  A special algorithm for the Fourier-transform Ghost Imaging (GI) scheme is
discussed based on the Compressive Sampling (CS) theory. Though developed
mostly in real space, CS algorithm could also be used for the Fourier spectrum
reconstruction of pure phase object by setting a proper sensing matrix. This
could find its application in diffraction imaging of X-ray, neutron and
electron with higher efficiency and resolution. Simulation and experiment
results are also presented to prove the feasibility.
