Biomedical Engineering Reference
In-Depth Information
b. Whitening: in whitening we remove the second order statistical dependence in
the data, i.e., the whitened data have unit variance and they are uncorrelated.
Let Z be zero mean random vector, then in terms of covariance matrix we can
write
EZZ T ¼ I
ð 13 Þ
where I is identity matrix.
Finally whitened data Z is expressed by Eq. ( 14 ):
Z ¼ D 1 = 2 : E T : X
ð 14 Þ
where E is matrix whose columns are unit norm eigenvectors of covariance
matrix.
C X ¼ EXX T
ð 15 Þ
D is diagonal matrix of eigenvalues of C X
5. Using the demixing matrix obtained above we obtain the mixing matrix A by
the equation
A ¼ pseudoinverse
ðÞ
ð 16 Þ
6. Finally denoised image is obtained by the mixing matrix A and the independent
component.
7. Then Otsu's thresholding is done and values below a certain threshold are set to
zero.
8. This gives the whitened denoisd image. To reconstruct the image from this we
add the mean to this image which was substracted earlier and multiply the
whitening matrix to obtain the final denoised image.
Experimental Results
This section presents the evaluation of the proposed artifact removal technique.
Initially, EEG signals are captured with occurrence of artifacts. Figure 4 shows the
four samples of EEG signal that is effected through noise and artifacts. We defined
n as the number of iterations and to plot our data to number of values to number of
iteration we defined j and also j as the original matrix value of data and k defines
the number of blocks available in data. Then Fig. 5 shows the result using ICA so
as to find the independent component. Figure 6 is a result of signal after imple-
mentation of wavelet denoising on the signals of Fig. 5 . From these figures, it has
been observed that the proposed artifact removal technique results in better
removal of artifacts. This will help in improving the performance of the further
processing of this EEG signal.
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