Digital holography is a two step process of recording a hologram on an electronic sensor and reconstructing it numerically. This thesis makes a number of contri- butions to the second step of this process. These can be split into two distinct parts: A) speckle reduction in reconstructions of digital holograms (DHs), and B) modeling and overcoming partial occlusion e®ects in reconstructions of DHs, and using occlusions to reduce the effects of the twin image in reconstructions of DHs. Part A represents the major part of this thesis. Speckle reduction forms an important step in many digital holographic applications and we have developed a number of techniques that can be used to reduce its corruptive effect in recon- structions of DHs. These techniques range from 3D filtering of DH reconstructions to a technique that filters in the Fourier domain of the reconstructed DH. We have also investigated the most commonly used industrial speckle reduction technique - wavelet filters. In Part B, we investigate the nature of opaque and non-opaque partial occlusions. We motivate this work by trying to ¯nd a subset of pixels that overcome the effects of a partial occlusion, thus revealing otherwise hidden features on an object captured using digital holography. Finally, we have used an occlusion at the twin image plane to completely remove the corrupting effect of the out-of-focus twin image on reconstructions of DHs.