NL means «Non Linear». Derived from the Unix pnmnlfilt program, it joins smoothing, despeckle and sharpen enhancement functions. It works on the whole layer, 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 3×3 block, it uses a hexagonal block whose size can be set with the Radius option.
This filter is found in the main menu under → → .
The filter does not work if the active layer has an alpha channel. Then the menu entry is disabled.
When checked, parameter setting results are interactively displayed in preview.
The Operating Mode is described below.
            Controls the amount of the filter to apply. Valid range is
            0.00-1.00. The exact meaning of this value depends on the selected
            operating mode. Note that this parameter is related to but not
            the same as the alpha parameter used in the
            pnmnlfilt program.
          
Controls the size of the effective sampling region around each pixel. The range of this value is 0.33-1.00, where 0.33 means just the pixel itself (and thus the filter will have no effect), and 1.00 means all pixels in the 3×3 grid are sampled.
This filter can perform several distinct functions:
            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 (i.e. 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 1.0 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 = 0.8,
            Radius = 0.6.
            For a more blatant effect try
            Alpha = 1.0,
            Radius = 1.0 .
          
            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  = 0.2,
            Radius = 1.0,
            and try increasing or decreasing the
            Alpha parameter to  get the desired
            effect. This type of filter is best for filtering out dithering
            noise in both bitmap and color images.
          
            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 (i.e. turning .gif
        files back into 24 bit files) you could try a pass of the optimal
        estimation filter (Alpha = 0.2,
        Radius = 1.0), a pass of the median filter
        (Alpha = 1.0, 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 trade-off between filtering effectiveness and losing detail.
        Experimentation is encouraged.