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REAL-TIME INDEPENDENT COMPONENT ANALYSIS IMPLEMENTATION AND APPLICATIONS By MARCOS DE AZAMBUJA TURQUETI [email protected] FERMILAB May 2010. What is it?. - PowerPoint PPT Presentation
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RTC 2010 1
REAL-TIME INDEPENDENT COMPONENT ANALYSIS IMPLEMENTATION AND APPLICATIONS
By
MARCOS DE AZAMBUJA [email protected]
FERMILAB
May 2010
RTC 2010 2
What is it?
•Independent component analysis or ICA is a mathematical technique used for extracting hidden parameters that underlie in sets of random variables or signals.•ICA is a type of blind source separation
method and common inputs sources are signals originated from audio, images or telecommunications.
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ICA Applications
RADAR
• A wide variety of systems can make use of ICA algorithms;
CCD signal processing SONAR
PIXEL detectors Medical ultrasonography Positron Emissions Scan machines
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Assumptions
•This technique is based on the assumption that signals from different sources are statistically independent and non-Gaussian.
•At most one signal can be Gaussian otherwise this technique does not work.
•Information about magnitude of the signal is lost.
•ICA can provide redundant outputs.
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ICA
Prep
roce
ssin
g
Centering
Whitening
High pass filter
Measure Gaussianity
Compute weight vector
Correlation filter
ICA
Algo
rithm
Post
Pro
cess
ing
Algo
rithm
Application Preprocessing
RedundancyElimination
Converged?
Yes
No
Algorithm implementation
J (Y) = H(Ygauss) - H(Y)
cov( X Y )= I
differential entropy (negentropy)
Dn= J(yn)-J(yn-1)
X= WTY
population correlation coefficient
sample correlation coefficient
make input variables zero mean
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A B
M1 M20 10 20 30 40 50 60 70 80 90 100
-1
-0.5
0
0.5
1
A M
agni
tude
Signal A
0 10 20 30 40 50 60 70 80 90 100-1
-0.5
0
0.5
1
Sample number
B M
agni
tude
Signal B
0 10 20 30 40 50 60 70 80 90 100
-0.5
0
0.5
M1
Mag
nitu
de
Variable M1
0 10 20 30 40 50 60 70 80 90 100-1
-0.5
0
0.5
1
Sampe number
M2
Mag
nitu
de
Variable M2
Algorithm simulation
Linear combination
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Whitening of the signal (decorrelating)
Variable M1
Var
iabl
e M
2
Variable M1 x M2
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.40
50
100
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
050100 Variable W1
Var
iabl
e W
2
Data whiten
-4 -2 0 2 4 60
50
100
-5
-4
-3
-2
-1
0
1
2
3
4
050100
cov( X Y )= I
Joint probability distribution of the mix signals before and after whitening.
Mix signals
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CAPTAN Network Compatible Hardware
Signal A recovered
Sig
nal B
reco
vere
d
Signal AxB recovered
-0.6 -0.4 -0.2 0 0.2 0.40
100
200
-0.5
0
0.5
0100200
Minimizing Gaussianity by rotating the axis and using Negentrophy to have a indication of Gaussianity.
Variable W1
Var
iabl
e W
2 Data whiten
-4 -2 0 2 4 60
50
100
-5
-4
-3
-2
-1
0
1
2
3
4
050100
Joint probability distribution of the whiten signal and ICA output.
X= WTY
J (Y) = H(Ygauss) - H(Y)
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Recovered signal
0 10 20 30 40 50 60 70 80 90 100-2
-1
0
1
2
A M
agni
tude
Signal B recovered
0 10 20 30 40 50 60 70 80 90 100-2
-1
0
1
2
Sample numberB
Mag
nitu
de
Signal A recovered
0 10 20 30 40 50 60 70 80 90 100-1
-0.5
0
0.5
1
A M
agni
tude
Signal A
0 10 20 30 40 50 60 70 80 90 100-1
-0.5
0
0.5
1
Sample number
B M
agni
tude
Signal B
Original signal Recovered signal
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Hardware platform for ICA implementation
•Due to the large number of operations involving arrays this algorithm is proper to be implemented by multi-core vectorial processors. •FPGA’s are also specially suitable due to flexibility and parallelism capabilities.•On this work parallel FPGA’s are being used as hardware platform for the algorithm implementation.
