The software that makes video astronomy possible is Cor Berrevoets' RegiStax (http://registax.astronomy.net). By now, several other software packages have developed similar capabilities, but RegiStax is the gold standard, and it's free.
RegiStax includes clear instructions which I shall not repeat here. You give it an AVI video file, and it aligns the images, sorts them in order of decreasing quality, suggests a cutoff point for discarding the bad ones, and then stacks them carefully, iterating to improve the match. Then you get to perform wavelet-based sharpening as shown in Figure B.4. Each slider controls wavelets of a particular frequency and hence details of a particular size. The first slider generally affects only grain; the second and third begin to bring out image detail. When the image looks the way you want, you can save it and do further processing, if needed, with Photoshop.
Registax isn't just for videos. You can use it to stack and enhance images from any source; newer versions are becoming increasingly suitable for deep-sky work.
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