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?