| Emmanuel Candès (left), Stanford University, will be awarded the 2015 AMS-SIAM George David Birkhoff Prize in Applied Mathematics "for his work on compressed sensing that has revolutionized signal processing and medical imaging and his related work on computational harmonic analysis, statistics and scientific computing." Candès holds the Barnum-Simons Chair in Mathematics and Statistics and is a professor of electrical engineering (by courtesy) and a member of the Institute of Computational and Mathematical Engineering at Stanford University. The Birkhoff Prize, jointly sponsored by the American Mathematical Society and the Society for Industrial and Applied Mathematics, will be awarded at the Joint Mathematics Meetings in January in San Antonio, Texas. Compressed sensing is a mathematical technique that has led to dramatic advances in the efficiency and accuracy of data collection and analysis. A prime example comes from medicine, particularly magnetic resonance imaging (MRI). An MRI machine collects data about the body part analyzed, and then an algorithm uses that data to create a picture of the body part. The machine should intelligently collect just the right number of data points, and the algorithm should use those points to reliably reconstruct a high-quality image. When working with doctors on the problem of reducing artifacts in MRI images, Candès and his post-doc Justin Romberg experimented with one particular reconstruction algorithm that worked with an unusually small number of data points. They noticed something strange: when tested, the algorithm reconstructed the image exactly, every time. Candès then realized they were on to something new. Together with collaborators Justin Romberg and Terence Tao, Candès went on to develop the technique that is now known as compressed sensing. This technique gains its power by meshing two different representations of the data, so that very few data points yield a highly accurate reconstruction. Their surprising results, together with those of David Donoho, sparked huge interest among mathematicians, statisticians, computer scientists, and engineers. The technique was rapidly taken up in such applications as the design of MRI systems and analog-to-digital converters. One group of engineers pushed compressed sensing to the limit and developed a digital camera that has just one pixel! Candès has continued to successfully apply the ideas growing out of this work to a variety of other theoretical and applied problems such as the theory of matrix completion. In his PhD thesis, Candès developed "curvelets," a new variant on the technique of data representation known as wavelets. He described this work in "What is a curvelet?", which appeared in the Notices of the AMS in December 2003. For a compelling description of Candès' work, see the entry in Timothy Gowers's blog, "ICM2014--Emmanuel Candès plenary lecture." Presented every three years, the Birkhoff Prize is awarded for an outstanding contribution to applied mathematics in the highest and broadest sense. The prize will be awarded at the Joint Mathematics Meetings, Sunday, January 11, 2015 at 4:25 PM, at the Henry B. Gonzalez Convention Center in San Antonio, Texas.
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