We have successfully applied Independent Component Analysis to the removal of background speckle noise from digital holograms. Additive noise removal techniques do not perform well on speckle, which is better characterized as multiplicative noise. In addition, speckle contains 3D information and so cannot be removed completely. We use a Blind Source Separation approach to the reduction of speckle noise in digital holograms. Independent Component Analysis computes a linear transformation of a multi-dimensional distribution that minimizes the statistical dependence between the components. It can be seen as an extension of Principal Component Analysis where the transformed bases do not need to be orthonormal. Although a linear technique, we show how Independent Component Analysis can be applied to the reduction of background speckle in digital holograms. Results are provided using simulated and optical data.