peak signal-to-noise ratio

The phrase peak signal-to-noise ratio, often abbreviated PSNR, is an engineering term for the ratio between the maximum value of a signal and the magnitude of background noise. Because many signals have a very wide dynamic range, PSNRs are usually expressed in terms of the logarithmic decibel scale. The PSNR is most commonly used as a measure of quality of reconstruction in image compression etc. It is most easily defined via the mean squared error which for two mxn images I and K is defined as:

\mathit{MSE} = \frac{1}{mn}\sum_i^m\sum_j^n ||I(i,j) - K(i,j)||^2

The PSNR is defined as:

\mathit{PSNR} = 10 \cdot \log \left( \frac{\mathit{MAX}_I^2}{\mathit{MSE}} \right)

= 20 \cdot \log \left( \frac{\mathit{MAX}_I}{\sqrt{\mathit{MSE}}} \right) Here, MAX_I is the maximum pixel value of the image. In most cases this is 255. The logarithm is base 10. For color images with three RGB values per pixel the definition of PSNR is the same. Only the MSE is the sum over all squared value differences divided by image size and by three. Typical values for the PSNR in image compression are between 20 and 40 dB.

Peak Signal-to-noise Ratio

See also