Digital Signal Processing Reference
In-Depth Information
Blind Sourc
e Separation
MIMO channels were studied in Chapter 5 as a general case of the blind
equalization problem. However, since we were dealing with digital commu-
nication channel, two hypotheses were implicitly presented: the transmitted
signals were modeled as a sequence of symbols from a finite alphabet and
these sequences were assumed to be i.i.d.
A more general scenario occurs when we discard the two aforemen-
tioned hypotheses and replace the idea of a MIMO transmission channel by a
generic MIMO system that engenders both mixture and distortion of a set of
input signals. The recovery of these original signals after the mixing process
constitutes the problem of source or signal separation and, similarly to the
equalization problem, we talk about
blind source separation
(BSS) when the
recovery is carried out by unsupervised methods.
Interest in source separation techniques has intensively grown from their
genesis in the beginning of the 1980s until nowadays. From a theoretical
standpoint, the general BSS problem remarkably captures the notion of infor-
mation extraction that, in a way, embodies the ensemble of methods and
tools considered in this topic. As a consequence, and from a more practi-
cal standpoint, source separation techniques are relevant in a great number
of applications. To mention a few, BSS is concerned with understand-
ing and extracting information from data as diverse as neuronal activities
and brain images, communications, audio, video, and sensor signals in
general.
A major tool to perform BSS is the so-called
independent component analy-
sis
(ICA), the relevance of which can be confirmed by the fact that ICA was
also the name of the most prestigious conference on source separation and
its applications, from its first version, in 1999, to its latest version in 2009.
Nevertheless signal or source separation involves not only ICA or blind tech-
niques, since semi-blind and factorization methods that make use of prior
information about the problem at hand must be considered in a number of
applications. This is reflected in the new name
latent variable analysis
(LVA),
used in the aforementioned conference in its ninth edition in 2010, which
emphasizes the general character of the problems in signal processing and
information extraction related to the theme.
The structure of this chapter is influenced by a general view on the
subject and by the idea of joining together key theoretical elements and
models of practical significance. Our aim is to present the theoretical
foundations of BSS together with some celebrated methods and algorithms
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