Decorrelation

<h2 id="process">Process</h2>
<p>Most decorrelation algorithms are <a href="/facts/Linear_operator/Q1PBKNVV">linear</a>, but there are also <a href="/facts/Nonlinear_system/4aYItALC">non-linear</a> decorrelation algorithms.
</p><p>Many data compression algorithms incorporate a decorrelation stage. For example, many <a href="/facts/Transform_coder/JGJISRFW">transform coders</a> 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 <a href="/facts/Karhunen%E2%80%93Lo%C3%A8ve_transform/HX3cIv6g">Karhunen–Loève transform</a>, or a simplified approximation such as the <a href="/facts/Discrete_cosine_transform/gPpDhPwP">discrete cosine transform</a>.
</p><p>By comparison, <a href="/facts/Sub-band_coder/HWMqu3DR">sub-band coders</a> 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.
</p><p><a href="/facts/Linear_predictive_coder/2Bl1xdSN">Linear predictive coders</a> 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.
</p><p>Decorrelation techniques can also be used for many other purposes, such as reducing <a href="/facts/Crosstalk/IT2LIwth">crosstalk</a> in a multi-channel signal, or in the design of <a href="/facts/Echo_canceller/Q26toK4x">echo cancellers</a>.
</p><p>In <a href="/facts/Image_processing/zenalNCf">image processing</a> decorrelation techniques can be used to enhance or stretch, <a href="/facts/Colour/XDvW7ESP">colour</a> differences found in each <a href="/facts/Pixel/UzwBvXBV">pixel</a> of an image. This is generally termed as 'decorrelation stretching'.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a>
</p><p>The concept of decorrelation can be applied in many other fields.
In <a href="/facts/Neuroscience/o5RV8Cas">neuroscience</a>, decorrelation is used in the analysis of the <a href="/facts/Neural_network/DDhJTfMc">neural networks</a> in the human visual system.
In <a href="/facts/Cryptography/e94PEVau">cryptography</a>, it is used in cipher design (see <a href="/facts/Decorrelation_theory/LAzw8MUN">Decorrelation theory</a>) and in the design of <a href="/facts/Hardware_random_number_generator/Kc7HIkgJ">hardware random number generators</a>.
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<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Equalization_(communications)/44Mc0WXw">Equalisation</a></li>
<li><a href="/facts/Randomness_extractor/YxS1Ia7x">Randomness extractor</a></li>
<li><a href="/facts/Eigenvalue_decomposition/a2nfF7hJ">Eigenvalue decomposition</a></li>
<li><a href="/facts/Whitening_transformation/q3MhJVIY">Whitening transformation</a></li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="http://www.cis.hut.fi/aapo/papers/NCS99web/node40.html">Non-linear decorrelation algorithms</a></li>
<li><a href="http://www.cs.utexas.edu/~nn/web-pubs/htmlbook96/dong/">Associative Decorrelation Dynamics in Visual Cortex</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Alley, Ronald E. (August 15, 1996). "Algorithm Theoretical Basis Document for Decorrelation Stretch" (PDF). eospso.gsfc.nasa.gov. Jet Propulsion Laboratory. Retrieved February 1, 2025. <a href="https://eospso.gsfc.nasa.gov/sites/default/files/atbd/ASTER_ATBD_99-2010.pdf" target="_blank">https://eospso.gsfc.nasa.gov/sites/default/files/atbd/ASTER_ATBD_99-2010.pdf</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
</ol>

Decorrelation open-in-new

Decorrelation