Emmanuel Candes

He is famous for his contribution to Compressive sensing. Famously he, in collaboration with T. Tao and using geometric functional analysis, proved that if a vector, e.g. a digital image, is sparse in a fixed basis, then one can reconstruct the vector with very high accuracy, in $\ell_2$ metric, from a small number of random measurements and only by solving a linear program.

E. Candes , T. Tao , "Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies", IEEE Trans. Inform. Theory, Nov. 2006

This paper, along with the work of David Donoho [1], founded the theoretical foundation of compressive sensing.

[1] D. Donoho , "Compressed Sensing", IEEE Trans. Inform. Theory, Mar. 2006