Quantum imaging (QI) has some unique advantages, such as nonlocal imaging and enhanced space resolution. However, the quality of the reconstructed images and the time of data acquisition leave much to be desired. Based on the framework of compressive sensing, we propose an optimization criterion for high-quality QI whereby total variation restriction is specifically utilized for noise suppression. The corresponding reported algorithm uses a combination of a greedy strategy and the interactive reweight least-squares method. The simulation and the actual imaging experiment both show a significant improvement of the proposed algorithm the over previous imaging method.