WDI² - Approximation Theory and Applications
March 10, 2017 - Innsbruck
The fourth installment of the Workshop Donau-Isar-Inn will take place on March 10th 2017 from 10am until 3pm at the University of Innsbruck. The workshop will be held at the Campus Technik.
Previous WDI2 Workshops
- Michael Sandbichler
- Karin Schnass
|Friday, March 10, 2017|
|10:15 - 10:45||Isar talk: Dominik Stöger (TU Munich)|
|10:45 - 11:30||Vltava lecture: Jan Vybiral (Charles University Prague)|
|11:30 - 12:00||Short presentations|
|12:00 - 14:00||Lunch|
|14:00- 14:45||Limmat lecture: Rima Alaifari (ETH Zürich)|
|14:45 - 15:15||Danube talk: Michael Speckbacher (ARI Vienna)|
|15:15 - open||Coffee, cake and conversation|
Dominik Stöger: "Blind Deconvolution and Demixing at Near Optimal Rate"
We consider simultaneous blind deconvolution of a number of source signals from its noisy superposition, a problem also referred to blind demixing and deconvolution. This signal processing problem occurs in the context of the Internet of Things where a massive number of sensors sporadically communicate only short messages over unknown channels. We show that robust recovery of message and channel vectors can be achieved via convex optimization when random linear encoding is applied at the devices and the number of required measurements at the receiver scales with the degrees of freedom of the overall estimation problem. Since the scaling is linear in the number of source signals this significantly improves over recent results.
Jan Vybiral: "Optimality and Lower Bounds in Approximation Theory"
Lower bounds in approximation theory show that some approximation problems can not be solved faster, with better accuracy or with less information than some threshold. They form a natural counterpart of estimates for specific algorithms and show, that these algorithms can not be essentially improved. We discuss the connection of lower bounds with geometry of Banach spaces, Gelfand numbers and entropy.
Rima Alaifari: "Phase Retrieval in Infinite Dimensions"
In phase retrieval problems, a signal is sought to be reconstructed from only the magnitudes of a set of complex measurements. The missing information of the phase of the measurements severely obstructs the signal recon-struction.
We study this problem in the setting where the signal belongs to an infinite-dimensional Hilbert (or Banach) space. This problem is inherently unstable, i.e. highly sensitive to noise in the measurements. We show that in some sense this property is independent of the redundancy of the measurements. However, the instabilities observed in practice are all of a certain type. Motivated by this observation, we introduce a new paradigm for stable phase retrieval. We demonstrate that in audio processing applications this new notion of stability is natural and meaningful and that in this new setting stability can actually be achieved for certain measurement systems.
This is joint work with I. Daubechies (Duke University), P. Grohs (University of Vienna) and R. Yin (Duke University).
Michael Speckbacher: "A planar large sieve and sparsity of time-frequency representations"
With the aim of measuring the sparsity of a real signal, Donoho and Logan introduced the concept of maximum Nyquist density, and used it to extend Bombieri’s principle of the large sieve to bandlimited functions. This lead to several recovery algorithms based on the minimization of the L1 -norm. With the aim of measuring the sparsity of the time-frequency distribution of a function, we introduce a notion of planar maximum Nyquist density, and extend the large sieve principle to time-frequency representations with a gaussian window, or equivalently, to Fock-spaces.
List of participants
- Rima Alaifari (ETH Zürich)
- Stefano Almi (TU Munich)
- Stephan Antholzer (University of Innsbruck)
- Martin Berger (University of Innsbruck)
- Wolfgang zu Castell (Helmholtz Zentrum München)
- Florian Dreier (University of Innsbruck)
- Frank Filbir (TU Munich)
- Brigitte Forster-Heinlein (University of Passau)
- Olga Graf (TU Munich)
- Rene Grothmann (University of Eichstätt)
- Markus Haltmeier (University of Innsbruck)
- Eva Höck (University of Innsbruck)
- Alex Jung (Aalto University)
- Felix Krahmer (TU Munich)
- Sara Krause-Solberg (TU Munich)
- Christian Kümmerle (TU Munich)
- Johannes Maly (TU Munich)
- Marie-Christine Pali (University of Innsbruck)
- Michael Sandbichler (University of Innsbruck)
- Johannes Sappl (University of Innsbruck)
- Karin Schnass (University of Innsbruck)
- Kristof Schröder (Helmholtz Zentrum München)
- Johannes Schwab (University of Innsbruck)
- Nada Sissouno (TU Munich)
- Michael Speckbacher (ARI Vienna)
- Dominik Stöger (TU Munich)
- Hessel Tuinhof (University of Innsbruck)
- Jan Vybiral (Charles University Prague)
- Christoph Wolf (Vizrt Austria GmbH)
The address of the Campus Technik is "Technikerstraße 13, 6020 Innsbruck"
Directions for public transportation:
From Innsbruck main station, take either the bus line "R" in the direction of "Rehgasse" or the tram "3" in the direction of "Höttinger Au/West". At the bus stop "Fürstenweg" change to the bus line "O" towards either "Aller-heiligen", "Peerhofsiedlung" or "Technik West" and get out at the bus stop "Technik".