Akademik Veri Yönetim Sistemi
MEDICAL & BIOLOGICAL ENGINEERING & COMPUTING, cilt.46, sa.10, ss.1051-1056, 2008 (SCI-Expanded)
https://pubmed.ncbi.nlm.nih.gov/18716817/
https://link.springer.com/article/10.1007/s11517-008-0385-0
ABSTRACT
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.