Imaging correlography is a technique for constructing high-resolution images of laser illuminated objects from measurements of backscattered (non-imaged) laser speckle intensity patterns. In this paper, we investigate the possibility of implementing an imaging correlography system with sparse arrays of intensity detectors. The theory underlying the image formation process for imaging correlography is reviewed, emphasizing the spatial filtering effects that sparse collecting apertures have on the reconstructed imagery. We then demonstrate image recovery with sparse arrays of intensity detectors through the use of computer experiments in which laser speckle measurements are digitally simulated. It is shown that the quality of imagery reconstructed using this technique is visibly enhanced when appropriate filtering techniques are applied. A performance tradeoff between collecting array redundancy and the number of speckle pattern measurements is briefly discussed.