Akademik Veri Yönetim Sistemi
MEDICAL & BIOLOGICAL ENGINEERING & COMPUTING, cilt.46, sa.10, ss.1051-1056, 2008 (SCI-Expanded)
https://link.springer.com/article/10.1007/s11517-008-0385-0
In the present study, standard Tikhonov
regularization (STR) Technique and the subspace regularization (SR) method have
been applied to remove the additive EEG noise on average auditory-evoked
potential (EP) signals. In methodological manner, the difference between these
methods is the formation of regularization matrices which are used to solve the
weighted problem of EP estimation. Those methods are compared to ensemble
averaging (EA) with respect to signal-to-noise-ratio (SNR) improvement in
experimental studies, simulations and pseudo-simulations. The results of tests
no superiority of the SR in comparison to STR has been observed. In addition,
the STR is found to be less computational complex. Moreover, results support
the theoretical fact that the STR was introduced to be optimum for smooth
solutions whereas the SR allows sharp variations in solutions. Thus, the STR is
found to be more useful in removing the noise with the average signal
remaining.
The regularization methods
showed better performance compared to EA. It was observed that, the STR is
marginally better than the SR in all cases. Note that the STR method is optimum
for smooth solutions whereas the SR allows sharp variations in the solutions.
The basis vectors are chosen from the dilated and shifted forms of a mother
wavelet which resemble the waveform of the auditory EP. The linear combination
of these smooth vectors models the EP. In line with the fact that a sharp
variation in the coefficients of this combination is not expected, we have not
observed the superiority of SR compared to the STR. In addition, the STR method
has less computational complexity than the SR method. Thus, the use of the STR
method is proposed instead of the SR for template auditory EP estimation. In
conclusion, the STR effectively reduces the experimental time (to one-fourth of
that required by EA). Both methods are closely related to Bayesian estimation
but there is a distinct property between them: the SR solves a linear system
where sharp variations are allowed besides; the STR provides the optimum smooth
solution for the same system. Since the waveform of the EP signal is similar to
a smooth wave having a fast positive peak and following a slower negative peak,
the nature of the STR is more suitable in case of EP estimation. The present
experimental and simulation based results support this theoretical suggestion
such that the STR provides more SNR enhancement. In both simulations and
pseudosimulations, the improvements were 20 dB. Besides, 5 dB
improvement was obtained in experimental studies. These data dependent
different achievements are originated by their autocorrelation functions which
directly form the regularization matrix (L 2) of
interest such that there were no ripples in both pre and post-stimulus
intervals in simulations in contrast to experimental data. In addition, actual
background EEG noise is different from a white noise.