40120130406002

International Journal of Electronics and JOURNALEngineering & Technology (IJECET), ISSN 0976 –
INTERNATIONAL Communication OF ELECTRONICS AND
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November-December (2013), © IAEME

COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)

ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 4, Issue 6, November-December, 2013, pp. 14-20
© IAEME: www.iaeme.com/ijecet.asp
Journal Impact Factor (2013): 5.8896 (Calculated by GISI)
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IJECET
©IAEME

EFFICIENT ALGORITHM BASED ON BLIND SOURCE SEPARATION
INDEPENDENT COMPONENT ANALYSIS USING MATLAB
Nishant Tripathi1 and Dr. Anil Kumar Sharma2
M. Tech. Scholar1, Professor & Principal2,
Department of Electronics & Comm. Engg. Institute of Engineering & Technology, Alwar-301030
(Raj.), India

ABSTRACT
Independent component analysis is a lively field of research and is being utilized for its
potential in statistically independent separation of images. ICA based algorithms has been used to
extract interference and mixed images and a very rapid developed statistical method during last few
years. So, in this paper an efficient result oriented algorithm for ICA-based blind source separation
has been presented. In blind source separation primary goal is to recover all original images using the
observed mixtures only. Independent Component Analysis (ICA) is based on higher order statistics
aiming at penetrating for the components in the mixed signals that are statistically as independent
from each other as achievable.
Keywords: ICA, Mixer Signal, Blind Source Separation, PSNR.
1. INTRODUCTION
Blind source separation is a technique that extracts the original signals from the mixture.
Such kind of technique find their unique application in the area of image processing, satellite
navigation of different object locating, mixed object image separation and several more biomedical
and neural networking areas. BSS-ICA can find a potential application in separating individual
images from a mixed noisy picture with knowing the actual proportion of their mixtures. The ICA
algorithm is based on the iteration to come across for the greatest of the non-gaussianity of variables.
This paper is structured in the subsequent sections: Initially a brief introduction of ICA is provided in
section I. Later on in section II, the basic algorithm is introduced which performs ICA by maximize
the non Gaussianity of the signal components. In Section III, the simulation results for noisy mixed
images separation using the algorithm have been shown.

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International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –

2. PRINCIPLES OF ICA
ICA is a method of performing blind signal separation that aims to pick up unknown sources
from a set of the experimental values, in which they are mixed in an unfamiliar manner. In
fundamental ICA model, the pragmatic mixture signals x (t) can be expressed as;
x (t) = As(t)

(1)

where A is an unknown mixing matrix, and s (t) represents the latent source signals which is
supposed to be statistically equally independent. The ICA model describes an additive noise vector n
(t) , and gives a more sensible, broad ICA model in the noising case:
x (t) = As (t) + n (t)

(2)

The independent components s(t) cannot be directly observed and the mixing coefficients A
and the noise n (t) is also assumed to be unknown. If noise is negligible, only the random variables
x(t) is observed and both the components s(t) and the coefficients A must be estimated using x(t)
.Then, the ICA solution is obtained in an unsupervised way that finds a de-mixing matrix C. The de
mixing matrix W is used to transform the observed mixture signals x (t) to give the independent
signals. That is:
sˆ (t) = Cx(t)

(3)

The signals sˆ (t) are the close estimation of the latent source signals s (t). If C = A-1, then the
recovered signals sˆ (t) are exactly the original sources s(t) . The components of sˆ (t), called
independent components, are required to be as mutually independent as possible. Some main
functions in ICA are;
•

•
•

Non-Gaussian Nature: The ICA is non-Gaussian in nature. In fact, without such a property
the close assessment is not possible at all. In most of conventional statistical theory, random
variables are assumed to have Gaussian distributions, so they don’t include and justify the
ICA.
Measures of non-Gaussianity: The non-Gaussian nature in ICA is measured effectively
through quantities analysis of the non Gaussianity of signal variables.
Kurtosis:The classical measure of non-Gaussianity is kurtosis or the fourth-order cumulate.
The kurtosis of y is classically defined by
Kurt(y) = E{x4} – 3(E{x2}) 2

(4)

Negentropy: Negentropy is also one of the most effective measures for non-Gaussian nature
of random variable. It is measured through information theoretic content in the variable.
3. PROPOSED ALGORTHEM
The proposed algorithm follows as:
• Pre-processing for ICA: It is quite essential and helpful to work on some pre-processing
on the available data. In this section, we talk about some pre-processing techniques that
make the difficulty of ICA estimation simpler and improved accustomed.
• Centering: It is generally the essential and compulsory pre-processing, which is used to
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•

