Spline and Spline Wavelet Methods with Applications to Signal and Image Processing

Volume II: Non-Periodic Splines

  • Amir Z. Averbuch
  • Pekka Neittaanmäki
  • Valery A. Zheludev

Table of contents

  1. Front Matter
    Pages i-xxv
  2. Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev
    Pages 1-8
  3. Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev
    Pages 9-30
  4. Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev
    Pages 31-50
  5. Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev
    Pages 51-85
  6. Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev
    Pages 87-114
  7. Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev
    Pages 115-126
  8. Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev
    Pages 127-144
  9. Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev
    Pages 145-169
  10. Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev
    Pages 171-188
  11. Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev
    Pages 189-214
  12. Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev
    Pages 215-237
  13. Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev
    Pages 239-273
  14. Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev
    Pages 275-297
  15. Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev
    Pages 299-361
  16. Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev
    Pages 363-392
  17. Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev
    Pages 393-407
  18. Back Matter
    Pages 409-426

About this book

Introduction

This book presents various contributions of splines to signal and image processing from a unified perspective that is based on the Zak transform (ZT). It expands the methodology from periodic splines, which were presented in the first volume, to non-periodic splines. Together, these books provide a universal toolbox accompanied by MATLAB software for manipulating polynomial and discrete splines, spline-based wavelets, wavelet packets and wavelet frames for signal/ image processing applications.

In this volume, we see that the ZT provides an integral representation of discrete and polynomial splines, which, to some extent, is similar to Fourier integral. The authors explore elements of spline theory and design, and consider different types of polynomial and discrete splines. They describe applications of spline-based wavelets to data compression. These splines are useful for real-time signal processing and, in particular, real-time wavelet and frame transforms.

Further topics addressed in this volume include: "global" splines, such as interpolating, self-dual and smoothing, whose supports are infinite; the compactly supported quasi-interpolating and smoothing splines including quasi-interpolating splines on non-uniform grids; and cubic Hermite splines as a source for the design of multiwavelets and multiwavelet frames.  

Readers from various disciplines including engineering, computer science and mathematical information technology will find the descriptions of algorithms, applications and software in this book especially useful.

Keywords

Frames Images Signals Splines Wavelets

Authors and affiliations

  • Amir Z. Averbuch
    • 1
  • Pekka Neittaanmäki
    • 2
  • Valery A. Zheludev
    • 3
  1. 1.School of Computer ScienceTel Aviv UniversityTel AvivIsrael
  2. 2.Department of Mathematical Information TechnologyUniversity of JyväskyläJyväskyläFinland
  3. 3.School of Computer ScienceTel Aviv UniversityTel AvivIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-22303-2
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-22302-5
  • Online ISBN 978-3-319-22303-2
  • About this book
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