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 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.
Program for the Abel lectures 2017:
1. Detection of gravitational waves and time-frequency wavelets, by Abel Laureate Yves Meyer, École Normale Supérieure Paris-Saclay
2. A Wavelet Zoom to Analyze a Multiscale World, by professor Stéphane Mallat, École Normale Supérieure
3. Wavelet bases: roots, surprises and applications, by professor Ingrid Daubechies, Duke University
4. Wavelets, sparsity and its consequences, professor Emmanuel Jean Candès, Stanford University
Thumbnail photo: Samfoto/John Petter Reinertsen.

[@evgenymamontov4647]

Great presentation! Now I know who is the mother wavelet!

[@andrefurlan]

The legend of the wavelets!

[@FelipeBatistadaSilva-f5q]

Such an amazing talk. Dr. Daubechies besides being a great renowned mathematician is also an inspiring speaker!!!!

[@martyb3783]

This is a great lecture for the non-mathematician. Well Done

[@Mohammed-su8dy]

It’s a great talk. I like how she started explaining the topic with an example. Thank you!

[@tanvir_ahmed]

"So, except for those two extremes, all 254's in between are the different levels of gray that we have; unlike the 50 that the other people might have." 1:37

[@yonaxl]

😂

[@slobodanblazeski0]

If I know how hard it was I would've never opened my mouth 44:25 :)

[@yalcnpak3677]

Amazing topic

[@oleksiishekhovtsov1564]

Wonderful lecture!

[@cescllopis]

IAMP - BERLIN 1981 !
We have been in the Kant Straße eating .Do You remember ?
Congratulations!

[@NoNTr1v1aL]

Amazing!

[@sunjaysunjay6062]

Excellent seismic exploration

[@shengyang7985]

Very enlightening!

[@優さん-n7m]

Can she explain how the 9/7 and 5/3 wavelets used in JPEG2000 work and how we actually implement them as quadrature mirror filter and then using lifting scheme? What is all that stuff?

[@arunchaudhary3764]

It's very nice lecture

[@davesabra4320]

useful beauty and beautiful utility