Since the information content of a hologram is so huge, data compression is important for a practical electroholographic display system. We have therefore investigated the block subsampling method and the interpolation of subsampled data. This procedure, however, also causes a blur on the displayed 3D image. Therefore, there is a trade-off relation between the information reduction rate and the image blur. It is not practical to apply 2D image compression to a hologram because the character of the holographic data is quite different from that of a 2D image. We have demonstrated that 2D compression techniques can be used effectively to compress the fringe pattern by first segmenting it and then performing a transform operation upon it. We have discussed both theoretical and experimental results and have compared the image quality of those two compression methods.