Digital holography is an inherently three-dimensional (3D) technique for the capture of real-world objects. Many existing 3D imaging and processing techniques are based on the explicit combination of several 2D perspectives (or light stripes, etc.) through digital image processing. The advantage of recording a hologram is that multiple 2D perspectives can be optically combined in parallel, and in a constant number of steps independent of the hologram size. Although holography and its capabilities have been known for many decades, it is only very recently that digital holography has been practically investigated due to the recent development of megapixel digital sensors with sufficient spatial resolution and dynamic range. The applications of digital holography could include 3D television, virtual reality, and medical imaging. If these applications are realised, compression standards will have to be defined. We outline the techniques that have been proposed to date for the compression of digital hologram data and show that they are comparable to the performance of what in communication theory is known as optimal signal quantisation. We adapt the optimal signal quantisation technique to complex-valued 2D signals. The technique relies on knowledge of the histograms of real and imaginary values in the digital holograms. Our digital holograms of 3D objects are captured using phase-shift interferometry.