Additional resources on expanders
Reingold's original paper
for Harvard CS 225: Pseudorandomness (Spring 2007). Lectures 7 to 9 are especially relevant.
Notes by Oded Goldreich
Additional resources on compressed sensing
Emmanuel Candes's website
has lots of material, in particular, many papers on compressed sensing, and a link to the l1 magic software package.
by Terry Tao, intented for a general audience.
A more technical post by Terry Tao
Finally, Rice University has