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The Award Princess of Asturias in the field of Scientific and Technical Research to 2020 has fallen in the mathematical Yves Meyer , Ingrid Daubechies , Terence Tao and Emmanuel Candès by having realidazo broad advances “related to the theories and techniques of modern mathematical processing of data and signals”, has unveiled this Tuesday the organization. They are responsible that today we can do photos with high resolution and take up little space in our mobile , that our home becomes a film every time we see a digital film or that the doctors can know what is happening inside of our body with all luxury of detail and minimal exposure. And, beyond that, his theories are basic to the Hubble Space Telescope has been taking amazing images that allow us to know something more in our universe, or even put “soundtrack”, thanks to the detection of the gravitational waves. A whole revolution.

In particular, the Foundation Princess of Asturias recognizes “his pioneering contributions and transcendental theories and modern techniques of mathematical processing of data and signals are the basis and support of the digital age –allowing you to compress graphics files with no loss of resolution, of the image, and the medical diagnosis –to allow to reconstruct accurate images from a reduced number of data– and the engineering and scientific research –to eliminate interference and background noise”. The four will also receive recognition, a sculpture of Joan Miro , and a cash prize of € 50.000 .

The first revolution in the images

Behind it all is the theory of the wavelet , Meyer and Daubechies took them to another level. The French mathematician Yves Meyer is professor emeritus of the École Normale Supérieure Paris-Saclay, and former member of the Scientific Committee of the Institute of Mathematical Sciences (ICMAT). He was responsible of finding the connection between the postulates of Grossmann and Morlet, creators of the theory of the wavelet, and the work of the argentine Alberto Calderon , linking the wavelet with the pure mathematics. For this contribution he was awarded the Abel 2017, considered the Nobel of Mathematics. Very briefly: the theory of wavelet-allows you to “atomize” complex signals in a type of particle mathematics called wavelet; that is to say, compress the signals to make them “manageable”, and numeric.

For his part, Ingrid Daubechies, mathematical and physical belgian, is the “mother” of the base of the compression system of JPEG 2000 image , a revolution at the time of transferring large amounts of visual information without losing quality. Daubechies has received many awards, among them the Prize Nemmers Mathematics Prize and the BBVA Foundation Frontiers of Knowledge in Basic Sciences. It has also been the first female president of the International Mathematical Union. He currently works as a professor at the University of Princeton.

Next to Daubechies, Meyer brought together previous work and related analytical tools used in the harmonic analysis. “This discovery led later to the demonstration, by Meyer, that the waves can form sets of mutually-independent mathematical objects called bases orthogonal . His work inspired Daubechies to construct the wavelet orthogonal with compact stand, and, later, the wavelet biortogonales, which revolutionized the field of engineering”, explained from the foundation.

Behind their contribution, we find the compression and storage of data , the elimination of noise, the medical imaging and digital cinema . The wavelet is also used in the study of the cosmos, to restore satellite images , in the deconvolution of the images from the Hubble space telescope and were key in the recent detection by LIGO of gravitational waves.

New breakthrough disruptive

If the theory of Meyer and Daubechies allowed to take large amounts of data and compress them so that then they were played back, to the beginning of XXI century two new mathematical, Terence Tao and Emmanuel Candès , considered the way “opposite”: that few data and with noise could be to reconstruct accurate images for diagnosis, for example, the state of a lung in a patient of coronavirus.

In 2006, the French Candès -professor of mathematics, statistics and electrical engineering at Stanford University, where he is also the Chair Barnum-Simons in Mathematics and Statistics, as well as a member of MacArthur 2017 – and australia’s Tao -who was a child prodigy who from the age of 24, he works as a professor of mathematics at UCLA, received the Fields Medal in August 2006, and a month later won a MacArthur Fellowship – wrote an article that was the second revolution in the treatment of data and signals with the development of theories of compressed sensing (detection compressed) or compressive sampling (sampling reduced) and matrix completion (termination of the array), the result of the collaboration between Terence Tao and Emmanuel Candès. This theory allows the reconstruction efficient sparse data based on very few measurements.

One of the main problems of the medical images and, generally, in all areas of signal processing, is how to reconstruct a signal from partial measurements and noisy. “Reconstruction techniques advanced, such as compressed sensing and matrix completion, enable the reduction of the number of samples needed, in medical imaging involves an exploration fastest of the patient,” say from the organization. An example: the mri scanners . Thanks to the contributions of Candès and Tao have been shortened significantly the time of scanning and exposure of the patients -that can be harmful – without which the tests have lost quality.

“This is translated into a lower sampling rate, less data, less use of storage resources, lower requirement of speed converters analog-to-digital and less time required for the transmission of data”, point from the foundation.

In short, this Award Princess of Asturias acknowledges that “the mathematical theories developed by Yves Meyer, Ingrid Daubechies, Terence Tao and Emmanuel Candès highlight the unifying role and cross-cutting the mathematics in different scientific disciplines and engineering, with practical solutions applicable in many areas, and constitute an example of the utility of the work in pure mathematics”. The demonstration that the numbers are not just theories.