Is There a Way to Reduce Purple-ish Discoloration from Dark Circles?

I have had quite severe dark circles since childhood. Having spoken to a local plastic surgeon he recommends the arcus marginalis release to deal with a fat bulge I have running along the eye socket. However he was unsure whether the procedure would remove all of the pink/purpleish discolouration I have running along the eye socket as seen below. Are there any surgical procedures that could reduce this discolouration, or perhaps you have any recommended topical treatments? Thanks very much

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