The Wavelet Transform for Image Processing Applications
Toufik Bouden, Mokhtar Nibouche · InTech eBooks · 2012
At the beginning of the 20 th century, Haar, a German mathematician introduced the first wavelet transform named after him (almost a century after the introduction of the FT, by the French J. Fourier).The Haar wavelet basis function has compact support and integer coefficients.Later, the Haar basis was used in physics to study Brownian motion (Graps, www.intechopen.comAdvances in Wavelet Theory and Their Applications in Engineering, Physics and Technology 396 1995).Since then, different works have been carried out either in the development of the theory related to the wavelet, or towards its application in different fields.In the field of signal processing, the great achievements reached in different studies by Mallat, Meyer and Daubechies have allowed the emergence of a wide range of wavelet-based applications.In fact, inspired by the work developed by Mallat on the relationships between the Quadrature Mirror Filters (QMF), pyramid algorithms and orthonormal wavelet bases (Mallat, 1989), Meyer constructed the first non-trivial wavelets (Meyer, 1989).However, the most important work was carried out by Ingrid Daubechies.Based on Mallat's work, Daubechies succeeded to construct a set of wavelet orthonormal basis functions, which have become the cornerstone of many applications (Daubechies, 1988).Few years later, the same author, in collaboration with others (Cody, 1994), presented a set of wavelet biorthogonal basis function, which later found their use in different applications, especially in image coding.Recently, JPEG2000, a biorthogonal wavelet-based compression has been adopted as the new compression standard (Ebrahimi et al., 2002).