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Buchtitelbild

2013 | OriginalPaper | Buchkapitel

1. Introduction to Finite Frame Theory

verfasst von : Peter G. Casazza, Gitta Kutyniok, Friedrich Philipp

Erschienen in: Finite Frames

Verlag: Birkhäuser Boston

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Abstract

To date, frames have established themselves as a standard notion in applied mathematics, computer science, and engineering as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions. The reconstruction procedure is then based on one of the associated dual frames, which—in the case of a Parseval frame—can be chosen to be the frame itself. In this chapter, we provide a comprehensive review of the basics of finite frame theory upon which the subsequent chapters are based. After recalling some background information on Hilbert space theory and operator theory, we introduce the notion of a frame along with some crucial properties and construction procedures. Then we discuss algorithmic aspects such as basic reconstruction algorithms and present brief introductions to diverse applications and extensions of frames. The subsequent chapters of this book will then extend key topics in many intriguing directions.

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Nächstes Kapitel Constructing Finite Frames with a Given Spectrum
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Metadaten
Titel
Introduction to Finite Frame Theory
verfasst von
Peter G. Casazza
Gitta Kutyniok
Friedrich Philipp
Copyright-Jahr
2013
Verlag
Birkhäuser Boston
Buch
Finite Frames

Print ISBN: 978-0-8176-8372-6

Electronic ISBN: 978-0-8176-8373-3

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-0-8176-8373-3_1

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