  In this paper we study a realistic setup for phase retrieval, where the
signal of interest is modulated or masked and then for each modulation or mask
a diffraction pattern is collected, producing a coded diffraction pattern (CDP)
[CLM13]. We are interested in the setup where the resolution of the collected
CDP is limited by the Fraunhofer diffraction limit of the imaging system.
  We investigate a novel approach based on a geometric quantization scheme of
phase-less linear measurements into (one-bit) coded diffraction patterns, and a
corresponding recovery scheme. The key novelty in this approach consists in
comparing pairs of coded diffractions patterns across frequencies: the one bit
measurements obtained rely on the order statistics of the un-quantized
measurements rather than their values . This results in a robust phase
recovery, and unlike currently available methods, allows to efficiently perform
phase recovery from measurements affected by severe (possibly unknown) non
linear, rank preserving perturbations, such as distortions. Another important
feature of this approach consists in the fact that it enables also
super-resolution and blind-deconvolution, beyond the diffraction limit of a
given imaging system.
