March 2019
Intermediate to advanced
530 pages
12h 13m
English
3.2.3.4 The Daubechies D4 scaling function
A family of MRAs which is very useful in digital image analysis is generated by the Daubechies scaling functions and their associated wavelets (Daubechies, 1988). The Daubechies D4 scaling function, for example, can be derived by placing the following two additional requirements on an MRA (Aboufadel and Schlicker, 1999):
1. Compact support: The scaling function ϕ(x) is required to be zero outside the interval 0 < x < 3. This means that the refinement coefficients ck vanish for k < 0 and for k > 3. To see this, note that
and similarly for k ≤ −4 and for k ≥ 6. Therefore, from the dilation equation,
and similarly ...
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