Peak signal-to-noise ratio (PSNR) is an engineering term for the ratio between the maximum possible power of asignal and the power of corruptingnoise that affects the fidelity of its representation. Because many signals have a very widedynamic range, PSNR is usually expressed as alogarithmic quantity using thedecibel scale.

PSNR is commonly used to quantify reconstruction quality for images and video subject tolossy compression.

PSNR is most easily defined via themean squared error (MSE). Given a noise-freem×n monochrome imageI and its noisy approximationK,MSE is defined as

${\displaystyle \mathit{M}\mathit{S}\mathit{E}=\frac{1}{mn}\sum _{i=0}^{m-1}\sum _{j=0}^{n-1}[I(i,j)-K(i,j){]}^2.}$

The PSNR (indB) is defined as

Here,MAX_I 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 linearPCM withB bits per sample,MAX_I is 2^B − 1.

Forcolor images with threeRGB 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 differentcolor space and PSNR is reported against each channel of that color space, e.g.,YCbCr orHSL.^[1][2]

PSNR is most commonly used to measure the quality of reconstruction of lossy compressioncodecs (e.g., forimage compression). The signal in this case is the original data, and the noise is the error introduced by compression. When comparing compression codecs, PSNR is anapproximation to human perception of reconstruction quality.

Typical values for the PSNR inlossy image and video compression are between 30 and 50 dB, provided the bit depth is 8 bits, where higher is better. The processing quality of 12-bit images is considered high when the PSNR value is 60 dB or higher.^[3][4] For 16-bit data typical values for the PSNR are between 60 and 80 dB.^[5][6] Acceptable values for wireless transmission quality loss are considered to be about 20 dB to 25 dB.^[7][8]

In the absence of noise, the two imagesI andK are identical, and thus the MSE is zero. In this case the PSNR is infinite (or undefined, seeDivision by zero).^[9]

Original uncompressed image

Q=90, PSNR 45.53dB

Q=30, PSNR 36.81dB

Q=10, PSNR 31.45dB

Exampleluma PSNR values for acjpeg compressed image at various quality levels.

Although a higher PSNR generally correlates with a higher quality reconstruction, in many cases it may not. One has to be extremely careful with the range of validity of this metric; it is only conclusively valid when it is used to compare results from the same codec (or codec type) and same content.^[10]

Generally, when it comes to estimating thequality of images andvideos as perceived by humans, PSNR has been shown to perform very poorly compared to other quality metrics.^[10][11]

PSNR-HVS^[12] is an extension of PSNR that incorporates properties of the human visual system such ascontrast perception.

PSNR-HVS-M improves on PSNR-HVS by additionally taking into accountvisual masking.^[13] In a 2007 study, it delivered better approximations of human visual quality judgements than PSNR andSSIM by large margin. It was also shown to have a distinct advantage overDCTune and PSNR-HVS.^[14]

• Czenakowski distance
• Data compression ratio
• Perceptual Evaluation of Video Quality (PEVQ)
• Structural similarity index measure (SSIM)
• Subjective video quality
• Video Multimethod Assessment Fusion
• Video quality

• Image compression
• Noise (graphics)
• Film and video technology
• Digital television
• Engineering ratios

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