Some programs, such as Sterling and Sterling2, have a feature that does this for you. In Sterling do Image -> Anti-Alias 4:1 and save the resulting fractal. You can do the same thing in any good graphics program, such as Photoshop, where you just hit control-alt-i.
It is often a good idea to sharpen the image after anti-aliasing, as it can look a little soft, but this is a matter of taste.
You may find that the new image is much smoother and less speckled than the original. Do give this a try at least once, as you may be surprised by the difference. I label my anti-aliased images with the suffix aa. To see what a difference anti-aliasing can make, compare these two pairs of images. Probably the best way to do so is to open each image in its own browser window and then flick between the two using alt-TAB. To do this hold down the shift key as you click on each image.
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