Abel Lectures: Wavelet bases: roots, surprises and applications
Professor Ingrid Daubechies from Duke University has her lecture.
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 as others.
Finally, hindsight shows that the new paradigm introduced by wavelet analysis was a first example of the power of sparse decompositions -- and thus a prelude to another paradigm shift, that of Compressed Sensing, about which more will follow, in the presentation by Emmanuel Candès.