We propose a task-specific digital holographic capture system for three-dimensional scenes, which can reduce the amount of data sent from the camera system to the receiver and can effectively reconstruct partially occluded objects. The system requires knowledge of the object of interest, but it does not require a priori knowledge of either the occlusion or the distance the object is from the camera. Subwindows of the camera-plane Fresnel field are digitally propagated to reveal different perspectives of the scene, and these are combined to overcome the unknown foreground occlusions. The nature of the occlusions and the effect of subwindows are analyzed thoroughly by using the Wigner distribution function. We demonstrate that a careful combination of reconstructions from subwindows can reveal features that are not apparent in a reconstruction from the whole hologram. We provide results by using optically captured digital holograms of real-world objects and simulated occlusions.