Blind Source separation (BSS) aims at estimating a set of source signals thanks to mixtures of these signals. The separation is said blind as we don’t know the mixture parameters and we try to estimate the sources by only knowing the observations. BSS is very up-to-date at present in signal processing because of the great number of applications for instance in acoustics, in telecommunications, in neurobiology or in astrophysics.
Apart from the classification between (over-)determined and the under-determined mixtures when the number of observations is greater than or equal to (resp. lower than) the number of sources, there exist different mixture models depending on the application and on the realism that we want to attain :
The linear instantaneous mixtures are the more simple. They consider that each observation is a sum of scaled versions of the source signals. If we assemble all the mixture coefficients in a matrix called mixture matrix, the problems deals with the identification of the inverse of this matrix up to a diagonal matrix and a permutation matrix.
The scaled and delayed mixtures are met when the source contributions are some scaled and delayed versions of the sources. This type of mixtures has been studied in our team and some time-frequency algorithms have been developed.
The convolutive mixtures are the most general linear ones but also the most complicated to separate. In this case the source contributions are some filtered version of the original sources.
The non-linear mixtures have been very few studied. Some particular classes of mixtures, for instance the post non-linear mixtures or the linear-quadratic mixtures have been dealed with however.
Blind Source Separation methods can be divided in three classes :
Independent Component Analysis (ICA) is a class of BSS methods which supposes that the source signals are independent from each other. Then we try to obtain output signals which are as independent as possible. One necessary condition to let the separation is non-Gaussianity : all the sources (except one eventually) must be non-Gaussian.
Sparse Component Analysis (SCA) supposes that the source signals have a sparse representation in the analysis domain (e.g. time-frequency or wavelet domains). The presence of a unique source in an atom or a "zone" of the analysis domain lets the identification of some mixture parameters.
Non-negative Matrix Factorization (NMF) supposes that the source and mixtures matrices are non-negative. We thus try to find two positive matrices whose product is equal to the observation matrix. This constraint is available for instance in astrophysics for blind separation of chemical species in interstellar dust clouds.
BSS algorithms developed in the team
Depending the cases, the following algorithms are available on-line under GPL license or CeCILL license so that you can download and modify them under the terms of the corresponding license.
The C-FICA algorithm is a time-domain convolutive extension of the famous FastICA algorithm which is very popular due to its simplicity of use and of its robustness. Our extension is available for convolutive mixtures which are the most general linear instantaneous mixtures.
The LI-TIFROM algorithm is a time-frequency BSS method for (underdetermined) linear instantaneous mixtures. It needs small sparsity hypothesis and is able to separate stationary, non-stationary and/or dependent sources.