Piotr Indyk just released his Tutorial on Compressed Sensing (or Compressive Sampling or Linear Sketching), given at the Workshop on Geometry and Algorithms last month.
His sparse recovery experiments wiki was mentioned earlier. Many items are of this presentation are detailed in Combining Geometry And Combinatorics: A Unified Approach to Sparse Signal Recovery by Radu Berinde, Anna Gilbert, Piotr Indyk, Howard Karloff and Martin Straus.
On a side note related to imaging: while taking a hit on the number of measurements (sketches) is not good (beause of the lower compression), there are instances where the physics makes it a difficult proposition to acquire a signal in some incoherent fashion. For background information on why, see the discussion with Ramesh Raskar (in CS: A Small Discussion with Ramesh Raskar and the Camera Culture Lab at MIT.) and with Greg Skinner (a specialist of Coded Aperture). In short, the SNR can go down real fast when a point like signal is too widespread on the detector, i.e. the Point Spread Function (PSF) is spread over too many pixels. This thought leads me to the question I have been pondering: can one map some of the current sparse measurement matrices (RIP-1) to an actual imaging Point Spread Function (PSF) that is not too wide on average.
While we are on the subject of Imaging, I have mentioned some internships offered by Thales on the subject of Compressed Sensing. The announcements are here and here. I talked to some of the folks at Thales and they tell me the internships are paid (900 euros but ask them from more accurate information) and are open to E.U. students as well if they apply early (need for clearance). Paid Internships on the French Riviera performing Compressed Sensing trade studies, I can think of worse student's jobs. I'll add the announcements on the CS Jobs page.