## Peak signal-to-noise ratio – wikipedia digital image watermarking project report

Peak signal-to-noise ratio, often abbreviated PSNR, is an engineering term for the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of its representation. *Digital image processing 3rd edition gonzalez* Because many signals have a very wide dynamic range, PSNR is usually expressed in terms of the logarithmic decibel scale.

PSNR is most commonly used to measure the quality of reconstruction of lossy compression codecs (e.g., for image compression). Digital image pro 10 The signal in this case is the original data, and the noise is the error introduced by compression. Digital image meaning When comparing compression codecs, PSNR is an approximation to human perception of reconstruction quality. Digital photo recovery software free download full version Although a higher PSNR generally indicates that the reconstruction is of higher quality, in some cases it may not. Digital image processing important questions 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. Digital image processing projects using matlab with source code [1] [2]

PSNR is most easily defined via the mean squared error ( MSE).

Elements of digital image processing Given a noise-free m× n monochrome image I and its noisy approximation K, MSE is defined as: M S E = 1 m n ∑ i = 0 m − 1 ∑ j = 0 n − 1 [ I ( i , j ) − K ( i , j ) ] 2 {\displaystyle {\mathit {MSE}}={\frac {1}{m\,n}}\sum _{i=0}^{m-1}\sum _{j=0}^{n-1}[I(i,j)-K(i,j)]^{2}}

The PSNR (in dB) is defined as: P S N R = 10 ⋅ log 10 ( M A X I 2 M S E ) = 20 ⋅ log 10 ( M A X I M S E ) = 20 ⋅ log 10 ( M A X I ) − 10 ⋅ log 10 ( M S E ) {\displaystyle {\begin{aligned}{\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}\left({{\mathit {MAX}}_{I}}\right)-10\cdot \log _{10}\left({\mathit {MSE}}\right)\end{aligned}}}

Here, MAX I is the maximum possible pixel value of the image. Digital image analysis pdf When the pixels are represented using 8 bits per sample, this is 255. Digital image sensor More generally, when samples are represented using linear PCM with B bits per sample, MAX I is 2 B−1. Digital image processing system For color images with three RGB values per pixel, the definition of PSNR is the same except the MSE is the sum over all squared value differences divided by image size and by three. Digital image processing questions 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. Applications of *digital image processing pdf* [3] [4]

Typical values for the PSNR in lossy image and video compression are between 30 and 50 dB, provided the bit depth is 8 bits, where higher is better. Digital image processing pdf For 16-bit data typical values for the PSNR are between 60 and 80 dB. Image enhancement in digital signal processing [5] [6] Acceptable values for wireless transmission quality loss are considered to be about 20 dB to 25 dB. *Advantages of digital image processing* [7] [8]

In the absence of noise, the two images I and K are identical, and thus the MSE is zero. Digital image basics In this case the PSNR is infinite (or undefined, see Division by zero). Artplus digital photo recovery 7 [9]