Abstract
The research fields of harmonic analysis, approximation theory and computer algebra are seemingly different domains and are studied by seemingly separated research communities. However, all of these are connected to each other in many ways.
The connection between harmonic analysis and approximation theory is not accidental: several constructions among which wavelets and Fourier series, provide major insights into central problems in approximation theory. And the intimate connection between approximation theory and computer algebra exists even longer: polynomial interpolation is a longstudied and important problem in both symbolic and numeric computing, in the former to counter expression swell and in the latter to construct a simple data model.
A common underlying problem statement in many applications is that of determining the number of components, and for each component the value of the frequency, damping factor, amplitude and phase in a multiexponential model. It occurs, for instance, in magnetic resonance and infrared spectroscopy, vibration analysis, seismic data analysis, electronic odour recognition, keystroke recognition, nuclear science, music signal processing, transient detection, motor fault diagnosis, electrophysiology, drug clearance monitoring and glucose tolerance testing, to name just a few.
The general technique of multiexponential modeling is closely related to what is commonly known as the Pad/'eLaplace method in approximation theory, and the technique of sparse interpolation in the field of computer algebra. The problem statement is also solved using a stochastic perturbation method in harmonic analysis. The problem of multiexponential modeling is an inverse problem and therefore may be severely illposed, depending on the relative location of the frequencies and phases. Besides the reliability of the estimated parameters, the sparsity of the multiexponential representation has become important. A representation is called sparse if it is a combination of only a few elements instead of all available generating elements. In sparse interpolation, the aim is to determine all the parameters from only a small amount of data samples, and with a complexity proportional to the number of terms in the representation.
Despite the close connections between these fields, there is a clear lack of communication in the scientific literature. The aim of this seminar is to bring researchers together from the three mentioned fields, with scientists from the varied application domains.
BibTeX  Entry
@Article{cuyt_et_al:DR:2016:5507,
author = {Annie Cuyt and George Labahn and Avraham Sidi and Wenshin Lee},
title = {{Sparse Modelling and Multiexponential Analysis (Dagstuhl Seminar 15251)}},
pages = {4869},
journal = {Dagstuhl Reports},
ISSN = {21925283},
year = {2016},
volume = {5},
number = {6},
editor = {Annie Cuyt and George Labahn and Avraham Sidi and Wenshin Lee},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/5507},
URN = {urn:nbn:de:0030drops55073},
doi = {10.4230/DagRep.5.6.48},
annote = {Keywords: Sparse Interpolation, Exponential Analysis, Signal Processing, Rational Approximation}
}
Keywords: 

Sparse Interpolation, Exponential Analysis, Signal Processing, Rational Approximation 
Collection: 

Dagstuhl Reports, Volume 5, Issue 6 
Issue Date: 

2016 
Date of publication: 

11.01.2016 