PSNR

PSNR, or peak signal-to-noise ratio, is an objective metric used to quantify the similarity between an original image or video frame and a degraded version produced by compression or processing. It is derived from the mean squared error (MSE) between corresponding samples. For an image with N samples and maximum possible pixel value MAX_I, MSE = (1/N) sum over all samples of (I(x) − K(x))^2. PSNR is defined as PSNR = 10 log10 (MAX_I^2 / MSE) = 20 log10 (MAX_I / sqrt(MSE)). MAX_I equals 2^B − 1 for B-bit images (for example, 255 for 8-bit, 65535 for 16-bit).

Calculation details include how color data are handled. For color images, MSE can be computed separately for each channel and then averaged, or computed on a luminance component. PSNR is commonly reported per channel and then averaged, or computed on the luminance channel in a color space such as YUV or YCbCr.

Usage and interpretation: PSNR is widely used in image and video coding to assess fidelity and compare codecs, compression levels, or processing algorithms. Higher PSNR indicates closer similarity to the original, with typical high-quality 8-bit reconstructions in the range of 30–40 dB. Values around 20–25 dB often reflect noticeable degradation, though these benchmarks depend on content and viewing conditions.

Limitations: PSNR does not always correlate well with perceived visual quality and does not account for perceptual factors such as human visual system sensitivity, masking, or structural distortion. Consequently, it is often complemented or replaced by perceptual metrics like SSIM, MS-SSIM, or other perceptual quality measures in research and industry contexts.