Abstract: A directionally dependent adaptive SIGMA median filter is developed for the noise removal in SAR interferometry (InSAR) derived digital elevation model (DEM). In this filter, the directionally dependent window is selected as the filter window. The performance of median filter, elevation dependent adaptive SIGMA median filter, and directionally dependent adaptive SIGMA median filter are tested on both InSAR Tandem DEM and simulated high-level noisy DEM. From the comparison, the directionally dependent adaptive SIGMA median filter is the most effective one not only in the noise removing but also in the boundary preserve.