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Accelerated SWT based de-noising
technique for EEG to correct the Ocular
Artifact
Mahesh Khadtare, Pragati Dharmale
3/19/2015 2
Plan of Session
I. Introduction
II. Overview
III. Stationary Wavelet Transform (SWT)
IV. Algorithmic & implementation of EEG denoise
V. Results
VI. Discussions
Introduction
• Every time we think, move, feel or remember something, our neurons are at
work. That work is carried out by small electric signals that zip from neuron to
neuron as fast as 250 mph [source: Walker]
• Using data recorded from the brain, the BCI processes it, interprets the
intention of the user, and acts on it, Figure shows Awake state and Asleep state
[source: Wikipedia].
• Eye movements and blinks cause a severe problem for EEG measurements
[Source: EEG Lead placements-EEGLab]
3/19/2015 3
Introduction Inspiration
• Brain Computer Interface(BCI)
3/19/2015 4
Neurologists
Introduction
The references used for research are Evenly spread
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Most are
recent years
3/19/2015
Overview
• Almost all existing approaches to ocular artifact (OA) detection and
removal use one or more electro oculogram (EOG) signals either
directly or indirectly as a reference.
• Some feature of the output of the algorithm (e.g., signal-to-noise ratio,
or SNR) is compared to the original artifact-free EEG.
• For real EEG, the artifact-free (“true”) EEG is not known, so the
performance of the algorithm on real data is usually reported ,often
based on visual inspection of the resulting waveforms.
• So the challenge is removal of EOG artifact without or less EEG
data distortion
6 3/19/2015
Overview
• What is Wavelet
– A small wave
• Wavelet Transforms
– Convert a signal into a series of wavelets
– Provide a way for analyzing waveforms, bounded in both frequency and duration
– Allow signals to be stored more efficiently than by Fourier transform
– Be able to better approximate real-world signals
– Well-suited for approximating data with sharp discontinuities
7 3/19/2015
Overview
Fourier Vs Wavelet Transform
Fourier Transform Wavelet Transform
Frequency Information only,
Time/space information is lost
Joint Time and Frequency Information
Single Basis Function Many Basis Functions
Computational Cost High Low computational costs
Analysis Structures:
- FS( periodic functions only)
- FT and DFT
Numerous Analysis structures:
CWT,
DWT(2 Band and M Band),
WP
SWT,
Frame structure
3/19/2015 8
Standard DWT
• Classical DWT is not shift invariant: This means that DWT of a translated version of a signal x is not the same as the DWT of the original signal.
• Shift-invariance is important in many applications such as:
– Change Detection
– Denoising
– Pattern Recognition
• In DWT, the signal is convolved and decimated (the even indices are kept.)
• The decimation can be carried out by choosing the odd indices.
3/19/2015
Standard DWT (2 Stage)
3/19/2015
High Pass
Low Pass
Low pass
High pass
Decimated Wavelet Transform-Analysis Stage
High Freq Details
Low freq Approx
Signal
2
2
SWT
• Apply high and low pass filters to the data
at each level
• Do not decimate
• Modify the filters at each level, by padding
them with zeroes
• Computationally more complex
3/19/2015
SWT (2 Stage)
3/19/2015
High Pass
Low Pass
Low pass
High pass
High Freq Details
Low freq Approx
Signal
Different Implementations
• A Trous Algorithm: Upsample the filter coefficients by inserting zeros
• Beylkin’s algorithm: Shift invariance, shifts by one will yield the same result by any odd shift. Similarly, shift by zeroAll even shifts.
– Shift by 1 and 0 and compute the DWT, repeat the same procedure at each stage
– Not a unique inverse: Invert each transform and average the results
• Undecimated Algorithm: Apply the lowpass and highpass filters without any decimation.
