from Foundation to the Real World
01. Sept. 2009 (13:00-17:40)
Am Campus 1 - Klosterneuburg AUSTRIA
about the location
List of Talks:
(ordered by name)
"Harmonic Analysis with Applications to Image Processing"
Harmonic Analysis with Applications to Image Processing This talk gives an introduction to wavelets and other similar tools used in image analysis, highlighting their connection with harmonic analysis, from Littlewood-Paley theorems to Calderon-Zygmund theory; it also shows how harmonic analysis theorems translate into properties useful for the practice of image processing.
"Harmonic Analysis at NuHAG (from the foundations to real world applications)"
Feichtinger, Hans G.
In the last 5 years, beginning with the special semester on Time-Frequency analysis at ESI, and the EUCETIFA (= the EUROPEAN CENTER FOR TIME-FREQUENCY ANALYSIS, Oct. 2005 - Sept. 2009) the Numerical Harmonic Analysis group NuHAG at the Faculty of Mathematics, University of Vienna, has become an highly visible international player in the area of application oriented HARMONIC ANALYSIS). A list of recent research projects is found at http://www.univie.ac.at/nuhag-php/home/research.php and an extentsive repository of publications, MATLAB-software modules and related infra-structure which will continue to make NuHAG a point of interest in the international landscape is found at http://www.univie.ac.at/nuhag-php/home/db.php
"Numerical Harmonic Analysis and real-life Applications"
In this talk we would like to describe fundamental concepts and methods of numerical harmonic analysis by showing their application on a real-life art restoration problem. From classical Fourier expansions and sampling theory, we approach the concepts of sparse recovery in combination with wavelets. In fact, all of this allowed us to re-puzzle one of the most important Italian Renaissance frescoes, destroyed by a bombing more than 60 years ago, and also to recover faithfully the colors of its missing parts. We conclude by illustrating more recent challenging research directions in numerical harmonic analysis, and further surprising applications.
"Wiener's Lemma: Theme and Variations"
Wiener's Lemma is a classical statement about absolutely convergent Fourier series and remains one of the driving forces in the development of Banach algebra theory. For the engineer Wiener's Lemma can be formulated as an important statement about the input-output relation of discrete time-invariant systems. In the first part of the talk we will discuss Wiener's Lemma and some of its reformulations. the second part, the variations, we discuss several, mostly non-commutative reincarnations of Wiener's Lemma. We will develop some of the theoretical background and explain why Wiener's Lemma is still useful and inspiring. The topics cover weighted versions of Wiener's Lemma, infinite matrix algebras, non-commutative tori and time-frequency analysis, convolution operators on non-commutative groups, and time-varying systems and pseudodifferential operators.
"Quantum Theta Functions, Moduli of Noncommutative Tori, and Gabor Frames for Modulation Spaces"
Manin, Yuri I.
Presenting joint results with Franz Luef (presently Outgoing Marie Curie Fellow, from NuHAG to Berkeley): Representations of the celebrated Heisenberg commutation relations in quantum mechanics (and their exponentiated versions) form the starting point for a number of basic constructions, both in mathematics and mathematical physics (geometric quantization, quantum tori, classical and quantum theta functions) and signal analysis (Gabor analysis). In paper to be presented we will try to bridge the two communities, represented by the two co--authors: that of noncommutative geometry and that of signal analysis. After providing a brief comparative dictionary of the two languages, we will show e.g. that the Janssen representation of Gabor frames with generalized Gaussians as Gabor atoms yields in a natural way quantum theta functions, and that the Rieffel scalar product and associativity relations underlie both the functional equations for quantum thetas and the Fundamental Identity of Gabor analysis.
"The Richness of Sparsity: How Harmonic Analysis will Transform Technology"
Many seemingly complex phenomena in areas such as physics, engineering or medicine, have a sparse representation in the sense that they can be described by a linear combination of a few elementary buildig blocks. This concept, known as sparsity, has gained tremendous attention in recent years, fueled by the advent of Compressed Sensing. I will demonstrate how insights from sparsity and compressed sensing lead to dramatic improvements in remote sensing, making it possible to solve inverse problems in radar imaging that were hitherto believed to be intractable. I will describe how a rigorous analysis of the underlying mathematical model is crucial for this advancement. In the second part of my talk I will discuss how the triumvirate of harmonic analysis, sparsity, and compressed sensing inspires a bold perspective on a number of important problems ranging from biochemistry to medical diagnostics. I will describe why and how a new paradigm, called transdisciplinary research, is key to achieve this breakthrough which has the potential to revolutionize technology in many areas.
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