Decorrelation is a general term for any process that is used to reduce
autocorrelation
Autocorrelation, sometimes known as serial correlation in the discrete time case, measures the correlation of a signal with a delayed copy of itself. Essentially, it quantifies the similarity between observations of a random variable at differe ...
within a signal, or
cross-correlation
In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a ''sliding dot product'' or ''sliding inner-product''. It is commonly used f ...
within a set of signals, while preserving other aspects of the signal. A frequently used method of decorrelation is the use of a matched
linear filter to reduce the
autocorrelation
Autocorrelation, sometimes known as serial correlation in the discrete time case, measures the correlation of a signal with a delayed copy of itself. Essentially, it quantifies the similarity between observations of a random variable at differe ...
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
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used with this or similar meanings in many scientific and technical disciplines, i ...
signal, this is often referred to as
signal whitening.
Process
Most decorrelation algorithms are
linear
In mathematics, the term ''linear'' is used in two distinct senses for two different properties:
* linearity of a '' function'' (or '' mapping'');
* linearity of a '' polynomial''.
An example of a linear function is the function defined by f(x) ...
, but there are also
non-linear
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathe ...
decorrelation algorithms.
Many data compression algorithms incorporate a decorrelation stage. For example, many
transform coders 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
A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequency, frequencies. The DCT, first proposed by Nasir Ahmed (engineer), Nasir Ahmed in 1972, is a widely ...
.
By comparison,
sub-band coders 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 coders 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 electronics, crosstalk (XT) is a phenomenon by which a signal transmitted on one circuit or channel of a transmission system creates an undesired effect in another circuit or channel. Crosstalk is usually caused by undesired capacitive, ...
in a multi-channel signal, or in the design of
echo canceller
Echo suppression and echo cancellation are methods used in telephony to improve voice quality by preventing echo from being created or removing it after it is already present. In addition to improving subjective audio quality, echo suppression i ...
s.
In
image processing
An image or picture is a visual representation. An image can be two-dimensional, such as a drawing, painting, or photograph, or three-dimensional, such as a carving or sculpture. Images may be displayed through other media, including a pr ...
decorrelation techniques can be used to enhance or stretch,
colour
Color (or colour in Commonwealth English; see spelling differences) is the visual perception based on the electromagnetic spectrum. Though color is not an inherent property of matter, color perception is related to an object's light absorp ...
differences found in each
pixel
In digital imaging, a pixel (abbreviated px), pel, or picture element is the smallest addressable element in a Raster graphics, raster image, or the smallest addressable element in a dot matrix display device. In most digital display devices, p ...
of an image. This is generally termed as 'decorrelation stretching'.
The concept of decorrelation can be applied in many other fields.
In
neuroscience
Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions, and its disorders. It is a multidisciplinary science that combines physiology, anatomy, molecular biology, ...
, decorrelation is used in the analysis of the
neural network
A neural network is a group of interconnected units called neurons that send signals to one another. Neurons can be either biological cells or signal pathways. While individual neurons are simple, many of them together in a network can perfor ...
s in the human visual system.
In
cryptography
Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), ...
, it is used in cipher design (see
Decorrelation theory) and in the design of
hardware random number generators.
See also
*
Equalisation
*
Randomness extractor
A randomness extractor, often simply called an "extractor", is a function, which being applied to output from a weak entropy source, together with a short, uniformly random seed, generates a highly random output that appears Independent and identic ...
*
Eigenvalue decomposition
*
Whitening transformation
A whitening transformation or sphering transformation is a linear transformation that transforms a vector of random variables with a known covariance matrix into a set of new variables whose covariance is the identity matrix, meaning that they ar ...
References
External links
Non-linear decorrelation algorithmsAssociative Decorrelation Dynamics in Visual Cortex
Signal processing
Image processing
Computational physics
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