  We apply the measurement reduction technique to optimally reconstruct an
object image from multiplexed ghost images (GI) while taking into account both
GI correlations and object image sparsity. We show that one can reconstruct an
image in that way even if the object is illuminated by a small photon number.
We consider frequency GI multiplexing using coupled parametric processes. We
revealed that the imaging condition depends on the type of parametric process,
namely, whether down- or up-conversion is used. Influence of information about
sparsity in discrete cosine transform and Haar transform bases on
reconstruction quality is studied. In addition, we compared ordinary and ghost
images when the detectors are additionally illuminated by noise photons in a
computer experiment, which showed increased noise immunity of GI, especially
with processing via the proposed technique.
