【作者】 徐鹏；

【导师】 尧德中；

【作者基本信息】 电子科技大学 ， 生物医学工程， 2006， 博士

【摘要】 稀疏性是度量构成信号的系数中非零分量数量的一个尺度。构成信号系数中的零分量越多，则该信号越稀疏。在很多场合下，都需要求取信号的稀疏表达或稀疏解。在本文中，围绕信号的稀疏特性在信号处理和脑电研究中的应用，对信号在过完备库中的稀疏表达特性进行了研究，改进了稀疏分解方法，并将稀疏性结合到脑电信号的处理和脑认知功能的研究中，发展了基于稀疏性的诱发脑电提取方法，发展了基于个体生理差异约束的稀疏分解去噪方法和具有稀疏性约束的脑电源定位方法。本文完成的主要工作如下： 1．基于匹配追踪方法，提出了一种能获得更加稀疏分解结果的双库匹配追踪方法(Two dictionaries matching pursuit，TDMP)，在该方法中，从对信号分解稀疏性的有利原则出发，在迭代过程中，将过完备库划分为新(未选择过的)、旧(已选择过的)原子库，通过引入退火降温阈值函数来约束迭代过程中最优原子的选择，使选择的最优原子比原始MP方法有更大的可能性落入对信号稀疏性有利的旧原子库中，从而实现对信号更加稀疏的分解。 2．改进了对l_p模约束问题的稀疏求解的优化策略，采用BFGS变尺度更新策略，和文献中常采用的牛顿下降方法比较，能在保持分解效果基本不变的前提下，有效的提高分解的效率。 3．基于脑电诱发电位(Eyoked potential，EP)和自发脑电等背景噪声在波形瞬态变化方面的差别，构造了小波和离散余弦的混合过完备库，利用MP方法在混合过完备库中的竞争学习，将瞬态信号和背景噪声近似在小波和离散余弦过完备库中分别表示出来，实现了多种情况下脑电诱发电位和背景噪声的分离。 4．提出了一种新的基于真实头模型的空间稀疏分解去噪方法。该方法考虑脑电信号产生的神经解剖生理机理，建立在头模型正演计算获得的传递矩阵过完备库基础上，利用匹配追踪方法(Matching pursuit，MP)或其它脑电源反演方法，把某一时刻记录的脑电空间电位分布分解为传递矩阵中的原子的稀疏组合近似或脑内的某种等效源分布，使保留下的信号成分和脑内源相关，从而实现对噪声的去除。 5．在FOCUSS算法迭代基础上，从脑神经活动的局部稀疏性出发，提出了一种更多还原

【Abstract】 Sparsity is to measure the number of null entries in the coefficients of a signal and alarger number of null entries avails for an sparser expression of signal. In manyscientific studies, it is necessary to decompose a signal sparsely or to solve a problemsparsely. The work in this dissertation is mainly expanded from the sparsity of the signaland its application in EEG problem. The work consists of two parts, one is focused onthe sparse expression of a signal, and the other is on the utilization of sparsity into EEGprocessing and EEG inverse problem. In the first part, mainly introduced is thedecomposition of a signal in an over-complete dictionary and one newly improvedsparse decomposition algorithm. In the work related with the neuro-physiological study,we mainly proposed such work as the way to evaluate the evoked potentials in themixed over-complete dictionary with sparse decomposition, a physiology dependentsparse decomposition method for EEG denoising and two EEG source imagingalgorithms combined with the sparsity of sources. The main work is as follows:1. Newly proposed is a modified MP method named two dictionaries MP (TDMP) todecompose signal more sparsely. In the iteration procedure of the two dictionariesMP, the over-complete dictionary is classified into two separate dictionaries withthe selected and unselected atoms, and in each iteration, the algorithm wasdesigned to have more chances than the original MP to choose the atom in theselected atom dictionary as the optimal atom by the constraint of a simulatedannealing threshold function, thus the algorithm avails for a more sparsedecomposition.2. Using the BFGS optimization strategy instead of the traditional Newton method to solve the l_p norm constrained sparse decomposition problem, which is often of large scale when decomposed in an over-complete dictionary. Compared with the usually adopted Newton descendent method, the solving based on BFGS can obviously improve the decomposition efficiency with a similar decomposition results.3. Based on the characteristic of signal to be evaluated, specifically designed a new method for the separation of a desired transient evoked potential (EP) from the更多还原