Stéphane Mallat: A Wavelet Zoom to Analyze a Multiscale World

Abstract:
Complex physical phenomena, signals and images involve structures of very different scales. A wavelet transform operates as a zoom, which simplifies the analysis by separating local variations at different scales. Yves Meyer found wavelet orthonormal bases having better properties than Fourier bases to characterize local properties of functions, physical measurements and signals. This discovery created a major scientific catalysis, which regrouped physicists, engineers and mathematicians, leading to a coherent theory of multiscale wavelet decompositions with a multitude of applications.
This lecture will explain the construction of Meyer wavelet bases and their generalization with fast computations. We shall follow the path of this human adventure, with ideas independently developed by scientists working in quantum physics, geophysics, image and signal processing but also neurophysiology of perception. The synthesis in the 1980's provoked by Yves Meyer's work was an encounter between applications and a pure harmonic analysis research program, initiated by Littlewood-Paley in the 1930's. It remains at the roots of open mathematical problems in high-dimension, for physics and big data analysis.
This lecture was held at The University of Oslo, May 24, 2017 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations.
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

[@cleisonarmandomanriqueagui9176]

The way he explained is remarkable . Very clear .

[@yuyingliu5831]

This is GOLD.

[@jaimelima2420]

I was able to do lots of connections in my mind among apparently disconnected things I've been studying by watching this. This is gold indeed. Thanks!

[@juliogodel]

Excellent. Watching everything I can from Stephan Mallat

[@associativemicrosemantics3930]

This was AMAZING! Thank you so much for making this available!

[@pclinhares1]

Good presentation, wavelets are a topic with many applications.

[@jmguevarajordan]

Very nice talk.

[@user-ww2lc1yo9c]

I have tried to learn this stuff 8 years ago on my own but being electronic engineer, I did not have the rigorous mathematical background which would give me tools to understand the maths. The problem I was trying to solve was how to implement a wavelet transform processor in hardware (as a hobby project). The wavelets I was looking at were from JPEG2000, and they are a lot harder than the very simple Haar wavelet.

[@sudhenduahir802]

Mallat talking on Wavelets.. wouldn't want to miss that..

[@mental_suicide]

gold af

[@Guido_XL]

Isn't it very revealing as to how little traffic a video like this experiences, in stark contrast to the idle senseless entertainment to which people tend to flock? I came across wavelet transform as a promising technique in the field of non-destructive testing with ultrasound. Although I have not yet found the time to delve into the subject deep enough as to be of any help to my peers in this matter, I still hope that it is not too late.