We investigate the application of Independent Component Analysis to the reduction of speckle in reconstructions from digital holograms. Independent Component Analysis computes a linear transformation of a multi-dimensional distribution that minimizes the statistical dependence between components. It can be seen as an extension of Principal Component Analysis where the transformed bases do not need to be orthonormal. We attempt speckle reduction across multiple hologram reconstructions. A number of situations are investigated, including recording two holograms over the interval of a day, changing the illumination between two holograms and adding a diffuser in the path of the object beam between subsequent hologram captures. This ensured significant speckle differences between the observations. Results are provided using simulated and optical data.