FILTER OUT HIGH FREQUENCY NOISE IN EEG DATA

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 Max. Ent 2007, Saratoga Springs, NY 07/11/2007

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

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

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

• The invasive EEG Records intracellular electric field potentials within 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 within neurons?

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.

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

• 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

• Some smoothing functions MFS 3 0. 33 0 0 FNS 3(1 0. 5 0. 25 0 0 ) FNS 3(2 0. 43 0. 29 0 0 )RS 0. 54 0. 23 0 0 3 FNS 5 0. 34 0. 24 0. 09 0 FNS 7 0. 26 0. 21 0. 12 0. 04 – Approximated calculation For example, FNS 5 is obtained by substituting this set (3/10, 4/10, 3/10) into the same set (3/10, 4/10, 3/10)

• Two drawbacks – Second order derivative calculation via Ta 3(r) is a gross approximation. – Introduction of some ad hoc empirical guidance to reduce noise in data and noise amplified by operation of the Ta 3(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?

Maximum entropy approach for denoise • 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 denoise in EEG studies? 1. pl is symmetric around l=0,

2. Additional information

– The preferred pl Maximizing entropy subject to constraints

– In principle, the Lagrangian multiplier can be determined if expectation value d 2 is given Unfortunately, we have no information regarding d 2 – A solution: Minimizing noise variance For a noise

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

Variance of second order derivative with smoothed field potentials

• Smoothing noise amplified in operation of second order derivative calculation – Minimizing variance of second order derivative with smoothed field potentials MES 3 Ta 3 0. 42 0. 28 0 0 MES 5 Ta 3 0. 29 0. 23 0. 12 0 MES 7 Ta 3 0. 22 0. 19 0. 12 0. 06

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

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

• Noise analysis – Variance analysis – K-value analysis CDS 2(Xs 2 ) K MFS 3 Ta 3 0. 44 1. 33 FNS 3 Ta 3(1) 0. 38 1. 01 FNS 3 Ta 3 (2) 0. 28 1. 13 RS 3 Ta 3 0. 57 1. 34 MES 3 Ta 3 0. 28 1. 14 FNS 5 Ta 3 0. 073 0. 63 MES 5 Ta 3 0. 048 0. 48 FNS 7 Ta 3 0. 019 0. 39 MES 7 Ta 3 0. 014 0. 27

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.

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

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