CAPTAN System (FERMILAB) Sensor Array
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Implementation constrains• In order for the algorithm to converge fast a maximum number of interactions to maximize the non-Gaussianity is allowed;•This maximum number of interactions depends on several factors such as:
• The system speed;• Type of signals being input into the algorithm;• Number of mixed sources;• Amount of noise on the system; (Gaussian
source)
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Real-time application example
Source separation can be used in many different applications such as:
•Video conference•Cell phones•Sonar•Medical
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0 20 40 60 80 100 120 140 160 180 2001600
1800
2000Capture signals
Mag
nitu
de
0 20 40 60 80 100 120 140 160 180 2001000
2000
3000
Mag
nitu
de
0 20 40 60 80 100 120 140 160 180 2001600
1800
2000
Mag
nitu
de
0 20 40 60 80 100 120 140 160 180 2001500
2000
2500
Mag
nitu
de
0 20 40 60 80 100 120 140 160 180 2001700
1800
1900
Mag
nitu
de
Sample Number
Test I - Four Sine Waves Test
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Test I - Results
0 20 40 60 80 100 120 140 160 180 2000
1
2
3
4
5
0 20 40 60 80 100 120 140 160 180 200-1
0
1
2
3
4
Sample Number
0 20 40 60 80 100 120 140 160 180 200-5
0
5
0 20 40 60 80 100 120 140 160 180 200-10
0
10
0 20 40 60 80 100 120 140 160 180 200-5
0
5
0 20 40 60 80 100 120 140 160 180 2000
5
10
0 20 40 60 80 100 120 140 160 180 200-5
0
5
Sample Number
Two microphones fastICA results:
Four microphones fastICA results:
Four microphones fastICA/ AIIA results:
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Test I - Results
0 20 40 60 80 100 120 140 160 180 200-5
0
5
0 20 40 60 80 100 120 140 160 180 200-2
0
2
0 20 40 60 80 100 120 140 160 180 200-5
0
5
0 20 40 60 80 100 120 140 160 180 200-5
0
5
0 20 40 60 80 100 120 140 160 180 200-5
0
5
Sample Number
Fast ICA algorithm results: AIIA algorithm results:
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0 1 2 3 4 5 6 7 8 9 10
x 104
1000
1500
2000
2500Chicken
AD
C c
ount
s
0 2 4 6 8 10 12
x 104
0
1000
2000
3000Pelican
Sample number
AD
C c
ount
s
Test II – Pelican x Chicken
0 2 4 6 8 10 12
x 104
500
1000
1500
2000
2500
3000Chicken+Pelican
Sample number
AD
C c
ount
s
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0 2 4 6 8 10 12 14
x 104
-20
0
20
0 2 4 6 8 10 12 14
x 104
-10
0
10
Test II - Results
Mix signals before fastICA: Signals after fastICA:
Signals after fastICA (8 microphones):
0 2 4 6 8 10 12 14
x 104
-10
0
10
0 2 4 6 8 10 12 14
x 104
-20
0
20
Sample Number
Signals after fastICA (12 microphones):
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0 1 2 3 4 5 6 7 8 9
x 104
-1
-0.5
0
0.5
1AK47 Rifle
0 1 2 3 4 5 6 7 8 9
x 104
-1
-0.5
0
0.5
1A10 Aircraft
Sample Number
0 1 2 3 4 5 6 7 8 9
x 104
0
500
1000
1500AK47 Rifle
Mag
nitu
de
0 1 2 3 4 5 6 7 8 9
x 104
0
500
1000
1500A10 Aircraft
Sample Number
Mag
nitu
de
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 105
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
AD
C c
ount
s
Sample Number
Test III – AK47 x Turbine
(A)
(A)
(B)
(B)
Red – configuration 1Green – configuration 2 (0.5 s delay)
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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 105
-20
0
20
40
60
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 105
-30
-20
-10
0
Test III – Recovered Signals
0 0.5 1 1.5 2 2.5
x 105
-20
0
20
40
60
0 0.5 1 1.5 2 2.5
x 105
0
10
20
30
fastICA/AIIAConfiguration 1
fastICA/AIIAConfiguration 2
AK47
AK47
Turbine
Turbine
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Conclusion
•This work shows that it is possible to use the ICA algorithm on real-time applications;
•It also demonstrates the capabilities of the algorithm as well as its limitations;
•Currently the algorithm is being implemented for applications that demand faster convergence time.
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Thank you!