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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)?

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You can transform your equation as follows:

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

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  • $\begingroup$ 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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