https://www.dagstuhl.de/22221

May 29 – June 3 , 2022, Dagstuhl Seminar 22221

Exponential Analysis: Theoretical Progress and Technological Innovation

Organizers

Annie Cuyt (University of Antwerp, BE)
Wen-Shin Lee (University of Stirling, GB)
Gerlind Plonka-Hoch (Universität Göttingen, DE)

For support, please contact

Susanne Bach-Bernhard for administrative matters

Michael Gerke for scientific matters

Motivation

Multi-exponential analysis might sound remote, but it touches our daily lives in many surprising ways, even if most people are unaware of how important it is. For example, a substantial amount of effort in signal processing and time series analysis is essentially dedicated to the analysis of multi-exponential functions of which the exponents are complex. The analysis of exponential functions whose exponents are very near each other is directly linked to super-resolution imaging. As for multi-exponential functions with real exponents, they are used to portray relaxation, chemical reactions, radioactivity, heat transfer, fluid dynamics.

For the analysis and representation of stationary signals and images, the conventional Fourier- and wavelet-based methods are particularly appropriate. However, in many areas in science and engineering we are faced with the problem to interpret digital signals and images which are not band-limited and have a non-stationary behaviour.

Frequently, there are even further obstacles. The acquisition of signal or image measurements may be very expensive and therefore limited. In other applications, measurement sets are huge but contaminated by noise. In a digital world overwhelmed by data, the problem of finding sparse representations for models using a minimum number of probes has become a priority, such as in Prony-like methods.

Till recently the multivariate problem statement suffered the curse of dimensionality. Fortunately, the data usage and computational complexity has been brought down tremendously, thereby opening a wealth of new possibilities.

Multi-exponential analysis is also fundamental to several research fields and application domains that are the subject of this Dagstuhl Seminar: remote sensing, antenna design, digital imaging, testing and metrology, all impacting some major societal or industrial challenges such as energy, transportation, space research, health and telecommunications.

The problem statement is closely related to different topics in CS&E. The connections with structured matrix theory, rational approximation theory, sparse interpolation, scale-and-shift techniques, tensor decomposition and non-convex optimisation, deserve further exploration and may lead to improved numerical algorithms.

The seminar aims to connect stakeholders from these seemingly separately developed fields: computational harmonic analysis, numerical linear algebra, computer algebra, nonlinear approximation theory, digital signal processing and their applications. Since exponential models are vital to being able to describe physical as well as biological phenomena, their analysis plays a crucial role in advancing science and engineering.

Motivation text license
  Creative Commons BY 4.0
  Annie Cuyt, Wen-Shin Lee, and Gerlind Plonka-Hoch

Related Dagstuhl Seminar

Classification

  • Computational Engineering / Finance / And Science
  • Mathematical Software
  • Numerical Analysis

Keywords

  • Spectral analysis
  • Structured matrices
  • Sparse interpolation
  • Remote sensing
  • Inverse problem

Documentation

In the series Dagstuhl Reports each Dagstuhl Seminar and Dagstuhl Perspectives Workshop is documented. The seminar organizers, in cooperation with the collector, prepare a report that includes contributions from the participants' talks together with a summary of the seminar.

 

Download overview leaflet (PDF).

Publications

Furthermore, a comprehensive peer-reviewed collection of research papers can be published in the series Dagstuhl Follow-Ups.

Dagstuhl's Impact

Please inform us when a publication was published as a result from your seminar. These publications are listed in the category Dagstuhl's Impact and are presented on a special shelf on the ground floor of the library.