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Brauer Lecture 3 – Ingrid Daubechies (Duke University)
February 5 @ 9:00 am - 10:00 am
The wavelet synthesis and beyond
Abstract: Wavelets emerged in the 1970s and 80s as the synthesis of ideas stemming from many different directions; the list of ingredients includes items as diverse as the study of singular integral kernel operators in harmonic analysis, square integrable group representations in quantum mechanics, the role of scaling in computer vision, efficient algorithms in computer graphics, the power on nonlinear expansion in approximation theory, and deep theoretical insights from statistics. All these fields not only contributed to the wavelet synthesis — they also all benefitted from it. With hindsight, wavelet expansions were a first example of sparse approximation — a forerunner for what has become known as compressed or compressive sensing, a development that has had its own tremendous impact in many fields of application. Compressive sensing is possible when we know the signal of interest can be represented sparsely in an appropriate dictionary of “elementary building blocks”. There are some indications that deep neural networks, the success of which is at present very little understood, may similarly use smaller “elementary” building blocks in their inner workings. The presentation will give a high level overview of these different facets of modern signal learning and processing.
There will be a pre-colloquium tea in Toy Lounge (Dey Hall) from 8:30-9:00am.