Without noise

With Gaussian noise

Insignal processing theory,Gaussian noise, named afterCarl Friedrich Gauss, is a kind ofsignal noise that has aprobability density function (pdf) equal to that of thenormal distribution (which is also known as the Gaussian distribution).^[1][2] In other words, the values that the noise can take are Gaussian-distributed.

The probability density function${\displaystyle p}$ of a Gaussian random variable${\displaystyle z}$ is given by:

${\displaystyle p(z)=\frac{1}{\sigma \sqrt{2\pi }}{e}^{-\frac{(z-\mu {)}^2}{2{\sigma }^2}}}$

where${\displaystyle z}$ represents the grey level,${\displaystyle \mu }$ themean grey value and${\displaystyle \sigma }$ itsstandard deviation.^[3]

A special case iswhite Gaussian noise, in which the values at any pair of times areidentically distributed andstatistically independent (and henceuncorrelated). Incommunication channel testing and modelling, Gaussian noise is used as additivewhite noise to generateadditive white Gaussian noise.

Intelecommunications andcomputer networking, communication channels can be affected bywideband Gaussian noise coming from many natural sources, such as the thermal vibrations of atoms in conductors (referred to as thermal noise orJohnson–Nyquist noise),shot noise,black-body radiation from the earth and other warm objects, and from celestial sources such as the Sun.

Principal sources of Gaussian noise indigital images arise during acquisition e.g.sensor noise caused by poor illumination and/or high temperature, and/or transmission e.g.electronic circuit noise.^[3] Indigital image processing Gaussian noise can be reduced using aspatial filter, though when smoothing an image, an undesirable outcome may result in the blurring of fine-scaled image edges and details because they also correspond to blocked high frequencies. Conventional spatial filtering techniques fornoise removal include: mean (convolution) filtering,median filtering andGaussian smoothing.^[1][4]

• Gaussian process
• Gaussian smoothing

• Stochastic processes
• Normal distribution
• Acoustics

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• Short description matches Wikidata