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

Volume I: Periodic Splines

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

Table of contents

  1. Front Matter
    Pages i-xxv
  2. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 1-8
  3. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 9-14
  4. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 15-34
  5. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 35-58
  6. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 59-68
  7. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 69-95
  8. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 97-131
  9. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 133-182
  10. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 183-214
  11. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 215-246
  12. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 247-273
  13. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 275-294
  14. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 295-330
  15. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 331-376
  16. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 377-397
  17. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 399-416
  18. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 417-464
  19. Amir Z. Averbuch, Pekka Neittaanmaki, Valery A. Zheludev
    Pages 465-478
  20. Back Matter
    Pages 479-496

About this book

Introduction

This volume provides universal methodologies accompanied by Matlab software to manipulate numerous signal and image processing applications. It is done with discrete and polynomial periodic splines. Various contributions of splines to signal and image processing from a unified perspective are presented. This presentation is based on Zak transform and on Spline Harmonic Analysis (SHA) methodology. SHA combines approximation capabilities of splines with the computational efficiency of the Fast Fourier transform. SHA reduces the design of different spline types such as splines, spline wavelets (SW), wavelet frames (SWF) and wavelet packets (SWP) and their manipulations by simple operations. Digital filters, produced by wavelets design process, give birth to subdivision schemes. Subdivision schemes enable to perform fast explicit computation of splines' values at dyadic and triadic rational points. This is used for signals and images upsampling. In addition to the design of a diverse library of splines, SW, SWP and SWF, this book describes their applications to practical problems. The applications include upsampling, image denoising, recovery from blurred images, hydro-acoustic target detection, to name a few. The SWF are utilized for image restoration that were degraded by noise, blurring and loss of significant number of pixels. The book is accompanied by a Matlab based software that demonstrates and implements all the presented algorithms. The book combines extensive theoretical exposure with detailed description of algorithms, applications and software.

The Matlab software can be downloaded from http://extras.springer.com

Keywords

Frames Images Signals Splines Wavelets

Authors and affiliations

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-8926-4
  • Copyright Information Springer Science+Business Media Dordrecht 2014
  • Publisher Name Springer, Dordrecht
  • eBook Packages Engineering
  • Print ISBN 978-94-017-8925-7
  • Online ISBN 978-94-017-8926-4
  • Buy this book on publisher's site
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