Compressive sensing for improved depth discrimination in 3D holographic reconstruction

Compressive holography has attracted significant interest since its introduction three about years ago. In this paper, we present an overview of our work on the ability to reconstruct a 3D volume from its 2D recorded compressive hologram. Using the single-exposure on-line (SEOL) setup, we show how CS applied to this naturally underdetermined problem enables the improved sectioning (or depth discrimination) of the reconstructed volume, when compared with standard in-line holography. We also present the mathematical guarantees for the reconstruction of the 3D volume features from its single 2D hologram and their physical implications for sectioning of 3D volume