Here we first propose a fast, one-shot, non-Bayesian method which performs a numerical synthesis of a moving aperture in order to reduce the noise in Digital Holography without prior information on its statistics. Starting from one single hologram capture, multiple uncorrelated reconstructions are provided by random sparse resampling masks, which can be incoherently averaged. Thus, the problem of the setup complexity introduced by multiple recordings gets solved. Besides, at the scope of performing DH display using a SLM, it is highly required to operate directly on the hologram, in order to obtain its denoised version without losing the coherence between amplitude and phase information. We then move a step forward, showing a novel encoding formula allowing us to directly synthesize denoised holograms to be optically displayed by SLMs.