Blind Source Separation of Convolutive Mixture

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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Cont.


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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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Blind Source Separation of Convolutive Mixture