With holographic displays requiring giga- or terapixel resolutions, data compression is of utmost importance in making holography a viable technique in the near future. In addition, since the first-generation of holographic displays is expected to require binary holograms, associated compression algorithms are expected to be able to handle this binary format. In this work, the suitability of a context based Bayesian tree model is proposed as an extension to adaptive binary arithmetic coding to facilitate the efficient lossless compression of binary holograms. In addition, we propose a quadtree-based adaptive spatial segmentation strategy, as the scale dependent, quasi-stationary behavior of a hologram limits the applicability of the advocated modelling approach straightforwardly on the full hologram. On average, the proposed compression strategy produces files that are around 12% smaller than JBIG2, the reference binary image codec.