Step 5Removing the noise signature
It is probably more effective to remove the noise signature by creating more noise. One thing to try is to open Photoshop and save an image as a jpg using bicubic compression, resize it, crop it and then save it for web, again as a jpg (removing the exif) and finally save it for web again as a jpg using a quality of about 50. This should destroy the noise signature beyond recognition, but the image might not look too good.
It wouldn't be good to do this ever time either since you will end up creating a new "signature." The best thing to do is to save each image using a different elaborate method every time. For instance, you might convert something to a flash video, take a screenshot and then save for web as a jpg compressed with a quality of about 50.
It may not work, but you could also try adding a small amount of random noise to the red and green channels. This might actually clean up the image and remove the signature, but I'm not sure.
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You can add random noise using some good pseudo-random generator, like Mersenne Twister (seed with something random) - choose random number of pixels at random positions and brighten/darken them a bit (or mess with both chroma and luma channels).
Then use either nearest-neighbor or lanczos interpolation to resize image (instead of bicubic), they modify the frequency spectrum and histogram characteristics much more.
The reason jpeg compression does the described degradation of noise is because jpeg quantization tables used for lower qualities used after discrete cosine transform basically remove highest frequencies ("the noise").