An intro to compressive sensing

Both my senior thesis in Mathematics and Computer Science in college were related to this new area of signal processing called Compressive Sensing, which I think is a really amazing area of research. The basic idea of compressive sensing is that given a few available measurements of a signal, where the number of measurements is far less than that necessary for exact reconstruction according to Shannon's theorem, it is still possible to exactly reconstruct a signal (with high probability) given there is certain structure present in the signal. There are amazing theoretical and practical results that are currently being developed based on compressive sensing ideas. For anyone who is interested in an introductory view of Compressive Sensing, I think this lecture is great. I also have a link to a compressive sensing page at Rice, in my 'some interesting links' section, which contains a number of great journal papers.