3/19/2015
Traditional parallel algorithm
14
EEG 1 EEG 2 EEG N
PE 1
EEG 1 EEG 2 EEG N
PE 2 PE N
Dependencies
• Scheme depends upon the PE’s Configuration
• PE’s Interconnectedness
• Message passing Protocols
• Data transmission bandwidth
Traditional distributed processing algorithm does not include any
parallel processing algorithm for Signal processing
3/19/2015
Proposed parallel algorithm
15
EEG 1
PE 1 PE 2 PE N
EEG 1
EEG N
PE 1 PE 2 PE N
EEG N
3/19/2015
16
EEG 1
G-PE 1 G-PE 2 G-PE
N
P-EEG 1
EEG N
G-PE 1 G-PE 2 G-PE
N
P-EEG N
Proposed parallel algorithm
3/19/2015
Mathematical Model Wavelet Coefficients
17
• Detail Coefficient:
• Approximate Coefficient:
n
nkhnxkylow ]2[].[][
3/19/2015
n
nkgnxkyhigh ]2[].[][
Algorithm Flow
Signal domain basis functions Transformed domain, Coeffs
Transformation
Analysis
Reconstruction
Signals
Recon Signal
basis functions
Modified Coefficients
Information
extraction
Wavelet Decomposition
• The maximum frequency of EEG data sample is 125 Hz.
• The original data can be decomposed in up to 10 detail levels (D1 –
D10) and a last approximation (Apr).
• The frequency limits of each scale are approx. calculated dividing by 2
the sampling rate. In the case of 250 Hz, these are (with a 5 scales
decomposition):
• D1: 64 – 128 Hz;
• D2: 32 – 64 Hz
• D3: 16 – 32 Hz;
• D4: 8 – 16 Hz;
• D5: 4 – 8 Hz;
• A5: 0 – 4 Hz.
Note that D2, D3, D4, D5, A5 approximately correspond to the EEG
frequency bands: Gamma,Beta,Alpha,Theta,Delta respectively.
19
GAMMA
ALPHA
BETA
THETA
DELTA
3/19/2015
General denoising procedure
• The involves three steps. The basic version of the procedure follows the steps described below:
• Decompose: Select a wavelet, select a level N. Compute the wavelet decomposition of the signal at level N.
• Zeroing or Thresholding detail coefficients: For each level from 1 to N, either make detail coefficient zero or select a threshold value and apply to the detail coefficients.
• Reconstruct: Compute wavelet reconstruction using the original approximation coefficients of level N and the modified detail coefficients of levels from 1 to N.
20 3/19/2015
Threshold method
• In wavelet denoising process, the threshold method is one of the main methods.
• Threshold function has important relationship with the continuity and accuracy of the reconstructed signals, and has a significant impact on wavelet denoising.
• At present, there are two choices of methods of which are hard threshold and soft threshold.
• But the hard threshold method makes the wavelet coefficients discontinuous in the threshold value position and leads to the oscillations of the reconstructed signals; while with the soft threshold method wavelet coefficient has improved continuity.
3/19/2015 21
Threshold method
• The key point of wavelet threshold denoising is the selection of threshold and how to choose the threshold function when dealing with wavelet coefficient after decomposition.
