**11. Conclusion**

Since the late 80s, the wavelet transform has been widely used in different scientific applications including signal and image processing. This ongoing growing success, which has been characterised by the adoption of some wavelet-based schemes, is due to features inherent to the transform, such as time-scale localisation and multiresolution capabilities. In this chapter, the basic concepts of the wavelet transform have been introduced. First, the historical development of the wavelet transform and its advent to the field of signal and image processing were reviewed. Then, its features and the mathematical foundations behind it were reviewed. To ease the understanding of the wavelet theory, the related notations and terms, such as the scaling function, multiresolution, filter bank and others were described and then briefly explained.

Depending on the application at hand, different algorithms for implementing the wavelet transform have been developed. Four of these algorithms, namely, Burt's pyramid, Mallat algorithm, Feauveau's scheme and the lifting scheme were briefly described. Finally, some wavelet based image processing applications were also given.
