those being the most important ones. Current methods are more or less all analysis/statistics/continuous math. I think, from what I gathered that new approach will come from the area of discrete maths. Mainly combinatorics. Also, this is where mad man part comes in, cellular automata kind of systems.
Discrete math in itself offers great tools to make r&d on paper, but requires severe computing power later on to prove right. New research also needs new minds un-poluted with "what can and can't be done" in order to bring new ways of thinking. I won't bore you with details, I had lots of ideas over the years, but pretty much all were fluke for lossless.
http://en.wikipedia.org/wiki/Fractal_compression