L-曲线估计正则化参数对高刺激率听觉诱发电位重建的影响

摘要

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.%探讨在暂态的听觉诱发电位(AEP)重建问题中,当一些L-曲线中出现多个拐点,给正则化参数的确定带来困难时,如何确立最优的正则化参数.本研究提出把高刺激率下AEP去卷积问题转化为一个线性系统逆问题处理,并且引入正则化技术修正目标函数,以解决由于变换矩阵的病态条件带来的无效解;同时采用一个十分典型的正则化参数估计常用方法(L-曲线法)估计正则化参数;针对L-曲线方法存在欠估计的情况,提出在参数选择过程中结合AEP的先验知识,选择L-曲线曲率图中其他曲率极大值点所对应的正则化参数.结果表明,L-曲线方法在大多数情况下,能较好的估计正则化参数,在存在欠估计问题时,则要重新正确选择正则化参数.再重建的暂态AEP与常规AEP的相关系数分别提高了0.14和0.21,相对误差分别下降了0.30和3.25,从而实现暂态AEP信号较好重建.正则化参数控制着目标函数中正则化的程度,对暂态AEP的重建性能影响很大,对于存在复杂曲率结构的L-曲线,根据AEP自身范数的取值范围能够方便地确定出合理的正则化参数,从而改善了AEP重建性能.