Regularization Parameter Selection And High-rate Stimulation Auditory Evoked Potentials Reconstruction

Auditory evoked potentials (AEPs) are weak electrical signals originated in auditory nervous system in response to external specific acoustic stimulation that presents to the subject repetitively. AEPs reflect the state and response of the structure of the nerve, hearing pathways and central nervous system in response to the particular sound stimulation. The conventional recording paradigm applying an stimulus sequence with equal stimulus intervals (SIs) and ensemble averaging method, is perfectly used in clinic. As the stimulus rate increases to a degree that an overlapping response arises on account of the superposition of transient AEPs to the successive stimuli; this overlapped AEP is called high stimulus rate AEP (HSR-AEP), and its transient AEP can be named as high-order AEP (HO-AEP). High stimulus rates can exert strong stresses on the auditory system which might reveal the pathology in the auditory system and brain at an earlier stage. In addition, it was reported that the latencies and amplitudes of AEPs are different in relation to the stimulation rate in anesthesia or sleep states; such characteristics make the HSR-AEP favorable to monitoring the depth of anesthesia, and assessing the sleep condition. Moreover, different reactions of neurons under low and high stimulus rates conditions will allow a more complete evaluation of auditory adaptation. Therefore, the study of HO-AEP is promising in clinic applications.From the engineering point of view, the HSR-AEP results from the convolution of a HO-AEP and a binary stimulus sequence. Early efforts in order to solve the deconvolution problem, were the use of the maximum length sequence-a stimulus sequence with unequal SIs (SI-jittering) rather than the constant ones. And the special autocorrelation features can effectively solve the problem of convolution.In recent years, based on the SI-jitter stimulation paradigms, some other more flexible and exciting means have been put forward. In addition, a new method using matrix inversion to solve the overlapping problem has been developed in the recovery of transient HO-AEP from40Hz steady-state responses. However, due to the lack of mathematical analysis of the model, the problem of how to ensure the performance of deconvolution calculation in the presence of interference, has not been solved. In practical applications, this technology needs to calculate the inverse of the transformation matrix to reconstruct the transient AEP; however, direct inverse of the matrix usually does not exist due to the ill-posedness of the problem. This paper is thus focusing on getting high quality of the transient AEP by virtue of the regularization theories. The major works of this thesis include three projects as follows:1. Using the classic Tikhonov regularization technique and L-curve parameter selection method to solve the ill-posed inverse problem to reconstruct the AEPs under the high stimulus-rate condition. Tikhonov is a kind of widely used classical regularization technique. The method aims to minimize the objective function with a stable function expansion. However the regularization parameter as the weighting factor between fidelity term and constraint has a direct impact on the reconstruction results. An L-curve method was developed accordingly to get an appropriate parameter. Although the L-curve method performs well in most cases, the deviate estimation was found frequently because of the occurrence of multi-corners. This study is to find a way to the estimation of an accurate regularization parameters in the presence of multiple-corners of L-curves indicated by the corresponding curvature plots. By comparing the restored AEPs and the conventional AEPs in normal and deviant groups, the correlation coefficients were increased by0.14and0.21respectively, and the relative errors reduced by0.30and3.25respectively. The experiment results show that appropriate regularization parameter can be determined by incorporating the knowledge of the actual AEP magnitude.2. To investigate the effects of different parameter selection methods on the reconstruction of high-order auditory brainstem response (ABR). In addition to L-curve, generalized cross validation (GCV) is another classic method that extensively used in the parameter selection problem. While for specific problems, the results sometimes have substantial differences for both methods. This study applies L-curve and GCV parameter selection criteria to compare the performance in the AEP reconstruction issue. We formed two groups by combining different stimulus-rates for the same subjects. The conventional AEP was also recorded as a benchmark of validation. The similarity measurement was defined by a correlation coefficient and relative-error between the conventional AEP and the reconstructed high-rate ABR. The results indicate that both L-curve and GCV are applicable for many cases, while GCV method usually yielded larger regularization parameters and higher similarity scores than L-curve method did. For some cases, L-curve demonstrated under regularization results indicating the less stable parameter estimation than GCV. 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.