Note

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EEG Artifact removal using ATAR¶

ATAR: Automatic and Tunable Artifact Removal Algorithm

ATAR Algorithm - Automatic and Tunable Artifact Removal Algorithm for EEG Signal.

Apply ATAR on short windows of signal (single channel):

Signal is decomposed in smaller overlapping windows and reconstructed after correcting using overlap-add method.

For more details, check [1]_

Operating Modes

1. Soft Thresholding

\[ \begin{align}\begin{aligned}\lambda_s (w) &= w & \quad \text{if } |w|<\theta_{\gamma}\\ &= \theta_{\alpha} \frac{1 - e^{\alpha w}}{1 + e^{\alpha w}} & \quad \text{otherwise}\end{aligned}\end{align} \]

2. Elimination

\[ \begin{align}\begin{aligned}\lambda_e (w) &= w & \quad \text{if } |w| \le \theta_{\alpha}\\ &= 0 & \quad \text{otherwise}\end{aligned}\end{align} \]

3. Linear Attenuation

\[ \begin{align}\begin{aligned}\lambda_a (w) &= w & \quad \text{if } |w| \le \theta_{\alpha}\\ &= sgn(w) \theta_{\alpha} \Big( 1 - \frac{|w| - \theta_{\alpha}}{\theta_{\beta}-\theta_{\alpha}} \Big) & \quad \text{if } \theta_{\alpha} < |w| \le \theta_{\beta}\\ &= 0 & \quad \text{otherwise}\end{aligned}\end{align} \]

Computing Threshold

\(f_{\beta}(r) = k_2 \cdot exp \Big(-\beta \frac{w_{max}}{k_2} \times \frac{r}{2} \Big)\)

\(\theta_{\alpha} = f_{\beta}(r) \quad \text{if } f_{\beta}(r) \ge k_1\) otherwise \(\theta_{\alpha} = k_1\)

\(\theta_{\gamma} = g_f \times \theta_{\alpha}\) , where a default value for ‘g_f = 0.8’ For Soft-threshold

\(\theta_{\beta} = b_f \times \theta_{\alpha}\) , where a default value for ‘b_f = 2’ For Linear Attenuation

# Importing libraries/spkit
import numpy as np
import matplotlib.pyplot as plt
import warnings
warnings.filterwarnings("ignore")

import spkit as sp
print('spkit version :', sp.__version__)

spkit version : 0.0.9.7

Load and filter EEG Signal¶

# Load sample EEG Data ( 16 sec, 128 smapling rate, 14 channel)
# Filter signal (with IIR highpass 0.5Hz)

X, fs, ch_names = sp.data.eeg_sample_14ch()
Xf = sp.filter_X(X.copy(),fs=128.0, band=[0.5], btype='highpass',ftype='SOS')
print(Xf.shape)

(2048, 14)

Artifact removal using ATAR: Single Channel

x = Xf[:,0]
xc1 = sp.eeg.ATAR(x,wv='db3', winsize=128, thr_method='ipr',beta=0.1, k1=10, k2=100,OptMode='soft',verbose=1)
xc2 = sp.eeg.ATAR(x,wv='db3', winsize=128, thr_method='ipr',beta=0.1, k1=10, k2=100,OptMode='linAtten',verbose=1)
xc3 = sp.eeg.ATAR(x,wv='db3', winsize=128, thr_method='ipr',beta=0.1, k1=10, k2=100,OptMode='elim',verbose=1)

  3%|▓                                                 |2112\65| Mode : soft
  6%|▓▓▓                                               |2112\129| Mode : soft
  9%|▓▓▓▓                                              |2112\193| Mode : soft
 12%|▓▓▓▓▓▓                                            |2112\257| Mode : soft
 15%|▓▓▓▓▓▓▓                                           |2112\321| Mode : soft
 18%|▓▓▓▓▓▓▓▓▓                                         |2112\385| Mode : soft
 21%|▓▓▓▓▓▓▓▓▓▓                                        |2112\449| Mode : soft
 24%|▓▓▓▓▓▓▓▓▓▓▓▓                                      |2112\513| Mode : soft
 27%|▓▓▓▓▓▓▓▓▓▓▓▓▓                                     |2112\577| Mode : soft
 30%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓                                   |2112\641| Mode : soft
 33%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓                                  |2112\705| Mode : soft
 36%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓                                |2112\769| Mode : soft
 39%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓                               |2112\833| Mode : soft
 42%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓                             |2112\897| Mode : soft
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 48%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓                          |2112\1025| Mode : soft
 51%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓                         |2112\1089| Mode : soft
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 72%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓              |2112\1537| Mode : soft
 75%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓             |2112\1601| Mode : soft
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 84%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓        |2112\1793| Mode : soft
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100%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓|2112\2113| Mode : soft
Done!

  3%|▓                                                 |2112\65| Mode : linAtten
  6%|▓▓▓                                               |2112\129| Mode : linAtten
  9%|▓▓▓▓                                              |2112\193| Mode : linAtten
 12%|▓▓▓▓▓▓                                            |2112\257| Mode : linAtten
 15%|▓▓▓▓▓▓▓                                           |2112\321| Mode : linAtten
 18%|▓▓▓▓▓▓▓▓▓                                         |2112\385| Mode : linAtten
 21%|▓▓▓▓▓▓▓▓▓▓                                        |2112\449| Mode : linAtten
 24%|▓▓▓▓▓▓▓▓▓▓▓▓                                      |2112\513| Mode : linAtten
 27%|▓▓▓▓▓▓▓▓▓▓▓▓▓                                     |2112\577| Mode : linAtten
 30%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓                                   |2112\641| Mode : linAtten
 33%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓                                  |2112\705| Mode : linAtten
 36%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓                                |2112\769| Mode : linAtten
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 75%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓             |2112\1601| Mode : linAtten
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Done!

