This filter is found in → → . NL means "Non Linear". Derived from the Unix pnmnlfilt program, it joins smoothing, despeckle and sharpen enhancement functions. It works on the whole image, not on the selection.
This is something of a swiss army knife filter. It has 3 distinct operating modes. In all of the modes each pixel in the image is examined and processed according to it and its surrounding pixels values. Rather than using 9 pixels in a 3x3 block, it uses an hexagonal block whose size can be set with the Radius option.
When Do preview is checked, parameter setting results are interactively displayed in preview.
Alpha: Meaning of this value depends on the selected option.
Radius: Controls the strength of the filter (0.33-1.00).
      This filter can perform several distinct functions, depending on
      the value of the parameter alpha.
    
alpha <= 0.5)
        
            
            The value of the center pixel will be replaced by the mean of
            the 7 hexagon values, but the 7 values are sorted by size and
            the top and bottom alpha portion of the 7
            are excluded from the mean. This implies that an
            alpha value of 0.0 gives the same sort of
            output as a normal convolution (ie. averaging or smoothing
            filter), where radius will determine the
            "strength" of the filter. A good value to start from for subtle
            filtering is alpha = 0.0,
            radius = 0.55.  For a more blatant
            effect, try alpha 0.0 and
            radius 1.0.
          
            An alpha value of 0.5 will cause the
            median value of the 7 hexagons to be used to replace the center
            pixel value. This sort of filter is good for eliminating "pop"
            or single pixel noise from an image without spreading the noise
            out or smudging features on the image. Judicious use of the
            radius parameter will fine tune the
            filtering. Intermediate values of alpha
            give effects somewhere between smoothing and "pop" noise
            reduction. For subtle filtering try starting with values of
            alpha = 0.4,
            radius = 0.6.  For a more blatant effect
            try alpha = 0.5,
            radius = 1.0 .
          
alpha <= 2.0)
        
            
            This type of filter applies a smoothing filter adaptively over
            the image. For each pixel the variance of the surrounding
            hexagon values is calculated, and the amount of smoothing is
            made inversely proportional to it. The idea is that if the
            variance is small then it is due to noise in the image, while if
            the variance is large, it is because of "wanted" image features.
            As usual the  radius parameter  controls
            the effective radius, but it probably advisable  to  leave  the
            radius between 0.8 and 1.0 for the variance calculation to be
            meaningful. The alpha parameter sets the
            noise threshold, over which less smoothing will be done. This
            means that small values of alpha will
            give the most subtle filtering effect, while large values will
            tend to smooth all parts of the image. You could start with
            values like
            alpha  =  1.2radius = 1.0alpha parameter  to  get the desired
            effect. This type of filter is best for filtering out dithering
            noise in both bitmap and color images.
          
alpha >= -0.9)
        
            
          This is the opposite type of filter to the smoothing filter. It
          enhances edges. The alpha parameter
          controls the amount of edge enhancement, from subtle (-0.1) to
          blatant (-0.9). The radius parameter
          controls the effective radius as usual, but useful values are
          between 0.5 and 0.9. Try starting with values of
          
            ,
          alpha = 0.3
          
            .
        radius = 0.8
          
The various operating modes can be used one after the other to get the desired result. For instance to turn a monochrome dithered image into grayscale image you could try one or two passes of the smoothing filter, followed by a pass of the optimal estimation filter, then some subtle edge enhancement. Note that using edge enhancement is only likely to be useful after one of the non-linear filters (alpha trimmed mean or optimal estimation filter), as edge enhancement is the direct opposite of smoothing.
            For reducing color quantization noise in images (ie. turning
            .gif files back into 24 bit files) you could try a pass of the
            optimal estimation filter (alpha 1.2,
            radius 1.0), a pass of the median filter
            (alpha 0.5, radius
            0.55), and possibly a pass of the edge enhancement filter.
            Several passes of the optimal estimation filter with declining
            alpha values are more effective than a
            single pass with a large alpha value. As
            usual, there is a tradeoff between filtering effectiveness and
            losing detail. Experimentation is encouraged.