• There are four commonly used methods to select threshold of which are Donoho-Johnstone methods:
1.Fixed-form (default)
2. Heursure
3. Rigsure
4.Minimax
3/19/2015 22
EEG Data
• EEG Database –
• Physionet EEG database
– 325 Recording with 7 Channel with different task
• Baseline, Rotation, Letter composing, Counting,
Multiplication
• Duration: 8 min (Sampling Frequency (fs): 256Hz)
• Typically : 840MB data size per recording
• Realtime EEG database
– 60min Recording with 4 Channels
– Eye blinking, all above activity
Source: http://sccn.ucsd.edu/~arno/fam2data/publicly_available_EEG_data.html
24
Signal
Data
Sensor
SW
T F
orw
ard
Tra
nsf
orm
Th
resh
old
ing
SW
T I
nver
se
EEG Signal Processing
The rate of
Execution Time* 60% 61% 30 % *1 Thread,
Conventional Corner Turn
Distribution Of Execution Time
3/19/2015
Recons-
tructed
Signal
Demo – Sample unit test
Algorithm Implementation
3/19/2015 25
Read All Channel EEG Data for
Signal Processing
Rearrange all channel Data (
Block formation and groups)
Rearrange Image Data ( Block
formation and Flipping )
DWT or SWT
forward
DWT or SWT
Inverse
Denoise Thresholds
G
P
U
C
P
U
Compute Thresholds
Code Snippet
CPU code
• Lifting Step Wavelet
• Wavelet levels and
direction
CUDA Kernel
• Row Kernel –
• Column Kernel
3/19/2015 26
__global__ void columnsKernel( double *d_Dst, double *d_Src, double *d_Kernel, int RowSize, int ColSize, int kernelRadius )
__global__, void rowsKernel( double *d_Dst double *d_Src, double *d_Kernel, int RowSize, int ColSize, int kernelRadius )
lifting_step_ti(double[,,] x, double[] h, int dir, int dist)
perform_wavelet_transf(double[, ,]x, int Jmin, int dir)
Test Results
3/19/2015 27
-30000
-20000
-10000
0
10000
20000
30000
40000
11
62
73
25
34
87
96
50
58
13
19
75
71
13
83
130
09
146
35
162
61
178
87
195
13
211
39
227
65
243
91
260
17
276
43
292
69
308
95
325
21
341
47
357
73
373
99
390
25
406
51
422
77
439
03
455
29
471
55
487
81
504
07
520
33
536
59
552
85
569
11
585
37
601
63
617
89
634
15
650
41
666
67
682
93
699
19
715
45
731
71
747
97
Am
p(m
icro
V)
Time (s)
Input EEG
Input EEG
-2000
-1000
0
1000
2000
11
96
03
91
95
87
87
83
79
79
61
17
55
137
14
156
73
176
32
195
91
215
50
235
09
254
68
274
27
293
86
313
45
333
04
352
63
372
22
391
81
411
40
430
99
450
58
470
17
489
76
509
35
528
94
548
53
568
12
587
71
607
30
626
89
646
48
666
07
685
66
705
25
724
84
744
43
Am
p(m
icro
V)
Time(s)
Denoise O/p MATLAB/C# Ch1/ CUDA
Denoise O/p MATLAB
EEG Denoising Timing
CPU / GPU Core
Details
Timing(sec) Speedup
Intel Core i3 – MATLAB 2 45.337 1x
Intel Core i3 – C# 2 12.121 3x
GeForce GT 525M 96 1.031 44x
Data size
512 x 8
Results – EEG Denoise
3/19/2015
Signal to Noise Ratio (SNR)
)log(10Pnoise
PsignalSNR
3/19/2015 29
From SNR, We decided accuracy of the wavelet. It is defined as the ratio of signal power to the noise power
corrupting the signal. A ratio higher than 1:1 indicates more
signal than noise.
Pnoise
PsignalSNR
SIGNAL
POWER
NOISE
POWER.
SNR in DB is calculated as-
)log(20Anoise
AsignalSNR
Comparison Five Wavelet Types
TASK ALL
COEFF.
Max SNR
WAVELET
TYPE
CD1,CD2
Max SNR
WAVELET
TYPE
BASELINE 119.6598 COIF1 13.2003 DMEY
COUNTING 9.4811 DMEY 18.35 SYM6
LETTER
COMPOSING
7.17 SYM6 14.29 SYM6
MULTIPLICATI
ON
9.37 DMEY 12.76 DMEY
ROTATION 7.8818 DB4 19.41 DMEY
30
3/19/2015 31
3/19/2015 32
References
• I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis”, IEEE Trans. Inform. Theory, vol. 36, pp. 961,1005, statiscal learning theory, Cambridge press MIT
• J. S. Sahambi, S. N. Tandon, and R. K. P. Bhatt, “Using wavelet transforms for ecg characterization”, IEEE Eng. in Medicine and Biology, pp. 77, 83, Jan/Feb 1997.
• Mukherjee S., “Classifying microarray data using support vector machines,” in Understanding And Using Microarray Analysis Techniques: A Practical Guide. Boston Kluwer Academic Publishers, 2003.
