Compressive sensing

The Shannon/Nyquist sampling theorem tells us that in order to not lose information when uni-formly sampling a signal we must sample at least two times faster than its bandwidth. In many applications, including digital image and video cameras, the Nyquist rate can be so high that we end up with too many samples and must compress in order to store or transmit them. In other ap-plications, including imaging systems (medical scanners, radars) and high-speed analog-to-digital converters, increasing the sampling rate or density beyond the current state-of-the-art is very ex-pensive. In this lecture, we will learn about a new technique that tackles these issues using compressive sensing [1, 2]. We will replace the conventional sampling and reconstruction operations with a more general linear measurement scheme coupled with an optimization in order to acquire certain kinds of signals at a rate significantly below Nyquist.