This document discusses a methodology for detecting action potentials (APs) in noisy neural recordings using unsupervised wavelet optimization. The methodology uses stationary wavelet transform for detection and discrete wavelet transform for clustering. It applies hard thresholding based on median absolute deviation, selects scales with maximum energy, sums and filters coefficients, and uses correlation similarity as a selection criteria to identify AP candidates. Results show the proposed method outperforms other detectors in terms of true positive rate at different signal-to-noise ratios and achieves improved spike sorting performance through unsupervised clustering based on shape similarity.

1. Automatic Detection of Action
Potentials in a Noisy Neural
Recording
I. Sadek, M. Elawady
Supervisor: Dr. Mathini Sellathurai
1B31XM Advanced Image Analysis

2. 2B31XM Advanced Image Analysis
Spike Detection and
Clustering With Unsupervised
Wavelet Optimization in
Extracellular Neural
Recordings
Vahid Shalchyan, Winnie
Jensen and Dario Farina
IEEE Trans. Biomed.
Engineering, 59(9):2576-2585,
2012.

3. Agenda
• Overview
• Related Work
• Methodology
• Results
• Conclusion
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4. Agenda
• Overview
• Related Work
• Methodology
• Results
• Conclusion
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5. Overview
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Action Potential (AP)
A series of changes result from applying an electric stimulation to excitable tissues
(i.e. nerves, all types of muscle).

6. Overview
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Problem Definition
The signals acquired from the microelectrodes are contaminated by background
noise
Noisy
Simulated APs
Filtered
Simulated APs

7. Agenda
• Overview
• Related Work
• Methodology
• Results
• Conclusion
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8. Related Work
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Methods Pros Cons
Amplitude Thresholding Low computational load
• Threshold selection for a tradeoff
between false negatives (FNs)
and false positives (FPs)
• Failed when spike amplitude are
close to or lower than the
background noise
Template Matching High detection performance
Spike shape knowledge are
required
Nonlinear Energy Operator
(NEO)
& Multi-resolution
Teager Energy Operator
(MTEO)
Easy implementation and
computational simplicity
Same as Amplitude Thresholding
Wavelet Transformation
If wavelet shape is selected
properly, the wavelet transform can
be seen as a bank of matched filters
Prior knowledge about spike
shapes are required

9. Agenda
• Overview
• Related Work
• Methodology
• Results
• Conclusion
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10. Methodology
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Wavelet Transform
Wavelets are defined by two primary functions :
•Wavelet function (mother wavelet) ψ(t)
•Scaling function (father wavelet) φ(t)
where a is scalar factor and b is translation factor
Haar Wavelet
Transform

11. Methodology
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Stationary Wavelet Transform (SWT)
DWT SWT

12. Methodology
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Wavelet Parameterization
Filter length = 4
One independent parameter (α)

13. Methodology
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Flowchart
Noisy
Signals
Filtered
Signals
Detection
(SWT)
Clustering
(DWT)

14. Methodology
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Flowchart
Noisy
Signals
Filtered
Signals
Detection
(SWT)
Clustering
(DWT)

15. Methodology
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Detection
SWT five levels
decomposition
Hard thresholding
Three maximum
energy scale
selection
Summation &
Filtering
Selection Criteria I
Final AP
Candidates
AP Candidates

16. Methodology
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Detection
SWT five levels
decomposition
Hard thresholding
Three maximum
energy scale
selection
Summation &
Filtering
Selection Criteria I
Final AP
Candidates
AP Candidates

17. Methodology
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Detection
SWT five levels
decomposition
Hard thresholding
Three maximum
energy scale
selection
Summation &
Filtering
Selection Criteria I
Final AP
Candidates
AP Candidates

18. Methodology
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Detection – Thresholding I
Median Absolute Deviation (MAD) Operator
Example:
• Consider the data (1, 1, 2, 2, 4, 6, 9).
• It has a median value of 2.
• The absolute deviations about 2 are (1, 1, 0, 0, 2, 4, 7).
• The sorted absolute deviations are (0, 0, 1, 1, 2, 4, 7).
• So the median absolute deviation (MAD) for this data is 1

