诱发电位反卷积技术的不适定问题及正则化解决方法

连续循环平均反卷积 (Continuous loop averaging deconvolution, CLAD) 是近年来用于提取高刺激率模式下听觉诱发电位(Audi t ory evoked potential, AEP)的一种行之有效的方法。但是，CLAD方法在频率域求解时，对 刺 激序列的频谱特性有严格的限制，给应用带来不便和局限。本文提出一种在时域实现反卷积 的方法，将其转化为线性变换矩阵的逆滤波处理。并且利用奇异值分解分析了由不良序列带 来的不适定问题，引入正则化技术改善病态矩阵对重建结果的影响。最后比较了若干种 典型刺激序列和不同噪声条件下AEP的恢复实验，结果表明本方法可以较好地解决不良序列 和一般噪声水平条件下暂态AEP信号的恢复重建。

Regularizatio n Solution to Ill posedness of Deconvolution Technique for Evoked Potentials

Continuous loop averaging deconvolution (CLAD) is a recently developed method to restore t he auditory evoked potential (AEP) under high stimulus rate condition. This meth od solves the deconvolution problem in frequency domain for computational effici ency, but suffers from stringent limitation in selecting a stimulus sequence wit h required spectral property. Hereby we propose a new method to solve the decon volution problem in time domain by constructing a linear transform matrix to mod el the convolution process. To understand the AEP distortion caused by the ill posed matrix generated from a bed stimulus sequence, we assess the matrix prope rty using singular value decomposition (SVD) technique and introduce Tikhonov r egularization method to deal with the ill posedness. In the stimulation experim e nt, we compare some typical sequences with different ill posedness conditions a nd restore the transient AEPs under various noise levels. These results justify the proposed approach to the AEP deconvolution with less restriction on the s equence selection.