[His work with][1] Dilworth, Ford, Konyagin, and Kutzarova solved an open problem in compressed image sensing. Thanks to [this blog post][2] of Tao from 2007, we can get a feel of the general mentality before this work. One of their key insights was to incorporate the sum-product phenomenon. 


  [1]: https://arxiv.org/abs/1008.4535
  [2]: https://terrytao.wordpress.com/2007/07/02/open-question-deterministic-uup-matrices/