Skip to main content
Top

2019 | OriginalPaper | Chapter

9. Using Tensor Products to Apply Wavelets to Images

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Previously we have used wavelets to analyze sound. We would also like to use them in a similar way to analyze images. In Chap. 8 we used the tensor product to construct two dimensional objects (i.e. matrices) from one-dimensional objects (i.e. vectors). Since the spaces in wavelet contexts are function spaces, we need to extend the strategy from Chap. 8 to such spaces. In this chapter we will start with this extension, then specialize to the resolution spaces V m, and extend the DWT to images. Finally we will look at several examples.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Footnotes
1
Note also that MATLAB has a wavelet toolbox which could be used for these purposes. We will however not go into the usage of this, since we implement the DWT from scratch.
 
Literature
5.
go back to reference C.M. Brislawn, Fingerprints go digital. Not. AMS 42(11), 1278–1283 (1995) C.M. Brislawn, Fingerprints go digital. Not. AMS 42(11), 1278–1283 (1995)
19.
go back to reference FBI, WSQ gray-scale fingerprint image compression specification. Technical report, IAFIS-IC (1993) FBI, WSQ gray-scale fingerprint image compression specification. Technical report, IAFIS-IC (1993)
21.
go back to reference M.W. Frazier, An Introduction to Wavelets Through Linear Algebra (Springer, New York, 1999)MATH M.W. Frazier, An Introduction to Wavelets Through Linear Algebra (Springer, New York, 1999)MATH
27.
go back to reference ISO/IEC, JPEG2000 part 1 final draft international standard. ISO/IEC FDIS 15444-1. Technical report, ISO/IEC (2000) ISO/IEC, JPEG2000 part 1 final draft international standard. ISO/IEC FDIS 15444-1. Technical report, ISO/IEC (2000)
38.
go back to reference J. Ma, G. Plonka, The curvelet transform. IEEE Signal Process. Mag. 27, 118–133 (2010)CrossRef J. Ma, G. Plonka, The curvelet transform. IEEE Signal Process. Mag. 27, 118–133 (2010)CrossRef
74.
go back to reference D.S. Taubman, M.W. Marcellin, JPEG2000. Image Compression. Fundamentals, Standards and Practice (Kluwer Academic Publishers, Boston, 2002) D.S. Taubman, M.W. Marcellin, JPEG2000. Image Compression. Fundamentals, Standards and Practice (Kluwer Academic Publishers, Boston, 2002)
Metadata
Title
Using Tensor Products to Apply Wavelets to Images
Author
Øyvind Ryan
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-030-01812-2_9

Premium Partner