If you resize a pink noise image, will the pink noise be preserved?

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I have a pink noise image of e.g. 500x500 resolution. If I resize the image to a new size with imresize, will the resulting image be pink-noise or will it be something close to it, but not the same?

What I thought is that with imresize, you change the image in a non-random way, so the result will not still be exactly pink-noise.