Compressive sensing [Instrumentation Notes]

Though mathematical theorems do not have exceptions, sometimes it is possible to "sneak around" the hypotheses of the theorems and achieve things that seem to be impossible. The Nyquist sampling theorem is a case in point. The theorem seems to sav that if vou have a low-pass signal, then you need to sample the signal at a rate that is more than twice the highest frequency in the signal. In fact, there are many ways of supplementing the hypotheses of the theorem and achieving better results. In this brief introduction to compressive sensing, we present one such technique and a simple application.The literature on compressive sensing is vast and is growing all the time. There are many, many other interesting applications of compressive sensing. The interested reader might want to read about the one pixel camera, for example.