Unsupervised selection of mother wavelets and parameter optimization for Wavelet denoising based artifact removal from neural signals

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

7. Correlation Value Vs Alpha
-4 -3 -2 -1 0 1 2 3 4
0.35
0.4
0.45
0.5
Minimize ArtifactsCorrelationValue
-4 -3 -2 -1 0 1 2 3 4
0.94
0.96
0.98
1
alpha
Maximize Non-Artifacts
α_opt2 = - 2.618
α_opt1 = - 2.094

8. Performance Metrics Vs Alpha
-4 -3 -2 -1 0 1 2 3 4
86
87
88
89
lamda
-4 -3 -2 -1 0 1 2 3 4
17.5
18
18.5
19
delSNR
alpha
-4 -3 -2 -1 0 1 2 3 4
1.1
1.15
1.2
1.25
PSDDistortion
-4 -3 -2 -1 0 1 2 3 4
7.6
7.8
8
8.2
8.4
x 10
-3
alpha
RMSE

9. Optimization of Parameter kA
0.2 0.4 0.6 0.8 1
0
20
40
60
80
100
lamda
0.2 0.4 0.6 0.8 1
8
10
12
14
16
delSNR
Parameter k
A
0.2 0.4 0.6 0.8 1
0
2
4
6
PSDDistortion
0.2 0.4 0.6 0.8 1
0.005
0.01
0.015
0.02
RMSE
Parameter kA
0.2 0.4 0.6 0.8 1
-0.4
-0.2
0
0.2
0.4
Minimize Artifacts
CorrelationValue
0.2 0.4 0.6 0.8 1
0.8
0.85
0.9
0.95
1
Maximize Non-Artifacts
Parameter k
A
kA_opt1 = 1
kA_opt2 = 0.7

10. Optimization of Parameter kD
1 1.5 2 2.5 3 3.5 4 4.5 5
0.461
0.462
0.463
0.464
Minimize Artifacts
1 1.5 2 2.5 3 3.5 4 4.5 5
0.9934
0.9934
0.9934
0.9934
k
D
Maximize Non-Artifacts
1 2 3 4 5 6
11
12
13
14
15
16
17
k
D
Avg.SNDRImprovement
kD_opt1 = 2.5
kD_opt2 = 5
17 dB SNDR
@ kD_opt1 = 2.5
15.94 dB SNDR
@ kD_opt2 = 5
1 1.5 2 2.5 3 3.5 4 4.5 5
0.8482
0.8482
0.8482
0.8482
PSD dis aft
1 1.5 2 2.5 3 3.5 4 4.5 5
9.9945
9.995
9.9955
x 10
-3
k2
RMSE aft
1 1.5 2 2.5 3 3.5 4 4.5 5
79.687
79.688
79.689
79.69
79.691
79.692
lamda
1 1.5 2 2.5 3 3.5 4 4.5 5
13.4296
13.4298
13.43
13.4302
13.4304
delSNR
k2