Tikhonov正则化参数选择对高速率刺激听觉诱发电位重建的影响

Effects of Parameter Selection of Tikhonov Regularization on Reconstruction of High-rate Auditory Evoked Potentials

目的探讨不同参数选择方法对高阶听觉脑干反应(Auditory Brainstem Response,ABR)信号重建的影响。方法采用L-curve和广义交叉验证(General Cross Validation,GCV)两种参数选择准则选取正则化参数,代入Tikhonov正则化目标函数,试图解决由于采用了刺激序列间抖动的去卷积技术得到的合成变换矩阵而产生的病态逆问题,从而重建出暂态高阶听觉诱发反应(Auditory Evoked Potentials,AEP)。采用2种不同的速率组合方式,通过计算重建ABR和常规ABR之间的相关系数和相对误差,比较2种正则化方法的效果。结果相对于L-curve,GCV方法得到的正则化参数普遍较大,重建的高阶暂态ABR与常规ABR之间的相关系数普遍较高,相对误差较小。L-curve准则有一些特例情况,求解的正则化参数估计不如GCV方法稳定。结论 GCV方法比L-curve方法能更好地解决高阶ABR重建的病态问题,取得更接近于真实情况的结果。

Objective To investigate the effects of different parameter selection methods on the reconstruction of high-order ABR（Auditory Brainstem Response）.Methods L-curve and generalized cross validation（GCV） parameter selection criteria were applied to select the regularization parameter,which was then called into the object function of Tikhonov regularization to solve the abnormal inverse problem caused by synthesis transfer matrix with de-convolution technique in the flutter of high rate stimulation scenario.Two different rate-combinations,A and B was formed during the validation stage to examine the performance.Correlation coefficients and relative-errors were calculated as similarity measurements between the conventional ABRs and the reconstructed high-rate ABRs to compare their efficacy.Results Both L-curve and GCV were able to produce satisfactory ABRs for many cases,with larger regularization parameters and higher correlation coefficient and smaller relative errors between reconstructed high-rate ABRs and conventional ABRs.GCV method usually yielded larger regularization parameters and higher similarity scores than that of L-curve method.For some special cases,L-curve demonstrated under regularization results indicating the less stable parameter estimation than GCV.Conclusion In this study of high-rate ABR reconstruction,GCV outperforms L-curve in solving the inverse problem in terms of the stability and closeness to true solution.