Digital Signal Processing Reference
In-Depth Information
Based on the discussed criteria, we presented some well-established algo-
rithms to perform ICA: Hérault-Jutten, Infomax algorithm, the nonlinear
PCA, JADE, EASI, and the FastICA algorithm.
It was also important to present some alternative paths toward solving
the BSS problem, as the incorporation of a priori knowledge of multiple
natures. In this sense, we presented BSS methods exploring the fact that
the power spectral densities of the sources are mutually distinct. Two other
important methods we showed were those based on nonnegativity (nonneg-
ative ICA) and sparsity (SCA) properties of the source signals. The Bayesian
approach was also discussed.
Finally, we considered two extensions of the linear and instantaneous
model: convolutive mixtures and nonlinear mixtures. To deal with the first
one, can employ methods derived from the linear and instantaneous case,
as long as we take into account the so-called filtering indeterminacy, which
generally requires additional information about the original sources. Meth-
ods for convolutive source separation in both time and frequency domains
were discussed. Concerning nonlinear mixtures, we discussed limitations of
nonlinear ICA and introduced the so-called PNL model, which allows the
efficient use of certain separation approaches, like those based on mutual
information minimization and on Gaussianization.
It is worth emphasizing that source separation is a theme that places itself
at the intersection of many science and engineering disciplines and applica-
tions. For this reason, different and rather rich standpoints about theoretical
and practical aspects are available in the existing literature. In particular,
important works like [12, 76, 137, 148, 156] must be considered in order to
attain a more complete view on the subject. Our purpose in this chapter
is signal processing oriented, and aims to show BSS as an essential area
in unsupervised signal processing theory, as well as to put together, in a
synthetic way, a number of definitions, criteria, and algorithms that can be
useful in the study and/or research of different kinds of readers.
