Each year, the Abel Prize is awarded for outstanding work in the field of mathematics. This year, the Abel Prize has been awarded to French mathematician Yves Meyer, for his “pivotal role in the development of the mathematical theory of wavelets”.

Wavelets are brief wave-like oscillations that serve as the building blocks of digital sound and image data. Intersecting mathematics, information technology, and computational science, Yves Myer’s work has led to developments in areas as diverse as data compression, noise reduction, medical imaging, digital cinema, deconvolution of the Hubble space telescope images, and the detection of gravitational waves created by the collision of black holes.

Meyer’s “work on wavelets has been transformative in the area of signal processing,” said mathematician Terence Tao, who presented the prize to Meyer by phone from the Norwegian Academy of Science and Letters.

The Abel Prize carries a cash prize of 6 million NOK (£600,000), and Yves Meyer will officially receive the prize from his Majesty King Harald V on 23rd May at an award ceremony in Oslo. To celebrate Yves Myer’s work, we have put together a selection of his titles, published by the American Mathematical Society. 

Abel
Wavelets, Vibrations and Scalings
Yves Meyer

Nov 1997 133pp, Illustrations
9780821806852 Hardback
CRM Monograph Series, Vol. 9
Discusses the relevance of wavelet analysis to problems in which self-similarities are important. This title is suitable for scientists wishing to apply wavelet analysis to multifractal signal processing.

Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions
Stéphane Jaffard & Yves Meyer

1996 110pp
9780821804759 Paperback
Memoirs of the American Mathematical Society, Vol. 123
In this book, wavelet analysis is related to the 2-microlocal spaces discovered by J. M. Bony. The authors then prove that a wavelet based multi-fractal analysis leads to a remarkable improvement of Sobolev embedding theorem. In addition, they show that chirps were hidden in a celebrated Riemann series.

Oscillating Patterns in Image Processing and Nonlinear Evolution Equations
The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures

2001 122pp
9780821829202 Paperback
University Lecture Series, Vol. 22
Image compression, the Navier-Stokes equations, and detection of gravitational waves are three unrelated scientific problems that can be studied from one perspective. This book considers image processing, precisely algorithms of image compression and denoising. It features results on the Navier-Stokes and other nonlinear evolution equations.