Application of non-linear Wavelet De-noising Leila Ayoubian Markazi and L. K. Stergioulas Department of Information Systems, Computing and Mathematics Brunel University Summer School, Inzell, September 17-21,2007

Outline Introduction to neuroscience Latency corrected wavelet filtering Adaptive wavelet filtering

Introduction The Electroencephalogram (EEG) is a measurement of ongoing electrical activity of the brain. Recorded with multiple metal electrodes placed in different locations of the scalp. If EEG activity is recorded in relation to a specific stimulus, it is then referred to as Event Related Potentials (ERPs).

P300 One of the ERP components that is commonly investigated in behavioural neuroscience research . It occurs due to allocation of attention resources to stimulus followed by memory updating The P300, manifests itself as a positive voltage approximately 300 milliseconds after the stimulus. In cognition terms, P300 is considered to represent stimulus evaluation time (latency) and attention engagement (amplitude). It’s worth noting that as the P300 is a particularly large component, it lends itself to single-trial analysis.

Brain Oscillations Delta (0.5-3.5 Hz): Delta rhythms are associated with different pathologies as well as deep sleep phase and they usually carry large amplitudes. Evoked delta oscillations are assigned to signal estimation and decision making. Theta (3.5-7.5 Hz): Theta rhythms are associated to drowsiness and childhood and they increase during sleep. Evoked theta oscillations are linked with conscious awareness, attention, and memory retrieval . Alpha (7.5-12.5 Hz): Alpha rhythms are associated with relaxed, waking state with eyes closed. They do not have a specific function and it could be correlated to various cognitive processes among which memory, sensory and motor are considered the most important ones. Beta (12.5-30Hz): Beta rhythms with lower amplitude than alpha rhythms are enhanced with alertness, anxiety or active thinking.

The Problem Accurate recovery of non-stationary ERP signals which are embedded in background noise (EEG). Separation of ERP (signal) from background EEG (noise) is a a challenging task due to its low signal-to-noise (SNR) ratio. Amplitude and latency variabilities of ERP signals.

Why Wavelet? Time domain analysis, e.g. averaging (Not suitable for non- stationary signals, does not consider single-trial variability). Frequency domain analysis (Not suitable for non- stationary signals, does not consider single-trial variability) Time-frequency domain analysis, e.g. STFT and Wigner (Suitable for non- stationary signals, but still does not consider single-trial variability) Statistical methods Time-scale domain analysis, e.g. wavelet (Variably-sized regions for the windowing operation which adjust to signal components).

Data Collection EEG data were recorded on a 32 channel BioSemi Active II system at a sampling frequency of 512 Hz. 28 subjects, 15 young adults and 13 older adults. A two-choice reaction time task. The EEG data was segmented (epoched) at -200 to 900ms. The correct artifact-free trials were then subjected to single-trial analysis.

Averages of ERP in time domain

Latency Corrected Wavelet Filtering of the P300 Component in ERPs

Step1: Application of Latency corrected filter The Latency Corrected (LC) filter is a time-domain iterative filter. It estimates the latency of the component of interest with respect to the peak amplitude of the P300 for every single-trial epoch. It then employs the calculated latency to align the component. The iterated ERPs are then averaged together in two distinct groups of young and old.

Averages of latency corrected ERPS b c a) Average of LC ERPs for old group. b) Average of LC ERPs for young group. c) Average of LC ERPs for both old and young groups.

Step2: Application of wavelet transform Discrete wavelet transform (DWT) using a Daubechies 4 wavelet . The original ERP signal is decomposed into different levels of high frequency components or details (D1-D6) and low frequency components or approximation (A1-A6). The levels of decompositions are chosen in such a way that the resulting frequency ranges correlates with the EEG rhythms: delta, theta, alpha and beta Reconstruction is performed by adding up ; S= A6+ D6+ D5+ D4+ D3+ D2+ D1.

Why Daubechies? Compact support: The compact support not only speeds up the calculation of coefficient but also allows the wavelet transformation to efficiently detect localized features in a signal. Arbitrary regularity (smoothness) and asymmetry: The regularity increases with the order resulting in smoother wavelet. The asymmetry property of Daubechies matches the irregular shape of ERPs. Orthogonality: Orthogonality provides conciseness and speed in calculation which found its application in data compression. Similarity: One criteria to choose a wavelet basis function is the similarity with the original signal, in this case ERPs. High level of correlation between reconstructed wavelet coefficients and ERPs (Wilson, 2004).

Frequency ranges corresponding to 6 levels of decomposition Decomposed Signal Frequency Range (Hz) cD1 125-250 cD2 62.5-125 cD3 31.25-62.5 cD4 15.625-31.25 (beta band) cD5 7.8125-15.625 (alpha band) cD6 3.9063-7.8125 (theta band) cA6 0-3.9063 (delta band)

Averaged Latency Corrected Wavelet Coefficients (LCWC) b a) Average LCWC of ERPs for old group. b) Average LCWC of ERPs for young group

Step3: Thresholding Application of hard thresholding algorithm. (Soft thresholding results in shrinking of the amplitude of LCWC). The threshold algorithm starts by selecting a value based on median of the averaged LCWC. The hard thresholding algorithm sets any coefficients less than or equal to the threshold value to zero, and keeps the value of the signal for those coefficients above the threshold value.

Thresholded average Latency Corrected Wavelet Coefficients (LCWC)

Step4: Mask generation In order to produce a non-biased mask for filtering purposes, the derived masks are combined by means of a “logical disjunction” operation. This generates a single mask, which is however patchy and discontinuous at places. To produce a uniform global mask, the smoothed version is produced.

Single-trial plots

Average plots Wilcoxon tests verified the statistical significance of P300 peak amplitude differences (p<0.0003) between the two age groups (old and young). a) Average LC and averaged filtered LCWC of ERPs for the old group. b) Average LC and averaged filtered LCWC of ERPs for the young group

Adaptive wavelet filtering of the P300

Processing stages of adaptive wavelet filtering Representation of the signal in the wavelet domain Signal in noise (time domain) Design and application of a filtering function to the wavelet coefficients of the signal Reconstruction of the filtered signal in the time domain

Representation of the signal in the wavelet domain Original single-trial epoch Wavelet coefficient of single-trial epoch

Wavelet decomposition of single-trial with Daubechies wavelet

Filtering in delta band Finding the peak amplitude. Finding two minimums that surrounds the peak amplitude.

Setting the boundaries for theta band Delta band Theta band

Filtering the theta band Calculate 80% of the total energy with in the selected time interval in theta band.

Setting the boundaries in alpha band Theta band Alpha band

Calculate 50% of the total energy with in the selected time interval Filtering the theta band Calculate 50% of the total energy with in the selected time interval

Original, Filtered and Smoothed Single-Trial ERP

Averages of ERP After filtering

Conclusion Oscillatory time-variant transient features in the brain are detected. Distinct functional components of P300 are extracted. Cleaner and more informative P300 components were achieved.

Related Publication S. Ayoubian, L. K. Stergioulas , S. Qazi, Anusha Ramchurn, & David Bunce “Wavelet Filtering of theP300 Component in Event-related Potentials” , 27th Annual Inter-national Conference of the IEEE Engineering in Medicine and Biology Society, New York, Aug 28- Sep3, 2006 S. Ayoubian, L. K. Stergioulas, Anusha Ramchurn, & David Bunce, “Latency Corrected Wavelet Filtering of the P300 Event-Related Potential in Young and Old Adults” , 3rd International Conference IEEE EMBS on Neural Engineering in Medicine and Biology Society, Hawaii, May 2- 5, 2007

Thank you!