Application of nonlinear Wavelet Denoising

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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

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Outline

• Introduction to neuroscience
• Latency corrected wavelet filtering
• Adaptive wavelet filtering

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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).

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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).
• Its worth noting that as the P300 is a
  particularly large component, it lends itself to
  single-trial analysis.

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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.

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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.

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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).

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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.

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Averages of ERP in time domain
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• Latency Corrected Wavelet Filtering of the P300
  Component in ERPs

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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.

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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.
Averages of latency corrected ERPS
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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.

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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).

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Frequency ranges corresponding to 6 levels of
decomposition
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Averaged Latency Corrected Wavelet Coefficients
(LCWC)

• a) Average LCWC of ERPs for old group. b) Average
  LCWC of ERPs for young group

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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.

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Thresholded average Latency Corrected Wavelet
Coefficients (LCWC)
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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.

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Single-trial plots
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Average plots
Wilcoxon tests verified the statistical
significance of P300 peak amplitude differences
(plt0.0003) 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
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Adaptive wavelet filtering of the P300
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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
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Representation of the signal in the wavelet domain

• Wavelet coefficient of single-trial epoch

• Original single-trial epoch

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Wavelet decomposition of single-trial with
Daubechies wavelet
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Filtering in delta band

• Finding the peak amplitude.
• Finding two minimums that surrounds the peak
  amplitude.

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• Setting the boundaries for theta band

Delta band
Theta band
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• Filtering the theta band

Calculate 80 of the total energy with in the
selected time interval in theta band.
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• Setting the boundaries in alpha band

Theta band
Alpha band
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Calculate 50 of the total energy with in the
selected time interval
Filtering the theta band
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Original, Filtered and Smoothed Single-Trial ERP
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Averages of ERP After filtering
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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.

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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

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• Thank you!