Non-Bayesian noise reduction in digital holography by random resampling masks

Images from coherent laser sources are severely degraded by a mixture of speckle and incoherent additive noise. In digital holography, Bayesian approaches reduce the incoherent noise, but prior information are needed about the noise statistics. On the other hand, non-Bayesian techniques presents the shortcomings of resolution loss or very complex acquisition systems, required to record multiple uncorrelated holograms to be averaged. Here we propose a fast non-Bayesian method which performs a numerical synthesis of a moving diffuser in order to reduce the noise. The method does not depend on prior knowledge of the noise statistics and the proposed technique is one-shot, as only one single hologram capture is required. Indeed, starting from a single acquisition multiple uncorrelated reconstructions are provided by random sparse resampling masks, which can be incoherently averaged. Experiments show a significant improvement, close to the theoretical bound. Noteworthy, this is achieved while preserving the resolution of the unprocessed image.