mp3 to wav to mp3 to wav same? Options

[gts]

If a file is encoded to mp3, then coverted back to a wav, and then that wav is convered back to mp3, will the both mp3s be the same?

[phong]

Do it enough, you can reduce the complexity of the result set. Sure it's not guaranteed to succeed. But what if you had a probability of sucess of 80%. Than statistically you just run it a bunch of times to guarantee sucess, which still comes in as polynomial.

This is a very good definition of a heuristic. Heuristics are used all the time to get "pretty good" answers to Hard problems. A good example is checking a number for primality. You can do this with 100% certainty by factoring (very slow), or a recently discovered algorithm that takes O(n^12) (still quite slow). There are other algorithms (some of which only work on certain sets of numbers) that when given a number to test and a seed number will tell you if it's prime or not, but get it wrong a certain percentage of the time (for the sake of example, we'll say they guess right 75% of the time). These tests can be run quickly, and changing the seed number results in an independant test. If you test a number with a few dozen seed numbers you can be sure that it's prime within a very small margin of error.

So, it's certainly possible to develop a heuristic to create a close approximation of the original mp3 file from a decoded wav file, and it would be much easier than getting the EXACT mp3 file back. Don't ask me to write it though, it doesn't sound like fun at all. I'd much rather work on graph coloring register allocation.

As far as "image enhancement" algorithms go... Most don't get much additional information from the image. Instead, they make up ficticious image data that looks pretty.