276.

[Cover] [Contents] [Index]

Page 47

ent to Equation (1.40), indicating that the speckle noise statistic C_v can be retrieved from a homogeneous area. Based on Equation (1.45), it can be seen that:

(1.46)

Substituting Equation (1.46) into Equation (1.44), the weighting coefficient k becomes (Lopes et al., 1990):

(1.47)

Based on Equation (1.47), Equation (1.43) can be converted into (Baraldi and Parmiggiani, 1995b):

(1.48)

Baraldi and Parmiggiani (1995) note two important points concerning the Lee filter:

1 If the filter is located around a textured area (such as forest or a city) in which C_x> >0, indicating that C_z> >C_v (see Equation (1.45)), then Equation (1.48) becomes This shows that, in an area of high contrast, the estimated noise-free pixel value is proportional to its original value z. In such a case, the filter tends to have a reduced smoothing effect, and the configuration of a textured area can be preserved.

2 If the filter is located around a homogeneous area, in which C_x≈0, then C_z≈C_v (see Equation (1.45)), and Equation (1.48) becomes This result indicates that the central pixel is replaced by a value that is proportional to the average of the neighbouring pixels, which also means that the smoothing effect of the filter is greater.

An adaptive filter can thus apply different degrees of smoothing, depending upon the homogeneity or heterogeneity of the windowed region.

The performance of the Lee filter is also affected by other factors such as the window size and coefficient of variation C_v of the noise. According to the second of the assumptions listed above, the noise-fading signal is approximated by the mean of a pixel’s neighbours within a given window. It can be inferred that the larger the window size, the greater is the degree of smoothing. The value of C_v affects the weighting coefficient k (see Equation (1.47)). According to Equation (1.43), the value k determines whether the

[Cover] [Contents] [Index]