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The currently used ghost-image schemes traditionally involve two-mode entangled light states or incoherent radiation. Here, we consider the application of four-mode entangled light states and show that multiplexed ghost images (MGI) formed by four-mode entangled quantum light states have mutual spatial correlations determined by the eighth-order field correlation functions. We develop a special algorithm to calculate high-order correlations of Bose operators. We also demonstrate that accounting of the MGI correlations allows us to improve the quality of the restored image of an object while processing the MGI by the measurement reduction method. We carry out computer modeling of the image recovery from the MGI. We establish that in the considered example the signal-to-noise ratio of the reduced ghost image is 4.6 times higher than the best signal-to-noise ratio for the ghost images themselves.

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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.

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