273.

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Page 44

Figure 1.27 (a) Test SAR image showing speckle noise, (b) Filtered image using 5×5 mean filter, (c) Filtered image using window size of 9×9.

(1.36)

where z_ij is the noise affected image pixel at location (i, j), x_ij is the signal that one wishes to recover, and v_ij is multiplicative noise. In order to simplify the expression, the subscripts are omitted in the following discussion. Normally, the mean μ_v of noise v takes a value of unity (Lee, 1986), and the noise standard deviation σ_v can be obtained from a local window located over a homogeneous area of the image, such as a water surface. The idea of extracting σ_v in this way is based on the second assumption, that the parameters x and v in Equation (1.36) are independent. The mean of a noise fading signal μ_z can be expressed by:

(1.37)

where μ_x and μ_v are the means of x and v, respectively. Using Equation (1.36), the variance σ_z² of z can be expressed as:

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