Discrete Wavelet Transformations. An Elementary Approach with Applications

  • ID: 2171829
  • February 2008
  • 564 Pages
  • John Wiley and Sons Ltd
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An "applications first" approach to discrete wavelet transformations

Discrete Wavelet Transformations provides readers with a broad elementary introduction to discrete wavelet transformations and their applications. With extensive graphical displays, this self–contained book integrates concepts from calculus and linear algebra into the construction of wavelet transformations and their various applications, including data compression, edge detection in images, and signal and image denoising.

The book begins with a cursory look at wavelet transformation development and illustrates its allure in digital signal and image applications. Next, a chapter on digital image basics, quantitative and qualitative measures, and Huffman coding equips readers with the tools necessary to develop a comprehensive understanding of the applications. Subsequent chapters discuss the Fourier series, convolution, and filtering, as well as the Haar wavelet transform to introduce image compression and image edge detection. The development of Daubechies filtersis presented in addition to coverage of wavelet shrinkage in the area of image and signal denoising. The book concludes with the construction READ MORE >

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* Introduction: Why Wavelets

* Vectors and Matrices

* An Introduction to Digital Images

* Complex Numbers and Fourier Series

* Convolution and Filters

* The Haar Wavelet Transformation

* Daubechies Wavelet Transformations

* Orthogonality and Fourier Series

* Wavelet Shrinkage: An Application to Denoising

* Biorthogonal Filters

* Computing Biorthogonal Wavelet Transformations

* The JPEG2000 Image Compression Standard

Appendix A: Basic Statistics



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"The book is a valuable reference for wavelet applications and the theory of underlying 2–band filterbanks." (
Mathematical Reviews, Issue 2009g)

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