Parallel application checkpoint image compression may be carried out in a parallel computer. The parallel computer may include a plurality of compute nodes, where each node is configured to execute one or more parallel tasks of the parallel application. The parallel tasks may be organized into an operational group for collective communications. In such a parallel computer, checkpoint image compression may include: 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.