C (m)= Y; cm(m) + Gp CpH = Y, CmH + (Gp - 1) Cp(rn)
Recall the channel frequency response cm(rn) derived previously in Eq. (5). The input-output relationship of the system in Eq. (11) can be written as
where y(l) is the impulse response of an approximately Gaussian filter. Similarly, Eq. (12) may be seen as the 1D counterpart of Eq. (9). The inclusion of these two forms of unsharp masking demonstrates the flexibility and versatility of the dyadic wavelet framework.
3. The reconstruction filters are simply zero-phase smoothing filters that will not create additional extrema.
The major difficulty in using a gradient filter is that reconstruction includes another gradient operator. As a result, a monotonically increasing function E(x) alone (as shown in Fig. 5a) will no longer guarantee that new extrema will not be introduced in each output channel. Moreover, it is not difficult to show that any nonlinear mapping will change the positions of original extrema. Therefore, we will assume the choice of Laplacian filters in the remainder of this chapter.
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