For example take this paper[PDF]. If I wanted to add Weather degradation into a clear photograph would it be worth it to look at that paper and try to reverse it? Also is there any specific approach to reversing an algorithm if it is at all possible?
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4Although that particular technique (of reversing an algorithm) can be extremely useful, I would think instead that finding the correct technique you were looking for would be more beneficial. As far as reversing an algorithm, think of how you reverse an equation in Mathematics, and do something similar - i.e. at each step in the algorithm, attempt to do the reverse step. Note that in some algorithms (lossy compression comes to mind) this is not always possible, as some of the data is lost because of the algorithm.
Yes. Just because something disagrees with your philosophy of the world does not make it a bad thing to read. It in fact makes it a good thing to read. Only reading texts which subscribe to your belief system is the equivalent of a person in power surrounding themselves with a group of "yes" men.
You should be constantly challenging your strongest beliefs to ensure you are on the right path.
There is no general approach. Take multiplying primes vs factoring into primes. It's dead easy to take:
A * B = C
and calculate C from A and B. Getting A and B from C is not so easy, even though there's only one solution.
You can see why trying to reverse (in general) the effects of any algorithm isn't so simple!
Yes, in certain cases it may be one useful technique, but if looking at the paper doesn't immediately give you an idea for how you might reverse it, I'd take it as a sign you should probably look for what you're actually after, first.
Draemon is correct, there is no general approach. In your case, I would read the paper.
Whether you want to add or remove weather degradation, you need to know what weather degradation looks like. That paper will have information on that, and might have an easy answer.
An example might be a paper on breaking a substitution cipher. You can certainly read the paper to learn how to encrypt something with a substitution cipher.