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Source separation, blind signal separation (BSS) or blind source separation, is the separation of a set of source
signals A signal is both the process and the result of Signal transmission, transmission of data over some transmission media, media accomplished by embedding some variation. Signals are important in multiple subject fields including signal processin ...
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 are a ...
and involves the analysis of mixtures of
signals A signal is both the process and the result of Signal transmission, transmission of data over some transmission media, media accomplished by embedding some variation. Signals are important in multiple subject fields including signal processin ...
; 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 A cocktail party is a party at which cocktails are served. It is sometimes called a cocktail reception. A cocktail party organized for purposes of social or business networking is called a mixer. Some events, such as wedding receptions, are ...
), 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 and
tensors In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other ...
, 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 Linear map, linear dimensionality reduction technique with applications in exploratory data analysis, visualization and Data Preprocessing, data preprocessing. The data is linear map, linearly transformed ...
and
independent component analysis In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate statistics, multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and ...
, 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 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 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.


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 using Python and the Shogun toolbox using Joint Approximation Diagonalization of Eigen-matrices (
JADE Jade is an umbrella term for two different types of decorative rocks used for jewelry or Ornament (art), ornaments. Jade is often referred to by either of two different silicate mineral names: nephrite (a silicate of calcium and magnesium in t ...
) algorithm which is based on
independent component analysis In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate statistics, multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and ...
, 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 Medical imaging is the technique and process of imaging the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology). Medical imaging seeks to revea ...
of the brain with
magnetoencephalography Magnetoencephalography (MEG) is a functional neuroimaging technique for mapping brain activity by recording magnetic fields produced by electric current, electrical currents occurring naturally in the human brain, brain, using very sensitive magn ...
(MEG). This kind of imaging involves careful measurements of
magnetic field A magnetic field (sometimes called B-field) is a physical 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 ...
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) is a physical field, varying in space and time, that represents the electric and magnetic influences generated by and acting upon electric charges. The field at any point in space and time can be regarde ...
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 Electroencephalography (EEG) is a method to record an electrogram of the spontaneous electrical activity of the brain. The bio signals detected by EEG have been shown to represent the postsynaptic potentials of pyramidal neurons in the neoc ...
(EEG) and
magnetoencephalography Magnetoencephalography (MEG) is a functional neuroimaging technique for mapping brain activity by recording magnetic fields produced by electric current, electrical currents occurring naturally in the human brain, brain, using very sensitive magn ...
(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 the arrangement of sound to create some combination of Musical form, form, harmony, melody, rhythm, or otherwise Musical expression, expressive content. Music is generally agreed to be a cultural universal that is present in all hum ...
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, s(t) = (s_1(t), \dots, s_n(t))^T, is 'mixed' using a matrix, A= _\in \mathbb^, to produce a set of 'mixed' signals, x(t)=(x_1(t), \dots, x_m(t))^T , as follows. Usually, n is equal to m. If m > n, then the system of equations is overdetermined and thus can be unmixed using a conventional linear method. If n > m, the system is underdetermined and a non-linear method must be employed to recover the unmixed signals. The signals themselves can be multidimensional. x(t) = A\cdot s(t) The above equation is effectively 'inverted' as follows. Blind source separation separates the set of mixed signals, x(t) , through the determination of an 'unmixing' matrix, B = _\in \mathbb^, to 'recover' an approximation of the original signals, y(t) = (y_1(t), \dots, y_n(t))^T.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 y(t) = B\cdot x(t)


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 Pennsylvania, United States * Independentes (English: Independents), a Portuguese artist ...
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 statistic ...
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 Pennsylvania, United States * Independentes (English: Independents), a Portuguese artist ...
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 Linear map, linear dimensionality reduction technique with applications in exploratory data analysis, visualization and Data Preprocessing, data preprocessing. The data is linear map, linearly transformed ...
*
Singular value decomposition In linear algebra, the singular value decomposition (SVD) is a Matrix decomposition, factorization of a real number, real or complex number, complex matrix (mathematics), matrix into a rotation, followed by a rescaling followed by another rota ...
*
Independent component analysis In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate statistics, multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and ...
P. Comon and C. Jutten (editors). “Handbook of Blind Source Separation, Independent Component Analysis and Applications” Academic Press, Shlens, Jonathon. "A tutorial on independent component analysis." * Dependent component analysis *
Non-negative matrix factorization Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix is factorized into (usually) two matrices and , with the property th ...
* Low-complexity coding and decoding * Stationary subspace analysis * Common spatial pattern *
Canonical correlation analysis In statistics, canonical-correlation analysis (CCA), also called canonical variates analysis, is a way of inferring information from cross-covariance matrices. If we have two vectors ''X'' = (''X''1, ..., ''X'n'') and ''Y'' ...


See also

* Adaptive filtering * Celemony Software#Direct Note Access * Colin Cherry * Deconvolution *
Factorial code {{Short description, Data representation for machine learning Most real world data sets consist of data vectors whose individual components are not statistically independent. In other words, knowing the value of an element will provide information a ...
s * Infomax principle *
Segmentation (image processing) In digital image processing and computer vision, image segmentation is the process of partitioning a digital image into multiple image segments, also known as image regions or image objects ( sets of pixels). The goal of segmentation is to simpl ...
* 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