FILTER OUT HIGH FREQUENCY NOISE IN EEG DATA USING THE METHOD OF MAXIMUM ENTROPY

1. FILTER OUT HIGH FREQUENCY NOISE IN EEG DATA USING THE METHOD OF MAXIMUM ENTROPY Chih-Yuan Tseng Department of Physics National Central University Jhongli Taiwan ROC MaxEnt 2007, Saratoga Springs, NY 07/11/2007

2. Outline • The task • Source localization from neural electric field potentialswithin cortices • The current source density method • Two drawbacks • Maximum entropy approach for de-noise • Performance analysis • Conclusion

3. The task • Cerebral cortex (grey matter) • Physiologically, it can be classified into six layers • Information processing center

4. Neural electric field potential • Current source: Ionic currents flow from intracellular into extracellular. • Current sink: vice versa

5. The invasive EEG • Records intracellular electric field potentialswithin six layers • Question: • How does one infer current sources and sinks of the electric field potentials from EEG measurements that allows one to study information processing withinneurons?

6. The current source density method • Localizing current source and sink from the field potential analysis • In 1975, Freeman and Nicholson proposed a current source density (CSD) method, which becomes a standard tool in neuroscience until now.

7. Field potential Current source and sink • Basic idea • According to continuity equation and Ohm’s law • Suppose electric conductivity is isotropic and homogeneous in cortices

8. Approximated calculation for current source and sink from a set of discrete data • Second order derivative – Finite difference formula • Smoothing high frequency noise via non-recursive filter

9. For example, FNS5 is obtained by substituting this set (3/10,4/10, 3/10) into the same set (3/10,4/10, 3/10) MFS3 0.33 0.33 0 0 FNS3(1) 0.5 0.25 0 0 • Some smoothing functions FNS3(2) 0.43 0.29 0 0 RS3 0.54 0.23 0 0 FNS5 0.34 0.24 0.09 0 FNS7 0.26 0.21 0.12 0.04 • Approximated calculation

10. Two drawbacks • Second order derivative calculation via Ta3(r) is a gross approximation. • Introduction of some ad hoc empirical guidance to reduce noise in data and noise amplified by operation of the Ta3(r) • How does one raise accuracy of second order derivative calculation and keep noise small in the meantime? • Are these smoothing functions good enough for EEG analysis? • Is there a systematic and objective approach without introducing ad hoc rules for developing smoothing functions?

11. 1. pl is symmetric around l=0, Maximum entropy approach for de-noise • The method of maximum entropy: Tool for assigning probability distribution • What kind of information is relevant to the system? i.e. What are constraints? • Basic idea for smoothing high frequency noise using the method of maximum entropy • What kind of information we need to know for de-noise in EEG studies?

12. 2. Additional information

13. The preferred pl Maximizing entropy subject to constraints

14. In principle, the Lagrangian multiplier can be determined if expectation value d2 is given Unfortunately, we have no information regarding d2 • A solution: Minimizing noise variance For a noise

15. The preferred a value is 0 Variance of smoothed field potentials Is this smoothing function good enough for our purpose?

16. Variance of second order derivative with smoothed field potentials

17. Smoothing noise amplified in operation of second order derivative calculation • Minimizing variance of second order derivative with smoothed field potentials

18. Performance analysis • Frequency analysis • For smoothing function, the transfer function: Suppose and substitute into

19. For second order derivative with smoothed data, the transfer function is given by

20. Noise analysis • Variance analysis • K-value analysis

21. Conclusions • We propose a maximum entropy approach to smooth noise in EEG studies without introducing any ad hoc rules • Two analyses shows the proposed ME smoothing functions to outperform conventional designs • One can easily extend the ME smoothing function for cases other than EEG studies with relevant information.

22. Acknowledgment: • This work is partially supported by National Science Council, Taiwan, ROC.

23. Thanks for your attention!!