Ultrafast nanocrystallography has the potential to revolutionize biology by
enabling structural elucidation of proteins for which it is possible to grow
crystals with 10 or fewer unit cells on the side. The success of
nanocrystallography depends on robust orientation-determination procedures that
allow us to average diffraction data from multiple nanocrystals to produce a
three dimensional (3D) diffraction data volume with a high signal-to-noise
ratio. Such a 3D diffraction volume can then be phased using standard
crystallographic techniques. "Indexing" algorithms used in crystallography
enable orientation determination of diffraction data from a single crystal when
a relatively large number of reflections are recorded. Here we show that it is
possible to obtain the exact lattice geometry from a smaller number of
measurements than standard approaches using a basis pursuit solver.Comment: Spence Festschrift on Ultramicroscop