Abstract
Incoherent holography has recently attracted significant research interest due to its flexibility for a wide variety of light sources. In this paper, we use compressive sensing to reconstruct a three-dimensional volumetric object from its two-dimensional Fresnel incoherent correlation hologram. We show how compressed sensing enables reconstruction without out-of-focus artifacts, when compared to conventional back-propagation recovery. Finally, we analyze the reconstruction guarantees of the proposed approach both numerically and theoretically and compare that with coherent holography.