Take a color photo. Separate the different colors and sort them. Plotting all three color channels red, green and blue. It will reveal something like the left image. The right shows all the channels mixed together and sorted.
From this I wonder. Could you with the graph on the right side create the three curves to the left. Does there exist a clustering method that will do this? Split the long vector into three different looking enough vectors. Perhaps the separation could be found somehow.
One way I think it could work is by cheating a little. By using a small scaled down version of the photo as a guide.
Such a method could be part of a new image compression system. Here you store a small scaled down version of the photo and lossy compressed enlargement information. This information is then used together with the small photo as a guide to get the big photo.
If this works I can formulate another power sentence. Everything can be improved with a guide.