Optical scanning holography (OSH) can measure three-dimensional (3D) fluorescence targets by recording incoherent holograms with two-dimensional Fresnel zone pattern (FZP) scanning and a single-pixel detector. However, the complexity of the optical setup has limited its applicability. Computational OSH (COSH) has been proposed as a solution to this problem and has shown to be feasible with optical applications such as ghost imaging or Hadamard transform single-pixel imaging. However, the problem with FZP’s scanning speed has limited its ability to visualize dynamic objects. In this study, dynamic objects were visualized using a high-speed digital micromirror device (DMD). In addition, a microscope based on COSH was constructed and then applied to capture moving images of dynamic objects behind dynamic scatterers. The experimental results show that the proposed method captures incoherent holograms with a frame rate of 1.387 Hz using a single-pixel detector. Moreover, numerical simulations indicate that the proposed method achieves imaging with a frame rate of approximately 28 Hz by using random sparse sampling and compressive sensing-based reconstruction.