Based on the theory of compressive sensing, the overall structure system of the single-pixel detection computational imaging, the design of the observation matrix and image reconstruction algorithm are analysed, and correlation algorithm is simulated by Matlab. Simulation results show that compressive sensing used to single-pixel detection computational imaging can reduce the sampling and can clearly reconstruct image. In addition, a long-range external imaging system prototype is built in the laboratory, and the imaging experiment is conducted in the indoors using parallel light source. The experimental results show that the imaging system has better spatial resolution. The single-pixel detection computational imaging is extended further by building dispersion optical path in the imaging system, the system structure of computational imaging spectrometer is established, the feasibility of which compressive sensing is used to the computational imaging spectrometer is analyzed, and the computational imaging spectrometer is analyzed in theory.