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Wavelets: Multi-Resolution Signal Processing

  • Apurba Das
Chapter
Part of the Signals and Communication Technology book series (SCT)

Abstract

Fourier Transform has been considered to be a well accepted transformation both for time domain and spatial signal analysis since late 1950s. A relatively new transformation technique named as wavelet transform has been utilized even in a better way for 1D and 2D signal decomposition, compression, encoding and different methods of analysis and synthesis. Conventional Fourier Transform lags of the localized analysis of signal in terms of frequency content. Discrete Wavelet Transform (DWT) refers to a class of transformations that differ not only in the transformation kernel employed but also in the fundamental nature of the basis functions and in the way in which they are applied. A set of scaled and shifted wavelet basis can be used to to represent any kind of signal in a time-frequency or space-frequency localized manner. The last section of this chapter deals with an application of the DWT to image compression. We have formally introduced and described the technique of Embedded Zero-tree Wavelet (EZW) coding for image compression based on levels of significance according to bit-budget.

Keywords

Discrete Wavelet Transform Wavelet Coefficient Filter Bank Image Compression Wavelet Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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    Shapiro, J.M.: Embedded image coding using zerotrees of wavelet coefficients. IEEE Trans. Signal Process. 41, 3445–3462 (1993)zbMATHCrossRefGoogle Scholar
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    Shapiro, J.M.: An embedded wavelet hierarchical image coder. In: Proceedings of IEEE International Conference Acoustics Speech, Signal Processing, San Francisco, CA, Mar 1992Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Image Processing Lab CDAC, KolkattaMinistry of Communication and ITKolkattaIndia
  2. 2.Imaging Tech Lab, Engineering and R&DHCL Technologies Ltd.ChennaiIndia

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