Source separation, blind signal separation (BSS) or blind source separation, is the separation of a set of source
signals from a set of mixed signals, without the aid of information (or with very little information) about the source signals or the mixing process. It is most commonly applied in
digital signal processing
Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner ar ...
and involves the analysis of mixtures of
signals; the objective is to recover the original component signals from a mixture signal. The classical example of a source separation problem is the
cocktail party problem, where a number of people are talking simultaneously in a room (for example, at a
cocktail party), and a listener is trying to follow one of the discussions. The human brain can handle this sort of auditory source separation problem, but it is a difficult problem in digital signal processing.
This problem is in general highly
underdetermined, but useful solutions can be derived under a surprising variety of conditions. Much of the early literature in this field focuses on the separation of temporal signals such as audio. However, blind signal separation is now routinely performed on
multidimensional data, such as
images
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimension ...
and
tensors,
[P. Comon and C. Jutten (editors). “Handbook of Blind Source Separation, Independent Component Analysis and Applications” Academic Press, ] which may involve no time dimension whatsoever.
Several approaches have been proposed for the solution of this problem but development is currently still very much in progress. Some of the more successful approaches are
principal components analysis
Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and ...
and
independent component analysis, which work well when there are no delays or echoes present; that is, the problem is simplified a great deal. The field of
computational auditory scene analysis Computational auditory scene analysis (CASA) is the study of auditory scene analysis by computational means.Wang, D. L. and Brown, G. J. (Eds.) (2006). ''Computational auditory scene analysis: Principles, algorithms and applications''. IEEE Press/Wi ...
attempts to achieve auditory source separation using an approach that is based on human hearing.
The human brain must also solve this problem in real time. In human perception this ability is commonly referred to as
auditory scene analysis
In perception and psychophysics, auditory scene analysis (ASA) is a proposed model for the basis of auditory perception. This is understood as the process by which the human auditory system organizes sound into perceptually meaningful elements. T ...
or the
cocktail party effect.
Applications
Cocktail party problem
At a cocktail party, there is a group of people talking at the same time. You have multiple microphones picking up mixed signals, but you want to isolate the speech of a single person. BSS can be used to separate the individual sources by using mixed signals. In the presence of noise, dedicated optimization criteria need to be used
[P. Comon, Contrasts, Independent Component Analysis, and Blind Deconvolution, "Int. Journal Adapt. Control Sig. Proc.", Wiley, Apr. 2004.]
HAL link
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Image processing
Figure 2 shows the basic concept of BSS. The individual source signals are shown as well as the mixed signals which are received signals. BSS is used to separate the mixed signals with only knowing mixed signals and nothing about original signal or how they were mixed. The separated signals are only approximations of the source signals. The separated images, were separated usin
Python
and th
Shogun toolbox
using Joint Approximation Diagonalization of Eigen-matrices (JADE
Jade is a mineral used as jewellery or for ornaments. It is typically green, although may be yellow or white. Jade can refer to either of two different silicate minerals: nephrite (a silicate of calcium and magnesium in the amphibole gro ...
) algorithm which is based on independent component analysis, ICA. This toolbox method can be used with multi-dimensions but for an easy visual aspect images(2-D) were used.
Medical imaging
One of the practical applications being researched in this area is medical imaging of the brain with magnetoencephalography (MEG). This kind of imaging involves careful measurements of magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and t ...
s outside the head which yield an accurate 3D-picture of the interior of the head. However, external sources of electromagnetic field
An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classica ...
s, such as a wristwatch on the subject's arm, will significantly degrade the accuracy of the measurement. Applying source separation techniques on the measured signals can help remove undesired artifacts from the signal.
