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Signal Analysis with Frame Theory and Persistent Homology

Please always quote using this URN:urn:nbn:de:0296-matheon-12345
  • A basic task in signal analysis is to character- ize data in a meaningful way for analysis and classification purposes. Time-frequency transforms are powerful strategies for signal decomposition, and important recent generalizations have been achieved in the setting of frame theory. In parallel recent developments, tools from algebraic topology, traditionally developed in purely abstract settings, have provided new insights in applications to data analysis. In this report, we investigate some interactions of these tools, both theoretically and with numerical experiments, in order to characterize signals and their frame transforms. We explain basic concepts in persistent homology as an important new subfield of computational topology, as well as formulations of time-frequency analysis in frame theory. Our objective is to use persistent homology for constructing topo- logical signatures of signals in the context of frame theory. The motivation is to design new classification and analysis methods by combining the strength of frame theory as a fundamental signal processing methodology, with persistent homology as a new tool in data analysis.

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Author:Mijail Guillemard, Gitta Kutyniok, Holger Boche, Friedrich Philipp
URN:urn:nbn:de:0296-matheon-12345
Document Type:Preprint, Research Center Matheon
Language:English
Release Date:2013/09/02
Institute:Technische Universität Berlin
MSC-Classification:26-XX REAL FUNCTIONS [See also 54C30] / 26-06 Proceedings, conferences, collections, etc.
Preprint Number:1030
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