Emmanuel J. Candès

Developed new directional multiscale bases and frames in applied harmonic analysis and with coauthors showed that these provide optimally sparse representations for images with edges and for solution operators of hyperbolic equations, yielding optimal algorithms in image processing and scientific computing by simple manipulations of the 'big' coefficients in those representations. Also collaborated in developing compressed sensing theory, inferring solutions to underdetermined systems of equations by exploiting sparsity of these solutions. With T. Tao, introduced the restricted isometry property in compressed sensing, widely used over the last five years throughout information theory, statistics, and applied mathematics With coauthors, developed the theory of matrix completion used in modern high-dimensional data analysis, revealing a deep understanding about the structure of low-rank approximations to partially observed random low-rank matrices. With coauthors, also developed theory of detecting subtle structures in graphs from noisy data.