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Exponential Analysis: Theoretical Progress and Technological Innovation (Dagstuhl Seminar 22221)

Authors: Annie Cuyt, Wen-shin Lee, Gerlind Plonka-Hoch, and Ferre Knaepkens

Published in: Dagstuhl Reports, Volume 12, Issue 5 (2022)

Abstract

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. Multi- exponential analysis is also fundamental to several research fields and application domains that have been the subject of this Dagstuhl seminar: remote sensing, antenna design, digital imaging, all impacting some major societal or industrial challenges such as energy, transportation, space research, health and telecommunications. This Seminar connected stakeholders from seemingly separately developed fields: computational harmonic analysis, numerical linear algebra, computer algebra, nonlinear approximation theory, digital signal processing and their applications, in one and more variables.

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Annie Cuyt, Wen-shin Lee, Gerlind Plonka-Hoch, and Ferre Knaepkens. Exponential Analysis: Theoretical Progress and Technological Innovation (Dagstuhl Seminar 22221). In Dagstuhl Reports, Volume 12, Issue 5, pp. 170-187, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Article{cuyt_et_al:DagRep.12.5.170,
  author =	{Cuyt, Annie and Lee, Wen-shin and Plonka-Hoch, Gerlind and Knaepkens, Ferre},
  title =	{{Exponential Analysis: Theoretical Progress and Technological Innovation (Dagstuhl Seminar 22221)}},
  pages =	{170--187},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2022},
  volume =	{12},
  number =	{5},
  editor =	{Cuyt, Annie and Lee, Wen-shin and Plonka-Hoch, Gerlind and Knaepkens, Ferre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.12.5.170},
  URN =		{urn:nbn:de:0030-drops-174473},
  doi =		{10.4230/DagRep.12.5.170},
  annote =	{Keywords: inverse problem, remote sensing, sparse interpolation, spectral analysis, structured matrices}
}

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DOI: 10.4230/DagRep.6.11.90

Inpainting-Based Image Compression (Dagstuhl Seminar 16462)

Authors: Christine Guillemot, Gerlind Plonka-Hoch, Thomas Pock, and Joachim Weickert

Published in: Dagstuhl Reports, Volume 6, Issue 11 (2017)

Abstract

Inpainting-based image compression is an emerging paradigm for compressing visual data in a completely different way than popular transform-based methods such as JPEG. The underlying idea sounds very simple: One stores only a small, carefully selected subset of the data, which results in a substantial reduction of the file size. In the decoding phase, one interpolates the missing data by means of a suitable inpainting process. It propagates information from the known data into the areas where nothing has been stored, e.g. by solving a partial differential equation or by clever copy-and-paste mechanisms. Inpainting-based codecs (coders and decoders) are more intuitive than transform-based ones, they are closer to biological mechanisms in our brain, and first results show that they may offer promising performance for high compression rates. However, before these ideas become practically viable, a number of difficult fundamental problems must be solved first. They involve e.g. the selection of the data and the inpainting operator, coding strategies, and the search for highly efficient numerical algorithms. This requires a collaborative effort of experts in data compression, inpainting, optimisation, approximation theory, numerical algorithms, and biological vision. In this Dagstuhl seminar we have brought together leading researcher from all these fields for the first time. It enabled a very fruitful and inspiring interaction which will form the basis for future progress.

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Christine Guillemot, Gerlind Plonka-Hoch, Thomas Pock, and Joachim Weickert. Inpainting-Based Image Compression (Dagstuhl Seminar 16462). In Dagstuhl Reports, Volume 6, Issue 11, pp. 90-107, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@Article{guillemot_et_al:DagRep.6.11.90,
  author =	{Guillemot, Christine and Plonka-Hoch, Gerlind and Pock, Thomas and Weickert, Joachim},
  title =	{{Inpainting-Based Image Compression (Dagstuhl Seminar 16462)}},
  pages =	{90--107},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2017},
  volume =	{6},
  number =	{11},
  editor =	{Guillemot, Christine and Plonka-Hoch, Gerlind and Pock, Thomas and Weickert, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.6.11.90},
  URN =		{urn:nbn:de:0030-drops-70406},
  doi =		{10.4230/DagRep.6.11.90},
  annote =	{Keywords: approximation, inpainting, interpolation, lossy image compression, optimisation, partial differential equations (PDEs), sparsity}
}

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Documents authored by Plonka-Hoch, Gerlind

Exponential Analysis: Theoretical Progress and Technological Innovation (Dagstuhl Seminar 22221)

Abstract

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Inpainting-Based Image Compression (Dagstuhl Seminar 16462)

Abstract

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