Conventional single-pixel cameras recover images only from the data recorded in one arm of the digital micromirror device, with the light reflected to the other direction not to be collected. Actually, the sampling in these two reflection orientations is correlated with each other, in view of which we propose a sampling concept of complementary compressive imaging, for the first time to our knowledge. We use this method in a telescopic system and acquire images of a target at about 2.0 km range with 20 cm resolution, with the variance of the noise decreasing by half. The influence of the sampling rate and the integration time of photomultiplier tubes on the image quality is also investigated experimentally. It is evident that this technique has advantages of large field of view over a long distance, high-resolution, high imaging speed, high-quality imaging capabilities, and needs fewer measurements in total than any single-arm sampling, thus can be used to improve the performance of all compressive imaging schemes and opens up possibilities for new applications in the remote-sensing area.