Ingrid Daubechies: Wavelet bases: roots, surprises and applications

This lecture was held by Ingrid Daubechies at The University of Oslo, May 24, 2017 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Ingrid Daubechies is a Belgian physicist and mathematician. She is best known for her work with wavelets in image compression. Abstract: Yves Meyer’s surprising construction of orthonormal bases consisting of dilates and translates of a single smooth function was followed soon after by the development of the Multiresolution Analysis framework in collaboration with Stephane Mallat. As already shown in the presentation by Stephane Mallat, this development was rooted in and used insights from a variety of fields -- ranging from pure harmonic analysis to statistics, quantum physics, geophysics and computer vision. The lecture will discuss some of those diverse roots in more detail, and also show how the new wavelet synthesis, sparked by Yves Meyer’s seminal work, led to further progress in all those fields as well