Correlated imaging is a new imaging method, which attracts a lot of attention in recent years. It offers great potential to solve some problems that traditional imaging technologies cannot solve. Among them, computational correlated imaging based on digital micromirror device(DMD) or spatial light modulator(SLM) developed most rapidly. When DMD was applied in correlated imaging system, high-quality images can be obtained at multi-wavelength, and multi-wavelength correlated imaging was redlized, by using the advantages of DMD′s high speed and wide reflective spectrum, with the assistance of compressed sensing. Several problems in the system need to be researched on, including the efficient generation of pseudo thermal light, the influence of diffraction effect and modulation noise on the signal, and the high-quality imaging reconstruction algorithm. After determining the optimal system parameters via numerical simulation, an experimental system was built to verify the effectiveness of the technology, which provide an reference to the practical process of correlated imaging.