Emmanuel Candès’, Terence Chi-Shen Tao’s, and Justin Romberg’s remarkable line of research on compressed sensing (CS) is considered one of the most important developments in signal processing over the past 50 years impacting applications ranging from medical imaging to astronomy. While the concept of signal structure—that a complicated signal can be simplified through a suitable transformation—had been a familiar concept in signal processing theory and applications, their work shows how this structure could be taken advantage of in acquisition. Their seminal 2006 paper “Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information,” published in the IEEE Transactions on Information Theory, demonstrated that structured signals could be reconstructed perfectly from very few samples. While traditional sampling theorems rely on the signal being bandlimited or otherwise smooth, their results proved that the number of incoherent measurements sufficient to capture a signal is determined by its complexity, a quantity roughly equivalent to the number of bits in an optimal compression of the signal. This, coupled with basic facts from modern approximation theory, demonstrated that severely undersampled signals can be reconstructed to high fidelity in many situations of practical interest. Their efforts spurred a flurry of research activity with hundreds of papers following up on their work and numerous application domains trying to utilize their novel ideas. CS has enabled a paradigm shift in several areas, including wireless sensor networks, where it enables more efficient data aggregation and improved data recovery, and energy-efficient network routing protocols, reduced data transmission requirements, and improved network security. Perhaps the greatest success of CS to date is in MRI imaging, where the technology is used to shorten the imaging process drastically without any loss of image quality and while using conventional machines. In astronomical imaging the first images of black holes using the Event Horizon Telescope were based around CS reconstruction methods.
A member of the U.S. National Academy of Science, Candès is the Barnum-Simons Chair in Mathematics and Statistics and director of Stanford Data Science at Stanford University, Stanford, CA, USA.