PSNR is a measure of the difference between two images (see for instance the article in wikipedia). Mathematica has a function for calculating the MSE (mean squared error) between two images
ImageDistance[img1, img2]
The default measure in this calculation is the Euclidean distance, which is probably what you need to calculate the PSNR. If not, ImageDistance
takes a DistanceFunction
option which is quite flexible.