evillamer
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You can use that same or similar software to "sharpen" a picture of something else, such as a human face, or a license plate number. You can even base some of your assumptions on the way in which pictures tend to get blurred when a camera isn't perfectly focused. This will give you a "pretty good guess" that sometimes produces remarkably good results. However, it also sometimes produces bad results, because your assumptions aren't always true. (Modern software can even be written such that, assuming you are hoping to make a license plate number readable, the software can "detect how well it worked", and even adjust its operating parameters accordingly. This would allow it to try different settings, and finally use the one that produced a result that was closer to what it expected or "hoped for". However, in reality, it's still a guess.) To take the extreme example, if I was the photographer, and I DELIBERATELY shifted the picture out of focus, then your assumption that it should be sharp is wrong, and, even if you could do so perfectly, making it sharp will "destroy" it.
Personally, I would leave anything that deliberately alters the signal in the "mastering process". (If I was remastering a CD, and I happened to know that it was converted with a specific brand of A/D converter, and also had a way to correct the specific errors introduced by that encoder, then I would so so.... although, even then, if my correction process generates other new errors, I have to decide whether my new version is really "better" or not.)
(This question comes up frequently in legal cases. If I start with a fuzzy blob that's supposed to be the bad guy's face on a security video, with enough signal processing I can probably "sharpen" it to the point where it looks like a human face. However, can I trust it to look like the right face? Or did my software do such a great job that it essentially created a face from insufficient information, in which case who it happens to look like is almost purely random? Or, even worse, does it offer so many options that, if I keep trying different settings, I can produce a result that looks like whomever I want it to - at which point I cheerfully declare "that's the guy" and stop trying new options?)
There has been quite alot of technology that tries to "restore" audio. Example will be BBE Sonic Max or Creative Xfi Crystalizer or Pioneer Sound Retriever to name a few.
http://www.tomsguide.com/us/creative,review-490-3.html
These audio processing software alter the transients quite abit. If done incorrectly or with certain music types, will likely exceed the volume headroom and distort.