Random sparse sampling and compressive sensing based reconstruction for computational optical scanning holography

Optical scanning holography (OSH) is one of the single-pixel imaging (SPI) techniques. Although OSH can obtain an incoherent hologram using a single-pixel detector, OSH needs a complicated optical setup to generate Fresnel zone patterns (FZPs). Computational OSH (COSH) has been proposed to overcome the complexity of OSH by using a spatial light modulator (SLM). However, the measurement time of COSH is restricted by the refresh rate of an SLM for changing FZPs. While the number of measurements can be reduced by applying compressive sensing in conventional OSH, the scanning trajectory of FZPs is limited to the spiral manner because of the requirement of sequential scanning using galvo mirrors. The spiral scanning trajectory induces undesired artifacts in reconstructed images under sparse sampling conditions. If holograms can be randomly subsampled, these undesired artifacts can be reduced. In this paper, under COSH's configuration, random sparse sampling of a hologram is proposed to overcome the problem of the limited trajectory of FZPs by discretely displaying FZPs on an SLM. In addition, compressive sensing is applied to reconstruct an object image from a randomly sampled hologram. The feasibility of the proposed method is confirmed numerically and experimentally. The experimental results indicate that the proposed method can identify the object even when the hologram is randomly subsampled with a sampling rate of 5%.