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Birkhäuser

Nonlinear Smoothing and Multiresolution Analysis

  • Book
  • © 2005

Overview

Authors:
  1. Carl Rohwer

    1. Department of Mathematics, University of Stellenbosch, South Africa

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  • Self-contained monograph presenting a new perspective in multiresolution analysis of times series
  • All the little-known surprising results are easily verifiable with simple computer simulations
  • Natural introduction to the more general mathematical morphology and complementary to signal analysis with digital filters
  • Essential to anyone involved in measurements and analysis, storage and transmission of information

Part of the book series: International Series of Numerical Mathematics (ISNM, volume 150)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Operators on Sequences

    • Carl Rohwer
    Pages 1-7

  3. Basic Rank Selectors, Pulses and Impulses

    • Carl Rohwer
    Pages 9-19

  4. LULU-Smoothers, Signals and Ambiguity

    • Carl Rohwer
    Pages 21-30

  5. LULU-Intervals, Noise and Co-idempotence

    • Carl Rohwer
    Pages 31-41

  6. Smoothing and Approximation with Signals

    • Carl Rohwer
    Pages 43-50

  7. Variation Reduction and Shape Preservation

    • Carl Rohwer
    Pages 51-70

  8. Multiresolution Analysis of Sequences

    • Carl Rohwer
    Pages 71-90

  9. The Discrete Pulse Transform

    • Carl Rohwer
    Pages 91-107

  10. Fair Comparison with Linear Smoothers

    • Carl Rohwer
    Pages 109-126

  11. Interpretation and Future

    • Carl Rohwer
    Pages 127-129

  12. Back Matter

    Pages 131-137
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Keywords

About this book

Thismonographisintendedasasimpleintroductiontotheso-calledLULU-theory and the practical use of LULU-smoothers leading up to a full Multiresolution Analysis of any ?nite sequence. The attempt has been to present the subject in a way that is retrospectively ordered to some extent, but preserves some of the twisted paths that intuition initially suggested. It is based on the few publications in the subject, some already submitted and lectures given at conferences and on invitation at public and private institutions. The ideas originated more than ?fteen years ago when the author was - volved in practical problems at the Institute for Maritime Technology in Sim- stown and advanced while the author was at the BMI in Stellenbosch. The author hopes that publication of this book will stimulate the interest of other researches and takes responsibility for any remaining typographical or technical errors. A growing love for this particular subject was one of the prime reasons for a return to academic life, and a perceived opportunity to consolidate various p- spectives and results. It is however only the encouragement, guidance and help of severalrespected people that have resulted in the e?ort presented here.

Authors and Affiliations

  • Department of Mathematics, University of Stellenbosch, South Africa

    Carl Rohwer

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