•

•

center the” x”, i.e. subtract its mean vector m. E{x} so as to make x a zero-mean variable.
This implies that input signal is zero-mean as well, as can be seen by taking expectations
on both sides of vector–matrix notation.
Whitening: It is an additional helpful pre-processing technique in ICA which is used to
first whiten the observed variables. This means that before the application of the ICA
algorithm (and after centering), we transform the observed vector x linearly so that we
obtain a new vector x which is white, i.e. its components are uncorrelated and their
variances is equal to unity.
Further preprocessing: The accomplishment of ICA for a specified data set may depend
very much on performing some application-dependent pre-processing steps. For example,
if the data consists of time-signals, some band-pass filtering may be very useful.
ICA Algorithm: Using the fixed point algorithm with the contrast function and fixing the
norm of the weights to one, the algorithm for the already sphered data, is:
w+ = E{xg(wTx)}- E{g’(wTx)}c

(5)

w = w+/ w

(6)

+

;

Where w* is a column vector with the estimation of one line of the matrix W. The algorithm
can be directly applied to themixed data X (usually not sphere):
W+=C-1E{Xg(WTX)}–E{g’(WTX)}W

(7)

W*=W+/W+T CW+

(8)

Where c = E {XXT} is the covariance matrix of the mixed data. This algorithm gives one
weight vector and thus only one independent component. The other components can be obtained
using deflation. Fig. 1 shows the flowchart for ICA based Algorithm. This is the shortest iteration to
achieve non-guassianity

Fig. 1 Flowchart for the ICA based algorithm
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The basic steps for algorithms are as follows:
(i)

Initialize the weight vector w (with random values);

(ii)

Let w+ = E {xg (wT x)} - E {g’ (wT x)} w …,
where g is the derivative of G

(iii)

Let w = w+ / ||w+ ||;

(iv)

If not converged, return to step 2.

This process is known as a one-unit learning algorithm. The above algorithm is only designed
to estimate one of the independent components to compute a matrix W without giving first choice to
any fussy independent component, the next algorithm may be added to the end of each iteration of
the above algorithm. Thus we obtain the algorithm as follows:
(1)

Center the data to make its mean zero;

(2)

Whiten the data to get xˆ(t) ;

(3)

Make i=1;

(4)

Choose an initial orthogonal matrix for W and make k=1;

(5)

Make wi (k) = [ (wi(k-1)T)3] - 3wi(k-1)

(6)

Make wi (k) = wi(k)/ wi(k)

(7)

If not converged, make k=k+1 and go back to step (5)

(8)

Make i=i+1.

(9)

When i<number of original signals, go back tostep (4).

4. RESULT AND ANALYSIS
We simulate the system with independent sources of different kurtosis values. These
basesstood normalized to have aentity variance and were mixed according to signal model. In
simulation result signals are producedarbitrarily and mixing process in MATLAB has been done.
The separated signal is recuperated using ICA algorithm. We have carefully chosen several different
merging combination of 5 different images to provide different sample of proportionate mixture of
mixed images and then has calculated the PSNR of original and ICA separated individual images
before mixing and and after de-mixing respectively. Thus algorithm performance analysis has been
described in figures (2-6) and comparison result related to PSNR is described in table-1.The peaksignal-to-noise ratio (PSNR), between the original image X and the mixed or separated image Y, is
calculated using Eqn. (9) and (10).
PSNR = 10 log ((M*N)2)/MSE
MSE = 1/MN ΣMi=1ΣNi=1 (Y(i,j) – X(i,j))2

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(9)
(10)


Fig. 2: Sample Numer.1





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TABLE.1: COMPARISON BETWEEN ORIGINAL IMAGE PSNR AND ICA EXTRACTED PSNR
Sample
Image
Original
Recovered
S. No
No.
Name
PSNR(Db)
PSNR(Db)
Bank
27.24
28.25
Cam1
25.93
21.22
1
Fig.1
Cam2
27.22
19.11
Bank
28.12
27.99
Cam1
27.62
25.45
2
Fig.2
Lena
25.32
25.88
Monk
27.97
22.34
Cam1
25.26
23.11
3
Fig.3
Bank
27.26
26.22
Cam2
27.41
26.2
Lena
28.24
27.11
4
Fig.4
Bank
27.69
26.33
Cam1
28.111
22.01
5
Fig.5
Monk
26.67
23.101
Lena
27.11
24.022

5. CONCLUSION
This paper proposes a short iterative efficient algorithm based blind source separation using
Independent component Analysis in MATLAB environment. This method is proposed to have
independent component analysis to separate mixed images. The simulation results showed that the
algorithm can blindly separate the original images from the mixed images with good accuracy.
However, this paper just does some elementary research under the basic noise-free ICA model. In
practice, we need to process many contaminated images, as they contain much unknown noise,
problem like this make it necessary for us to extend the basic framework of ICA during the process
of future research.
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