The spontaneous parametric down-conversion (SPDC) process provides a convenient source of entangled-photon pairs with strong spatial correlations. Such heralded single photons can be used to achieve a high signal-to-noise ratio, virtually eliminating background counts from the recorded images. By applying principles of image compression and associated image reconstruction, high-quality images of objects can be formed from raw data with an average of fewer than one detected photon per image pixel.