We establish a quantum theory of computational ghost imaging and propose quantum projection imaging where object information can be reconstructed by quantum statistical correlation between a certain photon number of bucket signal and DMD random patterns. The reconstructed image can be negative or positive depending on the chosen photon number. In particular, the vacuum state (zero-number) projection produces a negative image with better visibility and contrast-to-noise ratio. The experimental results of quantum projection imaging agree well with theoretical simulations and show that, under the same measurement condition, vacuum projection imaging is superior to conventional and fast first-photon ghost imaging in low-light illumination.