Additional resources on expanders

• Reingold's original paper.
• Course notes 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.
• Blog post by Terry Tao, intented for a general audience.
• A more technical post by Terry Tao.
• Finally, Rice University has extensive resources to explore.