  Coherent X-ray beams with energies $\geq 50$ keV can potentially enable
three-dimensional imaging of atomic lattice distortion fields within individual
crystallites in bulk polycrystalline materials through Bragg coherent
diffraction imaging (BCDI). However, the undersampling of the diffraction
signal due to Fourier space compression at high X-ray energies renders
conventional phase retrieval algorithms unsuitable for three-dimensional
reconstruction. To address this problem we utilize a phase retrieval method
with a Fourier constraint specifically tailored for undersampled diffraction
data measured with coarse-pitched detector pixels that bin the underlying
signal. With our approach, we show that it is possible to reconstruct
three-dimensional strained crystallites from an undersampled Bragg diffraction
data set subject to pixel-area integration without having to physically
upsample the diffraction signal. Using simulations and experimental results, we
demonstrate that explicit modeling of Fourier space compression during phase
retrieval provides a viable means by which to invert high-energy BCDI data,
which is otherwise intractable.
