Step 3Crop and resize the image
The way to get around this is by cropping and resizing the image. This will shift the position static pixels and when images are compared together make them just seem like noise.
This alone will not always remove the noise signature itself, but it is one way to make it harder to identify it.
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For example, using lanczos interpolation when scaling image in GIMP, it screws up higher frequencies (the visible noise) quite considerably (measured with power spectral density and correlated to original image).
See attached example measurement (shows PSD and correlation of frequencies spectrum after Fourier transform).