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{{short description|Process of reducing correlation within one or more signals}}
{{refimprove|date=February 2025}}
'''Decorrelation''' is a general term for any process that is used to reduce [[autocorrelation]] within a signal, or [[cross-correlation]] within a set of signals, while preserving other aspects of the signal.{{Citation needed|date=December 2024}} A frequently used method of decorrelation is the use of a matched [[linear filter]] to reduce the [[autocorrelation]] of a signal as far as possible. Since the minimum possible autocorrelation for a given signal energy is achieved by equalising the power spectrum of the signal to be similar to that of a [[white noise]] signal, this is often referred to as [[Whitening transformation|signal whitening]].
==Process==
=== Signal processing ===
Most decorrelation algorithms are [[Linear operator|linear]], but there are also [[Nonlinear system|non-linear]] decorrelation algorithms.
Many data compression algorithms incorporate a decorrelation stage.{{Citation needed|date=December 2024}} For example, many [[transform coder]]s first apply a fixed linear transformation that would, on average, have the effect of decorrelating a typical signal of the class to be coded, prior to any later processing. This is typically a [[Karhunen–Loève transform]], or a simplified approximation such as the [[discrete cosine transform]].
By comparison, [[sub-band coder]]s do not generally have an explicit decorrelation step, but instead exploit the already-existing reduced correlation within each of the sub-bands of the signal, due to the relative flatness of each sub-band of the power spectrum in many classes of signals.
[[Linear predictive coder]]s can be modelled as an attempt to decorrelate signals by subtracting the best possible linear prediction from the input signal, leaving a whitened residual signal.
Decorrelation techniques can also be used for many other purposes, such as reducing [[crosstalk]] in a multi-channel signal, or in the design of [[echo canceller]]s.
In [[image processing]] decorrelation techniques can be used to enhance or stretch, [[colour]] differences found in each [[pixel]] of an image. This is generally termed as 'decorrelation stretching'.<ref>{{cite web |last=Alley |first=Ronald E. |date=August 15, 1996 |title=Algorithm Theoretical Basis Document for Decorrelation Stretch |url=https://eospso.gsfc.nasa.gov/sites/default/files/atbd/ASTER_ATBD_99-2010.pdf |website=eospso.gsfc.nasa.gov |publisher=[[Jet Propulsion Laboratory]] |access-date=February 1, 2025}}</ref>
=== Neuroscience ===
In [[neuroscience]], decorrelation is used in the analysis of the [[neural network]]s in the human visual system. The raw inputs from [[cone cell]]s and [[rod cell]]s under go many steps of processing before it is handled by the [[visual cortex]]. These steps generally perform decorrelation, both spatial ([[surround suppression]] in the retina) and temporal (handling of movement in the [[lateral geniculate nucleus]]).<ref>Dawei W. Dong and Joseph J. Atick, Network–Temporal Decorrelation: A Theory of Lagged and Nonlagged Responses in the Lateral Geniculate Nucleus, 1995, pp. 159–178.</ref>
=== Cryptography ===
In [[cryptography]], decorrelation is used in cipher design (see [[Decorrelation theory]]) and in the design of [[hardware random number generator#Software whitening|hardware random number generators]].
== See also ==
* [[Equalization (communications)|Equalisation]]
* [[Randomness extractor]]
* [[Eigenvalue decomposition]]
* [[Whitening transformation]]
==References==
{{Reflist}}
== External links ==
* [http://www.cis.hut.fi/aapo/papers/NCS99web/node40.html Non-linear decorrelation algorithms]
* [http://www.cs.utexas.edu/~nn/web-pubs/htmlbook96/dong/ Associative Decorrelation Dynamics in Visual Cortex]
[[Category:Signal processing]]
[[Category:Image processing]]
[[Category:Computational physics]]
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{{signal-processing-stub}}
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