It can't be done.
Unlike the magic filters you see on CSI -- which is fiction, fairy tales, make believe, doesn't exist -- this cannot be undone. Once footage has been blurred in this way, there's no way to unblur it.
There's no undo filter.
This is a common question.
Since this was "like nudity" and not actual intentional removal of nudity, it may be damaged caused by that horrible "delogo" (or "de-logo") filter made for
VirtualDub and/or Avisynth. It's a destructive and crappy filter, with the net effect being little more than creating fuzzy square blobs on your video. Yuck.
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Like many, however, I'm sure somebody will read this and refuse to believe it, wasting hours on 'Googling' and downloading software that promises the impossible. I've used some of the most powerful forensic software currently in existence (Ikena, dTective, etc), plus a number of non-"professional" methods of restoration (
VirtualDub + Photoshop, Avisynth, others), and this is simply outside the realm of possibility. At best, you could extract a still that is "more in focus", but there's no way to magically un-blur video.
The only solution here is to find the pre-blurred source.
(Note:
No, this is not the same as the forensic "unswirl" commissioned by Interpol to catch infamous pedophile Christopher Neil several years ago. The swirl retained the original pixel information and was likely from a high resolution still photo, unlike the fuzzy blobs or fat pixels that are created by blurring nudity or faces in low-resolution video -- and that includes so-called "HD" video, which is still crummy resolution for print purposes. The swirl is non-lossy, while the standard blur/blob/pixel for nudity is HIGHLY lossy. It's not even close to the same.)