EEG
In electroencephalogram (EEG) and magnetoencephalography (MEG), the interference from muscle activity masks the desired signal from brain activity. BSS, however, can be used to separate the two so an accurate representation of brain activity may be achieved.[
]
Music
Another application is the separation of music
Music is generally defined as the The arts, art of arranging sound to create some combination of Musical form, form, harmony, melody, rhythm or otherwise Musical expression, expressive content. Exact definition of music, definitions of mu ...
al signals. For a stereo mix of relatively simple signals it is now possible to make a fairly accurate separation, although some artifacts remain.
Others
Other applications:[
* Communications
* Stock Prediction
* Seismic Monitoring
* Text Document Analysis
]
Mathematical representation
The set of individual source signals, , is 'mixed' using a matrix, , to produce a set of 'mixed' signals, , as follows. Usually, is equal to . If , then the system of equations is overdetermined and thus can be unmixed using a conventional linear method. If , the system is underdetermined and a non-linear method must be employed to recover the unmixed signals. The signals themselves can be multidimensional.
The above equation is effectively 'inverted' as follows. Blind source separation separates the set of mixed signals, , through the determination of an 'unmixing' matrix, , to 'recover' an approximation of the original signals, .[Aapo Hyvarinen, Juha Karhunen, and Erkki Oja. “Independent Component Analysis” https://www.cs.helsinki.fi/u/ahyvarin/papers/bookfinal_ICA.pdf pp. 147–148, pp. 410–411, pp. 441–442, p. 448]
Approaches
Since the chief difficulty of the problem is its underdetermination, methods for blind source separation generally seek to narrow the set of possible solutions in a way that is unlikely to exclude the desired solution. In one approach, exemplified by principal and independent
Independent or Independents may refer to:
Arts, entertainment, and media Artist groups
* Independents (artist group), a group of modernist painters based in the New Hope, Pennsylvania, area of the United States during the early 1930s
* Independe ...
component analysis, one seeks source signals that are minimally correlated
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statisti ...
or maximally independent
Independent or Independents may refer to:
Arts, entertainment, and media Artist groups
* Independents (artist group), a group of modernist painters based in the New Hope, Pennsylvania, area of the United States during the early 1930s
* Independe ...
in a probabilistic or information-theoretic sense. A second approach, exemplified by nonnegative matrix factorization, is to impose structural constraints on the source signals. These structural constraints may be derived from a generative model of the signal, but are more commonly heuristics justified by good empirical performance. A common theme in the second approach is to impose some kind of low-complexity constraint on the signal, such as sparsity in some basis for the signal space. This approach can be particularly effective if one requires not the whole signal, but merely its most salient features.
Methods
There are different methods of blind signal separation:
* Principal components analysis
Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and ...
* Singular value decomposition
In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any \ m \times n\ matrix. It is r ...
* Independent component analysis[Shlens, Jonathon. "A tutorial on independent component analysis." ]
* Dependent component analysis
* Non-negative matrix factorization
* Low-complexity coding and decoding
* Stationary subspace analysis
* Common spatial pattern
See also
* Adaptive filtering
An adaptive filter is a system with a linear filter that has a transfer function controlled by variable parameters and a means to adjust those parameters according to an optimization algorithm. Because of the complexity of the optimization algorit ...
* Celemony Software#Direct Note Access
* Colin Cherry
Edward Colin Cherry (23 June 1914 – 23 November 1979) was a British cognitive scientist whose main contributions were in focused auditory attention, specifically the cocktail party problem regarding the capacity to follow one conversati ...
* Deconvolution
* Factorial codes
* Infomax principle Infomax is an optimization principle for artificial neural networks and other information processing systems. It prescribes that a function that maps a set of input values ''I'' to a set of output values ''O'' should be chosen or learned so as to m ...
* Segmentation (image processing)
* Speech segmentation
References
External links
Explanation of Independent Component Analysis (ICA)
A tutorial-style dissertation by Volker Koch that introduces message-passing on factor graphs to decompose EMG signals
Blind source separation flash presentation
Removing electroencephalographic artifacts by blind source separation
{{DEFAULTSORT:Source Separation
Digital signal processing
Speech processing
de:Cocktail-Party-Effekt