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| Effects of Regularization Parameters Estimated by L-Curve on Restoration of Auditory-Evoked Potentials Using High Rate Stimulation Paradigm |
| School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, China |
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Abstract This paper discussed how to establish the best regularization parameters when multiple-corners of L-curve existed in many instances revealed in the corresponding curvature plots in the reconstruction of transient AEP. Restoring the transient auditory evoked potentials (AEPs) obtained at high rate stimulation requires a deconvolution process in the recently developed paradigm. We demonstrated it could be transferred into an inverse problem for a linear system, which requires regularization techniques to deal with the ill-conditioning issue raised from the underlying properties of the transform matrix. A well-established L-curve method was introduced, in which the difficult of obtaining optimal parameter was investigated. For the underestimated case, another new regularization parameter was chosen which was corresponding with other curvature maximum point, incorporating the knowledge of the actual AEP magnitude. This study demonstrated that in most cases, we got fine results by L-curve, however there were failed cases. By comparing the restored AEPs and the conventional AEPs in normal and deviant groups, we achieved the increase by 0.14 and 0.21 respectively in terms of correlation coefficients, and the reduction by 0.30 and 3.25 respectively in terms of relative errors. The regularization parameter that controls the regularizing degree of the objective function plays an important role in the AEP restoration performance. Experimental results showed that appropriate regularization parameter could be determined by incorporating the knowledge of the actual AEP magnitude.
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