RICAM Colloquium: Inverse Problems and Mathematical Imaging - Transfer Group
TITLE: Frame Theory: the mathematical foundation for acoustics, quantum physics, numerics and machine learning.
ABSTRACT:
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 and concept of frames. We will 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 - operators that can be
represented as a weighted version of the frame decomposition. 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.