  3%|▓                                                 |2112\65| Mode : elim
  6%|▓▓▓                                               |2112\129| Mode : elim
  9%|▓▓▓▓                                              |2112\193| Mode : elim
 12%|▓▓▓▓▓▓                                            |2112\257| Mode : elim
 15%|▓▓▓▓▓▓▓                                           |2112\321| Mode : elim
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 21%|▓▓▓▓▓▓▓▓▓▓                                        |2112\449| Mode : elim
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 27%|▓▓▓▓▓▓▓▓▓▓▓▓▓                                     |2112\577| Mode : elim
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 57%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓                      |2112\1217| Mode : elim
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 78%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓           |2112\1665| Mode : elim
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 93%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓    |2112\1985| Mode : elim
 97%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓  |2112\2049| Mode : elim
100%|▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓|2112\2113| Mode : elim
Done!

Artifact removal using ATAR: Multi-Channel

XR = sp.eeg.ATAR(Xf.copy(),verbose=0)
print(XR.shape)

(2048, 14)

Plots¶

t = np.arange(Xf.shape[0])/fs

plt.figure(figsize=(10,5))
plt.subplot(111)
plt.plot(t,x, label='$x$: raw EEG - single channel')
plt.plot(t,xc1,label=r'$x_{c1}$: Soft Thresholding')
plt.plot(t,xc2,label=r'$x_{c2}$: Linear Attenuation')
plt.plot(t,xc3,label=r'$x_{c3}$: Elimination')
plt.xlim([9,12])
plt.ylim([-200,200])
plt.legend(bbox_to_anchor=(0.5,0.99),ncol=2,fontsize=8)
plt.grid()
plt.title(r'ATAR Algorithm')
plt.xlabel('time (s)')
plt.show()

plt.figure(figsize=(12,8))
plt.subplot(211)
plt.plot(t,XR+np.arange(-7,7)*200)
plt.xlim([t[0],t[-1]])
plt.xlabel('time (sec)')
plt.yticks(np.arange(-7,7)*200,ch_names)
plt.grid()
plt.title('XR: Corrected Signal')
plt.subplot(212)
plt.plot(t,(Xf-XR)+np.arange(-7,7)*200)
plt.xlim([t[0],t[-1]])
plt.xlabel('time (sec)')
plt.yticks(np.arange(-7,7)*200,ch_names)
plt.grid()
plt.title('Xf - XR: Difference (removed signal)')
plt.suptitle('ATAR: Soft Thresholding (default mode)')
plt.tight_layout()
plt.grid()
plt.show()

plt.figure(figsize=(12,5))
plt.plot(t,Xf+np.arange(-7,7)*200)
plt.xlim([t[0],t[-1]])
plt.xlabel('time (sec)')
plt.yticks(np.arange(-7,7)*200,ch_names)
plt.grid()
plt.title('Xf: 14 channel - EEG Signal (filtered)')
plt.tight_layout()
plt.grid()
plt.show()

ATAR: Linear Attenuation Mode¶

XR = sp.eeg.ATAR(Xf.copy(),verbose=0,OptMode='linAtten')
print(XR.shape)

t = np.arange(Xf.shape[0])/fs
plt.figure(figsize=(15,5))
plt.subplot(121)
plt.plot(t,XR+np.arange(-7,7)*200)
plt.xlim([t[0],t[-1]])
plt.xlabel('time (sec)')
plt.yticks(np.arange(-7,7)*200,ch_names)
plt.grid()
plt.title('XR: Corrected Signal')
plt.subplot(122)
plt.plot(t,(Xf-XR)+np.arange(-7,7)*200)
plt.xlim([t[0],t[-1]])
plt.xlabel('time (sec)')
plt.yticks(np.arange(-7,7)*200,ch_names)
plt.grid()
plt.title('Xf - XR: Difference (removed signal)')
plt.suptitle('ATAR: Linear Attenuation Mode')
plt.tight_layout()
plt.show()

(2048, 14)

ATAR - Elimination Mode¶

XR = sp.eeg.ATAR(Xf.copy(),verbose=0,OptMode='elim')
print(XR.shape)

t = np.arange(Xf.shape[0])/fs
plt.figure(figsize=(15,5))
plt.subplot(121)
plt.plot(t,XR+np.arange(-7,7)*200)
plt.xlim([t[0],t[-1]])
plt.xlabel('time (sec)')
plt.yticks(np.arange(-7,7)*200,ch_names)
plt.grid()
plt.title('XR: Corrected Signal')
plt.subplot(122)
plt.plot(t,(Xf-XR)+np.arange(-7,7)*200)
plt.xlim([t[0],t[-1]])
plt.xlabel('time (sec)')
plt.yticks(np.arange(-7,7)*200,ch_names)
plt.grid()
plt.title('Xf - XR: Difference (removed signal)')
plt.suptitle('ATAR: Elimination Mode')
plt.tight_layout()
plt.show()