The dogma of signal processing maintains that a signal must be sampled at a rate at least twice its highest frequency in order to be represented without error. However, in practice, we often compress the data soon after sensing, trading off signal representation complexity (bits) for some error (consider JPEG image compression in digital cameras, for example). Clearly, this is wasteful of valuable sensing resources. Over the past few years, a new theory of "compressive sensing" has begun to emerge, in which the signal is sampled (and simultaneously compressed) at a greatly reduced rate.
As the compressive sensing research community continues to expand rapidly, it behooves us to heed Shannon's advice.
Compressive sensing is also referred to in the literature by the terms: compressed sensing, compressive sampling, and sketching/heavy-hitters.
The Compressive Sensing Resources:
Rice University Resources: http://dsp.rice.edu/cs
Nuit Blanche Blog: http://nuit-blanche.blogspot.com/
Compressive Sensing Research Groups:The Rice group led by Richard Baraniuk has been the leader in spearheading information diffusion on the subject of compressive sensing through theirRice Compressive Sensing Resource page. They also have a nice presentation of the now famous Rice Single pixel camera.
Terry Tao has made a list of the different matrices and their properties wrt compressive sensing in this page: Preprints in sparse recovery / Summary of properties of random matrices.
Feature Selection in Face Recognition: A Sparse Representation Perspectiveled by Allen Yang at Berkeley.
Duke DISP lab led by David Brady. Of particular interest is Ashwin Wagadarikar's page on the compressive sensing hyperspectral imager.
Gabriel Peyre, Chambolle's algorithm for the resolution of compressed sensing with TV regularization.