  Coherent X-ray photons with energies higher than 50 keV offer new
possibilities for imaging nanoscale lattice distortions in bulk crystalline
materials using Bragg peak phase retrieval methods. However, the compression of
reciprocal space at high energies typically results in poorly resolved fringes
on an area detector, rendering the diffraction data unsuitable for the
three-dimensional reconstruction of compact crystals. To address this problem,
we propose a method by which to recover fine fringe detail in the scattered
intensity. This recovery is achieved in two steps: multiple undersampled
measurements are made by in-plane sub-pixel motion of the area detector, then
this data set is passed to a sparsity-based numerical solver that recovers
fringe detail suitable for standard Bragg coherent diffraction imaging (BCDI)
reconstruction methods of compact single crystals. The key insight of this
paper is that sparsity in a BCDI data set can be enforced by recognising that
the signal in the detector, though poorly resolved, is band-limited. This
requires fewer in-plane detector translations for complete signal recovery,
while adhering to information theory limits. We use simulated BCDI data sets to
demonstrate the approach, outline our sparse recovery strategy, and comment on
future opportunities.
