In the previous chapter, we saw that the ideas of simple averaging and differencing lead to the development of Haar wavelets and that these wavelets can be used for image compression. In this chapter we will see that we can extend these ideas to weighted averages and differences and that particular choices of weighting coefficients lead to different systems of wavelets. Ingrid Daubechies (1988) chose coefficients that lead to wavelet systems that are particularly well suited to compression of certain types of images. The wavelet image encoding techniques we will investigate in the next chapter can be used with either the Haar wavelets or the wavelets developed in this chapter.
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