Editing Peak signal-to-noise ratio (section)

== Definition ==
PSNR is most easily defined via the [[mean squared error]] (''MSE''). Given a noise-free ''m''×''n'' monochrome image ''I'' and its noisy approximation ''K'', ''MSE'' is defined as
: <math>\mathit{MSE} = \frac{1}{m\,n}\sum_{i=0}^{m-1}\sum_{j=0}^{n-1} [I(i,j) - K(i,j)]^2.</math>

The PSNR (in [[decibel|dB]]) is defined as
: <math>\begin{align}
 \mathit{PSNR} &= 10 \cdot \log_{10} \left( \frac{\mathit{MAX}_I^2}{\mathit{MSE}} \right) \\ 
  &= 20 \cdot \log_{10} \left( \frac{\mathit{MAX}_I}{\sqrt{\mathit{MSE}}} \right) \\ 
  &= 20 \cdot \log_{10}(\mathit{MAX}_I) - 10 \cdot \log_{10} (\mathit{MSE}).
\end{align}</math>

Here, ''MAX<sub>I</sub>'' is the maximum possible pixel value of the image. When the pixels are represented using 8 bits per sample, this is 255. More generally, when samples are represented using linear [[Pulse-code modulation|PCM]] with ''B'' bits per sample, ''MAX<sub>I</sub>'' is 2<sup><var>B</var></sup>&nbsp;−&nbsp;1.

=== Application in color images ===
For [[color image]]s with three [[RGB]] values per pixel, the definition of PSNR is the same except that the MSE is the sum over all squared value differences (now for each color, i.e. three times as many differences as in a monochrome image) divided by image size and by three. Alternately, for color images the image is converted to a different [[color space]] and PSNR is reported against each channel of that color space, e.g., [[YCbCr]] or [[HSL and HSV|HSL]].<ref>{{cite web|last=Oriani|first=Emanuele|title=qpsnr: A quick PSNR/SSIM analyzer for Linux|url=http://qpsnr.youlink.org/|access-date=6 April 2011}}</ref><ref>{{cite web|title=pnmpsnr User Manual|url=http://netpbm.sourceforge.net/doc/pnmpsnr.html|access-date=6 April 2011}}</ref>