Peak signal-to-noise ratio (PSNR) is calculated with

$$\text{PSNR} = 10 \log \frac{\;\text{MAX}^2}{\text{MSE}}\;,$$

with MSE the mean square error and MAX the maximum signal value.

Why is the MSE used in calculating the PSNR, rather than RMSE (root mean square error)?


You can transform your equation as follows:

$$ \text{PSNR} = 10 \log \frac{\text{MAX}^2}{\text{MSE}} = 20 \log \frac{\text{MAX}}{\text{MSE}^{1/2}} = 20 \log \frac{\text{MAX}}{\text{RMSE}} $$

  • $\begingroup$ I asked my professor the same ,he quoted that we do that to reduce the time complexity. since, RMSE involves calculation of square roots which is a time expensive operation. $\endgroup$ – MOHANTEJA Mar 2 at 23:44

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