## Linear Enhancement and Unsharp Masking

3.1 Unsharp Masking

In general, unsharp masking can be seen as a generalized subtracting Laplacian operator. In this context, an early prototype of unsharp masking [7] was defined as

where

### 8x2 8y2

is the Laplacian operator. However, this original formula worked only at the level of finest resolution. More versatile formulas were later developed in two distinct ways.

One way to extend this original formula was based on exploiting the averaging concept behind the Laplacian operator. The discrete form of the Laplacian operator may be written as

As(i, j) = [s(i + 1, j)- 2s(i, j) + s(i - 1, j)} + W, j + 1)-2s(i, j) + s(i, j - 1)}

= -51s(i, j) - 1 [s(i + 1, j) + s(i - 1, j) + s(i, j) + s(i, j + 1) + s(i, j - 1)}J .

3.2 Inclusion of Unsharp Masking Within the RDWT Framework

We now show that unsharp masking with a Gaussian lowpass filter is included in a dyadic wavelet framework for enhancement by considering two special cases of linear enhancement.

In the first case, the transform coefficients of channels 0 < m < N - 1 are enhanced (multiplied) by the same gain G0 > 1, or Gm = G0 > 1, 0 < m < N - 1. The system frequency response is thus

This makes the input-output relationship of the system simply sc(l) = s(l) + (Go - 1)[s(l)-(s* cN)(l)}. (10)

Since cn (rn) is approximately a Gaussian low-pass filter, Eq. (10) maybe seen as the 1D counterpart of Eq. (8).

In the second case, the transform coefficients of a single channel p, 0 < p<N are enhanced by a gain Gp> 1; thus,

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