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Unsupervised selection of mother wavelets and parameter optimization
1. Unsupervised Selection of Mother Wavelets
and Parameter Optimization for Artifact
Removal in Neural Recordings
By
Md Kafiul Islam
Translational System and Signal Processing Group
National University of Singapore
2. Sequence of Optimization
1) Optimization of Parameter Alpha for Best
Mother Wavelet
2) Optimization of Parameter kA
3) Optimization of Parameter kD
3. Motivation to Choose Best Wavelet
To achieve best performance both in terms of artifact removal and signal distortion
2 4 6 8 10
65
70
75
80
85
90
lamda
db2
Best
2 4 6 8 10
12
14
16
18
delSNR
db2
Best
2 4 6 8 10
0.006
0.008
0.01
0.012
0.014
RMSE
db2
Best
2 4 6 8 10
0.5
1
1.5
2
2.5
No. of Trials
PSDDistortion
db2
Best
Comparison of Artifact Removal Performance between Best Mother Wavelet and
Daubechies Wavelet (Filter Length = 4)
2 4 6 8 10
60
70
80
90
lamda
Sym2
Best
2 4 6 8 10
12
14
16
18
20
delSNR
Sym2
Best
2 4 6 8 10
0.008
0.01
0.012
0.014
0.016
RMSE
Sym2
Best
2 4 6 8 10
0.5
1
1.5
2
2.5
3
No. of Trials
PSDDistortion
Sym2
Best
Comparison of Artifact Removal Performance between Best Mother Wavelet
and Symlet Wavelet (Filter Length = 4)
4. Purpose to Optimize Parameter kD and kA
To make the selection unsupervised
To achieve best performance both in terms of artifact removal and signal distortion
1 1.5 2 2.5 3 3.5 4 4.5 5
9
10
11
12
13
14
15 X: 3
Y: 14.5
Parameter k
D
Avg.SNDRImprove
The Maximum Value of Average SNDR Improvement Can be
Achieved Through an Optimized and Unsupervised Selection of
Parameter k_D
0 0.2 0.4 0.6 0.8 1
0
20
40
60
80
100 X: 0.6
Y: 80.97
lamda
0 0.2 0.4 0.6 0.8 1
10
12
14
16
18
X: 0.6
Y: 16.32
delSNR
0 0.2 0.4 0.6 0.8 1
0
1
2
3
X: 0.6
Y: 1.187
PSDDistortion
0 0.2 0.4 0.6 0.8 1
0.005
0.01
0.015
0.02
X: 0.6
Y: 0.009534
RMSE
Parameter k
A
The Best Performance Metrics Can be Achieved Through an Optimized
and Unsupervised Selection of Parameter k_A
5. Optimization of Parameter α for Best Wavelet
Wavelet Filter Design (Length = 4)
Low Pass Filter
High Pass Filter
Criteria for Optimal ‘α’: Options
Maximize Correlation between Artifactual
Signal and Reconstructed Signal in non-
artifactual regions (i.e. IDi is not artifact index)
Minimize Correlation between Artifactual
Signal and Reconstructed Signal in artifactual
regions (i.e. IDi is artifact index)
6. Optimization of Parameter α
• Steps for Optimization Procedure
1) Parameterize the wavelet filters w. r. t. α
2) Sweep α from –π to +π with increment of π/6
3) Compute the filter coef., hα & gα for each α
4) Perform proposed artifact removal process with the
wavelet filters, hα & gα
5) Minimize Correlation between r(n) and r’(n) only in
the artifact-index regions to find optimal alpha,
α_opt1
Or
6) Maximize Correlation between r(n) and r’(n) only in
the non-artifact-index regions to find optimal alpha,
α_opt2