If you take enough images with your digital camera, they can all be compared together and a unique signature can be determined. This means that even when you think that you are posting a photo anonymously to the internet, you are actually providing clues for the government to better tell who you are. The larger the sample size of images they have, the easier it is them to track down images coming from the same camera. Once they know all the images are coming from the same camera, all they then have to do is find that camera and take a picture to confirm it beyond a reasonable doubt.
It is important to remove this noise signature so that you cannot be tracked down. I cannot guarantee any of these methods will work beyond the shadow of a doubt because the woman doing research for the government
on how to find the signature is very good. Check out her papers if you're really
good at dense math, and pass along what you learn. I can only promise that this will make their work more difficult.