Basically, I'd like to bitwise XOR an image with another image of the same size but different content. Then, I rearranging all the pixels positions(shuffled the results). Then, I'd like to know what filters or image processing algorithms if I apply then restore the pixel positions and then remove the XORed image(by XORing it with the result), I would be able to get the same results as I apply the filters or the algorithms on the original image.
I know that all the filters or algorithms that requre two adjacent pixels to work are not suitable for my purpose. However, I'd like to know what filters or image processing algorithms do fall in this category.