The entangled optical quantum imaging efficiency is mainly affected by the sampling time cost of the digital micromirror device (DMD). The existing DMD sampling methods are to scan all pixels point by point, which result in the low imaging efficiency. To address this problem, this article uses the compressed sensing algorithm to sparsely sample the reference light based on the temporal and spatial correlation properties of the entangled light, and also uses the orthogonal matching pursuit (OMP) algorithm to obtain the target image from the coincidence counting result. In addition, this article analyzes the impact of different number of bundled pixels, DMD sampling block size, and image sparsity on imaging quality and efficiency. The effectiveness of the proposed method is evaluated by establishing an actual entangled optical quantum imaging system.