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Holographic reconstruction by compressive sensing

Techniques based on compressive sensing (CS) have been proposed recently for the optical capture of compressed holographic data. However, even though several remarkable articles have presented mathematical theories and numerical simulations, only a few experimental demonstrations have been reported. In this paper, we investigate the use of different metrics for the estimation of sparsity and show that the Gini index is the most consistent. In addition, we compare the sparsifying bases based on discrete cosine transform, Fourier transform and Fresnelets. We demonstrate that the Fresnelets basis is the best choice for the reconstruction of digital holograms by CS. Finally, we present an experimental set-up for optical acquisition of phase-shifted holograms with an imaging system based on a single-pixel sensor.