Applying a gamma filter

Most image files contain some type of high-frequency noise (speckling). While a low-pass filter reduces image speckles, it can also degrade some of the finer detail in the image. Special low-pass filters, called Gamma filters, can preserve image details by filtering on individual pixels in an image using the gray-level values in a square window surrounding each pixel. You can apply a speckle filter to preserve some of the linear features in the image. Gamma filtering is primarily used on radar data to remove high-frequency speckle, while preserving high-frequency features (edges). The input for the number of looks of the radar image is used to calculate the noise variance. You can specify an intensity or amplitude formate for the radar image.

The dimensions of a Gamma filter must be odd-numbered and can be from 3x3 to 11x11 pixels. Filter size greatly affects the quality of processed images. If a filter is too small, the noise filtering algorithm is not effective; if a filter is too large, subtle details of the image will be lost in the filtering process. A 7x7 filter usually gives the best result.

All pixels are filtered. In order to filter pixels located near edges of an image, edge pixels are replicated to give sufficient data.

For example:

In a 3x3 filter window

Algorithm:

The resulting gray-level value R for the smoothed pixel is:

R = I for Ci less than or equal to CuR = (B*I + SQRT(D))/(2*ALFA) for Cu < Ci < CmaxR = CP for Ci greater than or equal to Cmax

where:

NLOOK = number of looksVAR = variance in filter windowCP = center pixel gray-level valueI = mean gray-level in the filter windowCu = 1/SQRT(NLOOK)Ci = SQRT(VAR)/ICmax = SQRT(2)*CuALFA = (1 + Cu**2)/(Ci**2 - Cu**2)B = ALFA - NLOOK - 1D = I*I*B*B + 4*ALFA*NLOOK*I*CP

For the amplitude image, each gray level will be squared before applying the algorithm, and the square root of the calculated pixel is returned as the final result.