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| image1 = 512x512-No-Noise.jpg | |||
| alt1 = Without noise | |||
| caption1 = Without noise | |||
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| alt2 = With Gaussian noise | |||
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'''Gaussian noise''' represents [[statistical noise]] having [[probability density function]] (PDF) equal to that of the [[normal distribution]], which is also known as the [[Gaussian distribution]].<ref name="Barbu" /><ref name="Handbook"/> In other words, the values that the noise can take on are Gaussian-distributed. | |||
The probability density function <math>p</math> of a Gaussian random variable <math>z</math> is given by: | |||
: <math>p_G(z) = \frac{1}{\sigma\sqrt{2\pi}} e^{ -\frac{(z-\mu)^2}{2\sigma^2} }</math> | |||
where <math>z</math> represents the grey level, <math>\mu</math> the [[mean]] value and <math>\sigma</math> the [[standard deviation]].<ref name="Basel" /> | |||
A special case is ''white Gaussian noise'', in which the values at any pair of times are [[iid|identically distributed]] and [[statistically independent]] (and hence [[uncorrelated]]). In [[Channel (communications)|communication channel]] testing and modelling, Gaussian noise is used as additive [[white noise]] to generate [[additive white Gaussian noise]]. | |||
In [[telecommunications]] and [[computer networking]], [[Channel (communications)|communication channels]] can be affected by [[wideband]] Gaussian noise coming from many natural sources, such as the thermal vibrations of atoms in conductors (referred to as [[thermal noise]] or [[Johnson-Nyquist noise]]), [[shot noise]], [[Black body|black body radiation]] from the earth and other warm objects, and from [[Astronomical object|celestial sources]] such as the [[Sun]]. | |||
== Gaussian noise in digital images == | |||
Principal sources of Gaussian noise in [[digital image]]s arise during acquisition eg. [[sensor noise]] caused by poor illumination and/or high temperature, and/or transmission eg. [[Circuit noise level|electronic circuit noise]].<ref name="Basel" /> In [[digital image processing]] Gaussian noise can be reduced using a [[spatial 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 for [[Noise reduction|noise removal]] include: mean ([[convolution]]) filtering, [[median filter|median filtering]] and [[Gaussian smoothing]].<ref name="Barbu" /><ref name="HIPR2" /> | |||
== See also == | |||
* [[Gaussian process]] | |||
* [[Gaussian smoothing]] | |||
== References == | |||
{{Reflist|refs= | |||
<ref name="Handbook">{{cite web |url=http://www.sfu.ca/sonic-studio/handbook/Gaussian_Noise.html |title=Handbook for Acoustic Ecology |edition=Second |date=1999 |publisher=Cambridge Street Publishing |editor=Barry Truax |accessdate=2012-08-05}}</ref> | |||
<ref name="HIPR2">{{cite web | url=http://homepages.inf.ed.ac.uk/rbf/HIPR2/noise.htm | title=Image Synthesis — Noise Generation | accessdate=11 October 2013 | author=Robert Fisher, Simon Perkins, Ashley Walker, Erik Wolfart}}</ref> | |||
<ref name="Basel">{{cite web | url=http://miac.unibas.ch/SIP/06-Restoration.html | title=Image Restoration: Introduction to Signal and Image Processing | publisher=MIAC, University of Basel | date=2012-04-24 | accessdate=11 October 2013 | author=Dr. Philippe Cattin}}</ref> | |||
<ref name="Barbu">{{cite journal | url=http://www.hindawi.com/journals/aaa/2013/856876/ | title=Variational Image Denoising Approach with Diffusion Porous Media Flow | author=Tudor Barbu | journal=Abstract and Applied Analysis | year=2013 | volume=2013 | pages=8 | doi=10.1155/2013/856876}}</ref> | |||
}} | |||
{{physics-stub}} | |||
{{probability-stub}} | |||
{{DEFAULTSORT:Gaussian Noise}} | |||
[[Category:Noise]] | |||
[[Category:Stochastic processes]] | |||
[[Category:Time series analysis]] |
Latest revision as of 23:46, 6 July 2013
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Gaussian noise represents statistical noise having probability density function (PDF) equal to that of the normal distribution, which is also known as the Gaussian distribution.[1][2] In other words, the values that the noise can take on are Gaussian-distributed.
The probability density function of a Gaussian random variable is given by:
where represents the grey level, the mean value and the standard deviation.[3]
A special case is white Gaussian noise, in which the values at any pair of times are identically distributed and statistically independent (and hence uncorrelated). In communication channel testing and modelling, Gaussian noise is used as additive white noise to generate additive white Gaussian noise.
In telecommunications and computer networking, communication channels can be affected by wideband Gaussian noise coming from many natural sources, such as the thermal vibrations of atoms in conductors (referred to as thermal noise or Johnson-Nyquist noise), shot noise, black body radiation from the earth and other warm objects, and from celestial sources such as the Sun.
Gaussian noise in digital images
Principal sources of Gaussian noise in digital images arise during acquisition eg. sensor noise caused by poor illumination and/or high temperature, and/or transmission eg. electronic circuit noise.[3] In digital image processing Gaussian noise can be reduced using a spatial 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 for noise removal include: mean (convolution) filtering, median filtering and Gaussian smoothing.[1][4]
See also
References
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