4D compressive sensing holographic imaging of small moving objects with multiple illuminations

In previous work [Opt. Lett.44, 2827 (2019)OPLEDP0146-959210.1364/OL.44.002827], we presented a method based on digital holography and orthogonal matching pursuit, which is able to determine the 3D positions of small objects moving within a larger motionless object. Indeed, if the scattering density is sparse in direct 3D space, compressive sensing algorithms can be used. The method was validated by imaging red blood cell trajectories in the trunk vascular system of a zebrafish (Danio rerio) larva. We give here further details on the reconstruction technique and present a more robust version of the algorithm based on multiple illuminations.