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08492 Executive Summary – Structured Decompositions and Efficient Algorithms

Authors Stephan Dahlke, Ingrid Daubechies, Michael Elad, Gitta Kutyniok, Gerd Teschke



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Stephan Dahlke
Ingrid Daubechies
Michael Elad
Gitta Kutyniok
Gerd Teschke

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Stephan Dahlke, Ingrid Daubechies, Michael Elad, Gitta Kutyniok, and Gerd Teschke. 08492 Executive Summary – Structured Decompositions and Efficient Algorithms. In Structured Decompositions and Efficient Algorithms. Dagstuhl Seminar Proceedings, Volume 8492, pp. 1-5, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/DagSemProc.08492.2

Abstract

New emerging technologies such as high-precision sensors or new MRI machines drive us towards a challenging quest for new, more effective, and more daring mathematical models and algorithms. Therefore, in the last few years researchers have started to investigate different methods to efficiently represent or extract relevant information from complex, high dimensional and/or multimodal data. Efficiently in this context means a representation that is linked to the features or characteristics of interest, thereby typically providing a sparse expansion of such. Besides the construction of new and advanced ansatz systems the central question is how to design algorithms that are able to treat complex and high dimensional data and that efficiently perform a suitable approximation of the signal. One of the main challenges is to design new sparse approximation algorithms that would ideally combine, with an adjustable tradeoff, two properties: a provably good `quality' of the resulting decomposition under mild assumptions on the analyzed sparse signal, and numerically efficient design.
Keywords
  • Sparse signal representation
  • optimal signal reconstruction
  • approximation
  • compression

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