Introduction to Digital Image Processing

HADAMARD, HAAR AND DAUBECHIES TRANSFORMS 199

8.4.3. Daubechies Transforms

Daubechies (30) has discovered a class of transforms that utilize running averages

and running differences of the elements of a vector, as with the Haar transform. The

difference between the Haar and Daubechies transforms is that the averages and dif-

ferences are grouped in four or more elements.

The Daubechies transform of support four, called Daub4, can be defined in a

manner similar to the Haar recursive generation process. The first-level scaling and

wavelet matrices are defined as

(8.4-13a)

W

N

= (8.4-13b)

where

(8.4-14a)

(8.4-14b)

(8.4-14c)

. (8.4-14d)

In Eqs. 8.4-13a and 8.4-13 ...