The process is a forensic investigation. When a damaged frame of a 1977 print shows a hair in the gate, the restorers don't just delete the hair; they reconstruct the image underneath it using data from other frames. They compare the scan against the 1993 LaserDisc release (the last time the original trilogy was officially released unaltered) to ensure accuracy.
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To own a clean version of the original 1977 cut, you must hunt one of two things: star wars 1977 original version exclusive