12
StatePublished - Jun 4 2012

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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