19. Methodology
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Detection – Thresholding II
Threshold level at each scale is computed as follows:
Where N is the number of samples (n) and σj is the noise standard
deviation at scale j which is estimated with (MAD) operator
80% of this threshold level are used to keep the highest 20% candidates
for detection

20. Methodology
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Detection – Thresholding III
Hard thresholding can be described as follows:
 wavelet coefficient after thresholding at scale j

21. Methodology
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Detection
SWT five levels
decomposition
Hard thresholding
Three maximum
energy scale
selection
Summation &
Filtering
Selection Criteria I
Final AP
Candidates
AP Candidates

22. Methodology
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Detection – Energy Selection
The signal energy at each scale (Ewj) is calculated as
 Wavelet coefficient after thresholding at scale j
 Average value at each scale

23. Methodology
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Detection
SWT five levels
decomposition
Hard thresholding
Three maximum
energy scale
selection
Summation &
Filtering
Selection Criteria I
Final AP
Candidates
AP Candidates

24. Methodology
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Detection – Summation & Filtering
S(n) is calculated as the summation of the absolute values of the wavelet
coefficients
 Wavelet coefficient after thresholding at scale j
for removing flase peaks, S(n) is filtered with smoothing window W(n)

25. Methodology
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Detection
SWT five levels
decomposition
Hard thresholding
Three maximum
energy scale
selection
Summation &
Filtering
Selection Criteria
Final AP
Candidates
AP Candidates

26. Methodology
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Detection – Selection Criteria
The optimal wavelet basis selection is based on the correlation similarity
(wave form x(n) and wave form y(n))
Where E is the expected value operator
 Designated label for i(n)  Median value of APs
KD = 0.4  Rejects very far outliers

27. Methodology
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Flowchart
Noisy
Signals
Filtered
Signals
Detection
(SWT)
Clustering
(DWT)

28. Methodology
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Clustering
DWT five levels
decomposition
ClusteringSelection Criteria
II
Final
Classified APs
Classified APs
Final AP
Candidates
Based on normal
distance
measurement
KC = 0.8  represents the high similarity of shapes
between APs

29. Agenda
• Overview
• Related Work
• Methodology
• Results
• Conclusion
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30. Results
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Detector Output
a-band pass filtered data b-THR detector c-NEO detector
d-MTEO detector e-DWT product detector f-Proposed method

31. Results
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Comparison of average TPR vs SNR

32. Results
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Detection Performance
1st
2nd

33. Agenda
• Overview
• Related Work
• Methodology
• Results
• Conclusion
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34. Conclusion
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• Introduce unsupervised optimization for the best
basis selection of detection & clustering APs.
• Improve the spike sorting performance by applying
unsupervised criterion based on the correlation
similarity.

35. References
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• Rieder, P.; Gerganoff, K.; Gotze, J.; Nossek, J.A., “Parameterization and
implementation of orthogonal wavelet transforms,” Acoustics, Speech,
and Signal Processing, 1996. ICASSP-96. Conference Proceedings.,
1996 IEEE International Conference on , vol.3, no., pp.1515,1518 vol. 3,
7-10 May 1996.
• Shalchyan, V.; Jensen, W.; Farina, D., “Spike Detection and Clustering
With Unsupervised Wavelet Optimization in Extracellular Neural
Recordings,” Biomedical Engineering, IEEE Transactions on , vol.59,
no.9, pp.2576,2585, Sept. 2012.
• Zhou, X.; Zhou, C.; Stewart, B.G., “Comparisons of discrete wavelet
transform, wavelet packet transform and stationary wavelet transform in
denoising PD measurement data,” Electrical Insulation, 2006.
Conference Record of the 2006 IEEE International Symposium on , vol.,
no., pp.237,240, 11-14 June 2006.

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