1. A method of parallel application checkpoint image compression in a parallel computer, the parallel computer comprising a plurality of compute nodes, each compute node configured to execute one or more parallel tasks of the parallel application, the parallel tasks organized into an operational group, the method comprising: generating, by each task of the parallel application, an image for checkpointing the parallel application; selecting, by an image management task, one of the images as a base template image; constructing, by the image management task, a binary radix tree, including storing differences between each task's image and the base template image in the binary radix tree; and storing, by the image management task as a checkpoint for the parallel application, the binary radix tree and the base template image, without storing every task's image.