1. REAL-TIME INDEPENDENT COMPONENT ANALYSIS IMPLEMENTATION AND APPLICATIONS By MARCOS DE AZAMBUJA TURQUETI turqueti@fnal.gov FERMILAB May 2010 1RTC 2010

2. What is it? 2RTC 2010 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.

3. ICA Applications 3RTC 2010 RADAR A wide variety of systems can make use of ICA algorithms; CCD signal processingSONAR PIXEL detectorsMedical ultrasonography Positron Emissions Scan machines

4. Assumptions 4RTC 2010 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.

5. 5RTC 2010 ICA Preprocessing Centering Whitening High pass filter Measure Gaussianity Compute weight vector Correlation filter ICA Algorithm Post Processing Algorithm Application Preprocessing Redundancy Elimination Converged? Yes No Algorithm implementation J (Y) = H(Y gauss ) - H(Y) cov( X Y )= I differential entropy (negentropy) D n = J(y n )-J(y n-1 ) X= W T Y population correlation coefficient sample correlation coefficient make input variables zero mean

6. 6RTC 2010 A B M1M2 Algorithm simulation Linear combination

7. Whitening of the signal (decorrelating) 7RTC 2010 cov( X Y )= I Joint probability distribution of the mix signals before and after whitening. Mix signals

8. CAPTAN Network Compatible Hardware 8RTC 2010 Minimizing Gaussianity by rotating the axis and using Negentrophy to have a indication of Gaussianity. Joint probability distribution of the whiten signal and ICA output. X= W T Y J (Y) = H(Y gauss ) - H(Y)

9. Recovered signal 9RTC 2010 Original signalRecovered signal

10. Hardware platform for ICA implementation 10RTC 2010 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

11. RTC 201011 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)

12. Real-time application example 12RTC 2010 Source separation can be used in many different applications such as: Video conference Cell phones Sonar Medical

13. Test I - Four Sine Waves Test 13RTC 2010

14. Test I - Results Two microphones fastICA results: Four microphones fastICA results: Four microphones fastICA/ AIIA results: 14RTC 2010

15. Test I - Results Fast ICA algorithm results: AIIA algorithm results: 15RTC 2010

16. Test II – Pelican x Chicken 16RTC 2010

17. Test II - Results Mix signals before fastICA:Signals after fastICA: Signals after fastICA (8 microphones):Signals after fastICA (12 microphones): 17RTC 2010

18. Test III – AK47 x Turbine (A) (B) Red – configuration 1 Green – configuration 2 (0.5 s delay) 18RTC 2010

19. Test III – Recovered Signals fastICA/AIIA Configuration 1 fastICA/AIIA Configuration 2 AK47 Turbine 19RTC 2010

20. Conclusion 20RTC 2010 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.

21. Thank you! 21RTC 2010