Multi-dimensional Imaging by Compressive Digital Holography

In recent years compressive sensing has been successfully introduced in digital holography. Compressive sensing represents a paradigm shift from traditional sampling theorems, by providing a theoretical and algorithmic framework for reconstruction of (traditionally considered) undersampled signals. Here we demonstrate that digital holography is an efficient and physically realizable sensing modality that synergizes with the compressive sensing framework for 2D and 3D applications. This is done by reviewing theoretical bounds of compressive digital holographic sensing as well as reviewing several applications such as reconstruction of objects from undersampled holograms, reconstruction of partially occluded objects, inference of 3D objects from their 2D holograms and improved depth sectioning of 3D objects from their holograms.