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8/3/2019 Blind Source Separation of Convolutive Mixture
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BLIND SOURCE SEPARATION OF
CONVOLUTIVE MIXTURE
Guided By Presented By
Er. Manorama Swain Indu sekhar samanta
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Motivation for work
Introduction
Blind source separation
Independent component analysisFuture work
Conclusion
References
Outlines
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Motivation For Work
Blind source separation is receiving a growing
interest due to its applications in diverse fields such
as array processing,multi user communications, etc.
While most of the work has been developed in thecontext of instantaneous mixtures, the more
difficult problem of convolutive mixtures has
received less attention.
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INTRODUCTION
It is a well-established statistical signal processing technique that aims at
decomposing a set of multivariate signals into a base of signals as
statistically independent/ uncorrelated as possible, with the minimal loss
of information content.
The BSS problem arises in many fields of studies, including speech
processing, data communication, biomedical signal, and the mixing and
filtering processes of the unknown input sources.
An extensive part of the literature has been directed toward the simple
case of linear instantaneous mixing; when the observed signals are a
linear combination of the sources and no time-delays are involved in the
mixing model.
A more challenging case is when the mixing system is linear convolutive;
i.e., when the sources are mixed through a linear filtering operation and
the observed signals are linear combinations of the sources and their
corresponding delayed versions.
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BLIND SOURCE SEPARATION
Blind source separation (BSS) refers to the problem of
recovering signals from several observed Linear mixtures.
The strength of the BSS model is that only mutual statistical
independence between the source signals is assumed and not
a priori information about, e.g., the characteristics of the
source signals, the mixing matrix or the arrangement of thesensors is needed.
Therefore BSS can be applied to a variety of situations such as,
e.g., the separation of simultaneous speakers, analysis of
biomedical signals obtained by EEG or in wirelesstelecommunications to separate several received .
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Cont
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Cont..
With respect to audio signals, a linear mixture of sources is commonlyreferred to as "cocktail Party problem".
How can humans select the voice of a particular speaker from anensemble of different voices corrupted by music and noise in thebackground?
One approach to solve this problem is to record the mixed audio signals
with microphone arrays and subsequently apply blind source separationmethods . Several simultaneously active signal sources at different spatiallocations can then be separated by exploiting mutual independence of thesources.
In the field of audio processing BSS is applicable, e.g., to the realization ofnoise robust speech, recognition, high-quality hands-free
telecommunication systems or speech enhancement in hearing aids. Because temporal redundancies (statistical regularities in the time
domain) are "clumped "in this way into the resulting signals , the resultingsignals can be more effectively deconvolved than the original signals.
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An illustration of BSS using four source
signals
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Linear mixtures of the source signals due to
some external circumstances..
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Estimates of the source signals..
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INDEPENDENT COMPONENT
ANALYSIS
Independent component analysis (ICA) belongs to a
class of blind source separation method for separating
data into underlying components , where such data can
take the form of images, sounds, telecommunication
channels or stock market prices .
It is a computational method for separating a
multivariate signal into additive subcomponents
supposing the mutual statistical independence of thenon-Gaussian source signals . It is a special case of blind
source separation.
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Cont..
ICA defines a generative model for the observed
multivariate data, which is typically given as a Large data
base of samples. In the model, the data variables are
assumed to be linear mixtures of some unknown latentvariables, and the mixing system is also unknown.
The latent variables are assumed non gaussian and
mutually independent , and they are called the
independent components of the observed data. Theseindependent components, also called sources or factors,
can be found by ICA
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Cont
ICA is superficially related to principal component analysis andfactor analysis.ICA is a much more powerful technique ,
however , capable of finding the underlying factors or sources
when these classic methods fail completely.
The data analyzed by ICA could originate from many different
kinds of application fields , including digital images ,document
data bases , economic indicators and psychometric
measurements . In many cases ,the measurements are given
as a set of parallel signals or time series ; the term blind
source separation is used to characterize this problem.
Typical examples are mixtures of simultaneous speech signals
that have been picked up by several microphones, brain
waves recorded by multiple sensors , interfering radio signals
arriving at a mobile.
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Cont.
When the independence assumption is correct, blind ICA
separation of a mixed signal gives very good results. It isalso used for signals that are not supposed to begenerated by a mixing for analysis purposes. A simpleapplication of ICA is the cocktail party problem, wherethe underlying speech signals are separated from a sample
data consisting of people talking simultaneously in a room.Usually the problem is simplified by assuming no timedelays and echoes. An important note to consider is that ifN sources are present, at least N observations 13
(e.g. microphones) are needed to get the original signals.
This constitutes the square (J = D, where D is the inputdimension of the data and J is the dimension of themodel). Other cases of underdetermined (J < D) andoverdetermined (J > D) have been investigated.
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Non-Gaussianity, motivated by the central limit theorem, is onemethod for measuring the independence of the components. Non-Gaussianity can be measured, for instance, by kurtosis orapproximations of entropy. Mutual information is another popularcriterion for measuring statistical independence of signals.
x(t)= As(t) .(1)
y(t)= Wx(t) ...(2)
ICA goal is finding a linear transform given by matrix W so that
the Output y(t) is the copy or estimate of source signal s(t):
In which s(t)=[s1, s2, ...sn] is a 1xn vector
composed by n source signals, x(t)=[ x1, x2,.xn]T
is a (nx1) vector composed of n measuring signals and the (nxn) matrixA is called as mixture matrix.
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