Frame Theory: the mathematical foundation for acoustics, quantum physics, numerics and machine learning

Euler Institute

Date: 13 July 2023 / 16:00 - 17:00

USI Campus Est, room C1.03, Sector C

Speaker: Peter Balazs, Acoustics Research Institute Vienna of the Austrian Academy of Sciences

In this overview talk we give a broad reflection of frame theory and the connection to various application areas, in particular acoustics.
We will introduce the basic definition of frames and link them to the concept of coherent states in quantum physics. We will talk about time-frequency analysis and its link to frame theory. As a particular form of quantization operators we will present frame multipliers. We will show how they are applied in signal processing as time-variant filters. We will introduce the representation of operators using frames, and show the link to numerical approaches like FEM/BEM and the applications to acoustical simulations. We will present sound signals of a particular application in acoustics: audio inpainting. Finally, we will hint at the connection of frames to deep neural networks, as an outlook.

Peter Balazs is an Austrian mathematician working at the  Acoustics Research Institute Vienna of the Austrian Academy of Sciences. He is director of the Acoustics Research Institute since 2012. He studied mathematics and physics at the University of Vienna. In 2001, he graduated with honors in mathematics and finished his PhD with distinction in 2005. Peter has been part of the Acoustics Research Institute since 1999. His PhD thesis was written at the Numerical Harmonic Analysis Group (NuHaG), University of Vienna. The cooperation formed during his thesis also resulted in him becoming a fellow of the Harmonic Analysis and Statistics for Signal and Image Processing (HASSIP) EU network. He joined the Laboratoire d'Analyse, Topologie, Probabilités (LATP), CMI and LMA, CNRS Marseille from November 2003 to April 2004 and in March,  May and June 2006. He also worked with the FYMA, UCL, Louvain-La-Neuve in August 2005. For the project FLAME (Frames and Linear Operators for Acoustical Modeling and Parameter Estimation). In 2011, Peter Balazs was honored with the high reputed Start-Preis (Austrian ERC starting grant equivalent).

Host: Michael Multerer