272.

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Figure 1.26 Results of median and mean filtering for step edge and double pulse.

plexity, we illustrate the concept of the adaptive filter using the Lee filter, which is a relatively simple model.

1.8.3.1 Lee filter

The effectiveness of the Lee filter is dependent on the following three assumptions (Lee, 1980), which have also been adopted by the other filter models such as the RGMAP filters (Lopes et al., 1990; Baraldi and Parmiggiani, 1995a).

1 SAR speckle is modelled as a multiplicative noise (note that the visual effect of multiplicative noise is that the noise level is proportional to the image grey level).

2 The noise and signal are statistically independent.

3 The sample mean and variance of a pixel is equal to its local mean and local variance computed within a window centred on the pixel of interest.

These three assumptions define the noise model described below. The model is specified by the mean and standard deviation. The first assumption implies that:

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