You describe two types of noise that you want to remove. (By the way, the wikipedia page for noise reduction is not bad, see the "in images" section).
One type is odd-point noise. This is often called “speckle” or “salt and pepper” noise and is usually removed by some kind of averaging filter. There's a nice page outlining some algorithms for this in mathworks .
The second type is strings. This is more complicated, and I would not call it noise, it would depend on the type of input image. This document seems appropriate, but it is not available for free online, so you may have to buy it or go to your local university library.
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