Compressing a data file representing an image wherein one or more regions within the image are identified. At least one of the regions is selected and the data corresponding to the selected region is compressed at a different rate that the data corresponding to non-selected regions of the image. The different compression rates are selected to maintain a desired fidelity in an image reconstructed from the compressed data file. The different compression rates can be predetermined, selected by a user, or automatically selected. Compression rates can be based upon the type of image to be compressed such as x-ray, CT scan or MRI images, the structure that is being analyzed, parameters regarding the use of the image, system parameters such as storage capacity available, or bandwidth of a communication channel used to transmit the compressed file.