Compressive Sensing is a pretty dramatic new development in Digital Signal Processing that is having a big impact even beyond that field.
It's very useful for neural nets and things like that. Anyway you can think of it as a way of compressing readings from a sensor with a very low computational burden ( a simple microcontroller could compress full video images for example) and then reconstructing the full data later on a PC.
It uses relatively simple ideas of random projection and sparseness. It is a very hot topic of research at the moment. Unfortunately that means most/all the papers about it are complex to the point of being unreadable.
However I have very simple FreeBASIC code for you here:http://code.google.com/p/lemontree/
Look in the moving average compressive sensing file.
You can easily translate it into your preferred programming language and you too can do Compressive Sensing at Home.