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We know the Structural Similarity Index (SSIM) holds the following properties:

  • Unique maximum: S(x, y) = 1 if and only if x = y
  • Boundedness: S(x, y) ≤ 1
  • Symmetry: S(x, y) = S(y, x)

My question is: do we know simple some properties like these for Peak signal-to-noise ratio (PSNR)? And for MSE? Do some of the above properties hold for PSNR and MSE? For instance, I have never obtained a PSNR value higher than 80 and, in microscopy super-resolution, never higher than 30.

PS: Do you know any other interesting property of any metric?

Theo Deep
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    It would be great if you split this post into 2, one for each metric, so that people can focus on one metric at time. Can you please do that? – nbro Dec 21 '22 at 08:13
  • Of course! Do you mean one for properties of PSNR and another one for properties of MSE? I put them together because PSNR is highly determined by MSE. Thanks! – Theo Deep Dec 21 '22 at 19:18

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