I'm happy to be proven wrong, but I think this one is impractical.
Which they didn't cause it's not possible, I mean, left to reader.
[edit: I put it with the myth you need to erase data on a hard disk randomly multiple times http://www.nber.org/sys-admin/overwritten-data-gutmann.html ]
I've never seen it actually shown so that to me makes it dodgy. If it was possible it'd be a pretty cool demo.
(And I assume I don't need to say removing camera blur, the famous photoshop swirls incident etc is not the same.)
This NIST publication says: "for ATA disk drives manufactured after 2001 (over 15 GB) clearing by overwriting the media once is adequate to protect the media from both keyboard and laboratory attack."
Tech changes have "altered previously held best practices regarding magnetic disk type storage media". It does not seem to confirm that multiple erases were unnecessary before.
In the same vein, check out http://www.ee.columbia.edu/~wliu/CVPR05_LiuWei1.pdf
I would assume most of the time people "smudge" the data they want to be removed from a photo. Though, as stated, adding new information to the image has got to be the best way to do this. (a blackout.)
There are some things that were not mentioned.
1) Obviously you're talking about traditional spinning platter drives, and not SSDs.
2) The complete drive needs to be overwritten to be sure all data has gone. The safest way to do that is to use an ATA secure erase command. This will overwrite all the sectors marked as bad. DBAN is good, but it will not overwrite sectors marked as bad. (The risk from this is small.)
If the high-frequency data that was removed is unique enough that it can't be either guessed or recovered then a blur might be just fine.
If the high-frequency data is something that can be easily guessed, extrapolated, etc. then a blur does not provide much protection as far as the information content goes.