大脑是一个极为精巧和完善的信息处理系统，大脑中信息的载体是神经元发放的放电信号。通常由电极记录到的信号包含不止一个神经元的放电，因此需要把来自不同神经元的放电波形分离开来，这在脑科学的许多研究中都是首先要解决的一个问题。本论文针对神经元放电检测与聚类研究中的几个难点问题，研究了相应的解决方案。 在信噪比较低的情况下，现有的神经元放电检测算法的性能受到很大影响。本论文首先采用数学形态学峰-谷提取算子对细胞外记录的放电信号进行预处理，然后再通过阈值交叉把神经元放电检测出来。对神经元放电的仿真数据和实验记录的数据的检测结果都表明，采用数学形态学预处理可以降低放电检测的错误率。 小波变换已经被广泛应用来提取神经元放电的特征，但是放电信号经过小波变换后，不同类别之间的差异信息可能分布在不同频率范围的多个小波系数上，如何把这些差异较大的小波系数选出来也是一个非常关键的问题。本论文借用核密度估汁的方法来估计小波系数的分布，并进一步求出该分布的峰的个数。那些分布中有两个或多个峰、并且各个峰之间距离较远的小波系数是最有代表性的特征。应用模糊C均值方法对选出来的小波系数进行聚类，结果表明使用核密度估计的方法能优先把最有代表性的特征挑选出来。 多小波是传统的单小波的一个直接推广，它在信号去噪、数据压缩方面都已展现出较大的优势。本论文针对在低信噪比情况下由小波变换得到的神经元放电的特征区分度不高的问题，用多小波变换代替小波变换来提取神经元放电波形的特征。利用基于单链临近度准则的分层聚类算法来解决小波/多小波特征系数所形成的狭长簇分布的问题，并采用了一个离群点移除过程来处理那些由混叠在一起的神经元放电波形导致的异常点。对仿真数据的聚类结果表明多小波比单小波特征提取的效果要好。 关键词：神经元放电波形分离；数学形态学；核密度估计；多小波变换；分层聚类

 The brain is an extremely sophisticated and comprehensive information processing system. Spikes fired by neurons are the carrier of information in the brain. As the signals recorded by an electrode contain spikes emitted by more than one neuron, it is an indispensable step in many neuroscience researches to assign these spikes to their producing neurons. In this thesis, we provide corresponding solutions to several problems occurring in the neural spike detection and clustering research. As the performance of available neural spike detection algorithms deteriorates in low signal-noise-ratio cases, we firstly adopt a peak-valley-extractor in mathematical morphology to preprocess the signals recorded extracellularly, and then detect the spike event by threshold crossing. Simulated neural spike data and experimentally recorded data are used to test this spike detect algorithm, and the results prove that the preprocessing procedure can reduce error rate in detection. Wavelet transform has been widely used in extracting features of neuronal spikes. However, as the dissimilar information of different spike shapes may be distributed in several disorderly wavelet coefficients, it is very important to select the most discriminative wavelet coefficients feature. We use kernel density estimation to get an estimated distribution of wavelet coefficients, and then find the number of modes in that distribution. Those bimodal or multimodal distributions with a further distance between these modes are selected as representative features. After the clustering procedure by fuzzy C means, the results suggest that kernel density estimation based feature selection method is effective in that it selects the most distinguished features. As a direct extension of traditional wavelet, multiwavelets has demonstrated advantages in signal denoising and data compression. Considering the wavelet coefficients features are not so discriminative in heavy noises cases, we employ multiwavelets transform to extract features of neuronal spikes. Hierarchical clustering using the single linkage rule is adopted to resolve the elongated cluster formed by wavelet / multiwavelets coefficients features. An outlier removal process is designed by discarding those anomaly samples resulted from overlapping spikes. The clustering results for simulated spike data prove multiwavelets outperforms wavelet as a feature extraction method. Key words: neuronal spike sorting; mathematical morphology; kernel density estimation; multiwavelets transform; hierarchical clustering