LOCETISA
Localized Frame Expansions in Time-Scale Analysis
| Coordinatore | UNIVERSITAT WIEN
Organization address
address: UNIVERSITATSRING 1 contact info |
| Nazionalità Coordinatore | Austria [AT] |
| Totale costo | 179˙137 € |
| EC contributo | 179˙137 € |
| Programma | FP7-PEOPLE
Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) |
| Code Call | FP7-PEOPLE-2012-IIF |
| Funding Scheme | MC-IIF |
| Anno di inizio | 2014 |
| Periodo (anno-mese-giorno) | 2014-10-01 - 2016-09-30 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
UNIVERSITAT WIEN
Organization address
address: UNIVERSITATSRING 1 contact info |
AT (WIEN) | coordinator | 179˙137.20 |
Mappa
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Obiettivo del progetto (Objective)
'A frame expansion is a representation of a general signal (function) as a weighted superimposition of basic building blocks. Diverse operations on functions can be understood by first considering their action on these basic atoms. Similarly, several subtle properties of functions (e.g. smoothness, decay, directional regularity) are encoded in the coefficients (weights) involved in the representation.
The usefulness of frame expansions, both in theory and applications, comes from the possibility of designing dictionaries of atoms with prescribed properties. The counterpart of this flexibility is redundancy. In order to construct dictionaries with certain properties one often has to give up perfect independence between different atoms, thus yielding a redundant expansion.
Redundant representations also entail a number of technical problems because not all operations on the coefficients of a frame expansion have an exact counterpart in the signal being represented. The theory of localized frames aims at overcoming these technical obstacles by relaxing the notion of independence to the one of low correlation. This project addresses these topics with a special emphasis on time-scale analysis, aiming at providing a framework where the tools associated with a redundant frame perform comparably to the ones associated with a non-redundant one, and give in addition a very valuable extra flexibility.'