Decorrelation

# Decorrelation

Discussion

Encyclopedia
Decorrelation is a general term for any process that is used to reduce autocorrelation
Autocorrelation
Autocorrelation is the cross-correlation of a signal with itself. Informally, it is the similarity between observations as a function of the time separation between them...

within a signal, or cross-correlation
Cross-correlation
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long-duration signal for a shorter, known feature...

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
Linear filter
Linear filters in the time domain process time-varying input signals to produce output signals, subject to the constraint of linearity.This results from systems composed solely of components classified as having a linear response....

to reduce the autocorrelation
Autocorrelation
Autocorrelation is the cross-correlation of a signal with itself. Informally, it is the similarity between observations as a function of the time separation between them...

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
White noise
White noise is a random signal with a flat power spectral density. In other words, the signal contains equal power within a fixed bandwidth at any center frequency...

signal, this is often referred to as signal whitening.

Although most decorrelation algorithms are linear, non-linear decorrelation algorithms also exist.

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
Discrete cosine transform
A discrete cosine transform expresses a sequence of finitely many data points in terms of a sum of cosine functions oscillating at different frequencies. DCTs are important to numerous applications in science and engineering, from lossy compression of audio and images A discrete cosine transform...

.

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 modeled 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 cancellers.

In image processing
Image processing
In electrical engineering and computer science, image processing is any form of signal processing for which the input is an image, such as a photograph or video frame; the output of image processing may be either an image or, a set of characteristics or parameters related to the image...

decorrelation techniques can be used to enhance or stretch
Stretch
Stretch can refer to:*Stretching is a form of exercise or a pre-exercise discipline, sometimes called Warming up*Stretch ceiling, a type of ceiling made from polymer.*Stretch ratio in the mechanics of materials*Stretched tuning of certain string instruments...

, colour differences found in each pixel
Pixel
In digital imaging, a pixel, or pel, is a single point in a raster image, or the smallest addressable screen element in a display device; it is the smallest unit of picture that can be represented or controlled....

of an image. This is generally termed as 'decorrelation stretching'.

The concept of decorrelation can be applied in many other fields.
In neuroscience
Neuroscience
Neuroscience is the scientific study of the nervous system. Traditionally, neuroscience has been seen as a branch of biology. However, it is currently an interdisciplinary science that collaborates with other fields such as chemistry, computer science, engineering, linguistics, mathematics,...

, decorrelation is used in the analysis of the neural network
Neural network
The term neural network was traditionally used to refer to a network or circuit of biological neurons. The modern usage of the term often refers to artificial neural networks, which are composed of artificial neurons or nodes...

s in the human visual system.
In cryptography
Cryptography
Cryptography is the practice and study of techniques for secure communication in the presence of third parties...

, it is used in cipher design (see Decorrelation theory
Decorrelation theory
In cryptography, decorrelation theory is a system developed by Serge Vaudenay for designing block ciphers to be provably secure against differential cryptanalysis, linear cryptanalysis, and even undiscovered cryptanalytic attacks meeting certain broad criteria...

) and in the design of hardware random number generators.