In this paper, a method for lossless compression of large digital mammograms is proposed. In order to efficiently remove the spatial redundancy from the mammographic images, we use a geometric predictor based on irregular sampling and the Delaunay Triangulation. The difference between the predicted and the original (i.e. the error image) is calculated and encoded using JPEG-LS approach. For faster convergence, we build the triangulation using the pixels most significant bits, and code separately the least significant bits using the PNG approach. Comparisons with other proposed approaches are based on a database of high-resolution digital mammograms. The preliminary results indicate that our method can offer average compression ratios 43%, 40%, 45%, and 25% higher than JPEG 2000, JPEG-LS, JPEG-lossless, and PNG, respectively.