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Wavelet Frames: Multiresolution Analysis and Extension Principles

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Wavelet Transforms and Time-Frequency Signal Analysis

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

After reviewing the basic ideas of frame theory from a functional analysis point of view, we discuss two approaches for the construction of (affine) wavelet frames. The theory of Frame Multiresolution Analysis as introduced in [1] is presented in a streamlined form, and the main result of the theory is completed. The interplay between redundancy and robustness in frame expansions is illustrated by a simple example. We then restate Ron and Shen’s Unitary Extension Principle and give a simple direct proof different from the original derivation in [2].

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Authors
  1. John J. Benedetto
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  2. Oliver M. Treiber
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, Fl, 32816, USA

    Lokenath Debnath

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Benedetto, J.J., Treiber, O.M. (2001). Wavelet Frames: Multiresolution Analysis and Extension Principles. In: Debnath, L. (eds) Wavelet Transforms and Time-Frequency Signal Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0137-3_1

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  • DOI: https://doi.org/10.1007/978-1-4612-0137-3_1

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6629-7

  • Online ISBN: 978-1-4612-0137-3

  • eBook Packages: Springer Book Archive

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