基于贝叶斯理论和时空约束的脑电源成像方法研究

发布时间：2018-04-25 09:35

本文选题：EEG源成像 + 贝叶斯概率框架　；参考：《华南理工大学》2016年博士论文

【摘要】：脑电图(electroencephalography,EEG)是一种重要的脑功能成像技术。EEG具有诸多优势,比如无创性、无放射性、高时间分辨率和经济性。因此,EEG已在认知神经科学和临床上有着广泛的应用。根据头皮记录的EEG信号重构皮层脑活动称为EEG源成像。准确估计脑活动的位置和尺寸有助于我们理解认知过程的基本机理以及脑损伤的病理学特征。在临床上,比如癫痫治疗,准确确定病灶的位置和尺寸对手术治疗有着重要的意义。EEG源成像是一个严重病态的问题,存在无穷多解满足EEG记录。因此我们需要先验假设约束解空间以得到唯一解。传统的方法包括基于2范数约束和基于稀疏约束的源成像方法。然而,基于2范数约束的源成像方法的结果相比于“真相”过于弥散,且对源尺寸不敏感。与此相反,基于稀疏约束的源成像算法的结果过度局灶性,不能重构弥散源的尺寸。准确重构弥散源的位置和尺寸依然是一个极具挑战的问题。由于EEG信号中具有丰富的时域信息,许多研究已证明利用EEG信号中的时域信息能提高源成像的性能。本文在贝叶斯概率框架下,根据时域-空域先验约束,利用贝叶斯推断和凸优化技术,研究EEG弥散源成像算法,以更准确的重构脑活动。本文的主要贡献如下:1.基于贝叶斯概率框架,提出了基于状态空间表达式的EEG源成像方法:时空正则化EEG弥散源成像算法(spatio-temporally regularized algorithm for M/EEG patch source imaging,STRAPS)。该方法利用一个多变量自回归模型表示源信号在时间和空间上的相关性。考虑到卡尔曼滤波器在存储和计算上的挑战,STRAPS利用递推最小二乘法计算源信号的近似解。相比于传统方法,STRAPS能更准确的估计弥散源的位置、尺寸和波形。与类似的模型相比,STRAPS在获得较满意的估计同时具有更低的计算复杂度和存储需求。2.在经验贝叶斯框架下,提出了基于马尔科夫随机场和时间基函数的源成像算法:贝叶斯弥散源电磁时空成像(Bayesian Electromagnetic Spatio-Temporal Imaging of Extended Sources,BESTIES)。BESTIES利用马尔科夫随机场表示源在空间上的相互关系,在时间上假设源信号是若干时间基函数的线性组合。利用变分贝叶斯推断和凸优化技术,得到了一个数据自驱动的源成像算法。MRF参数和时间基函数对源信号的贡献完全由EEG数据确定。与传统的基于2范数和稀疏约束的算法,BESTIES得到更准确的脑活动空间和时间模态估计。3.基于贝叶斯概率框架,提出了基于差分域稀疏和时间基函数的源成像算法:基于条件均值的差分域稀疏的弥散源成像(Variation Sparse Source Imaging based on Conditional Mean for Electromagnetic Extended Sources,VSSI-CM)。VSSICM利用源信号在差分域(相邻源之间的差)上的稀疏性,重构弥散源的尺寸。在时域上,将EEG记录和源信号同时投影到由若干时间基函数构成的子空间。VSSI-CM利用Laplace先验分布实现源信号在差分域上的稀疏。与传统的MAP估计不同,VSSI-CM将后验均值作为源信号估计。利用凸分析,将Laplace分布表示为不同尺度的高斯分布的上界。同时利用双环算法,得到一个完全数据自驱动的算法。实验结果显示,相比于传统方法,VSSI-CM能更准确的估计皮层活动的位置和尺寸。同时,VSSI-CM也得到比MAP估计更好的重构结果。4.基于经验贝叶斯框架,提出了基于矩阵分解的源成像算法框架:基于时空基函数的源成像算法(Spatio-Temporal Basis Functions Source Imaging,STBFSI)。STBFSI将源信号分解为若干未知的时间基函数的线性叠加。在空间上,利用经验贝叶斯框架,假设源信号的协方差是若干协方差基的加权和。利用自相关决策(automatic relevance determination,ARD)机制,根据EEG信号自动确定与源信号相关的空间协方差基、时间基函数的数目以及各自的波形。STBFSI提供了一个基于时间-空间约束的源成像算法的框架,使得能够很灵活的利用其他成像模态(比如f MRI)的信息。
[Abstract]:Electroencephalography (EEG) is an important brain functional imaging technique,.EEG has many advantages, such as noninvasive, non radioactive, high time resolution and economy. Therefore, EEG has been widely used in cognitive neuroscience and clinic. The reconstruction of cortical brain activity based on the EEG signal of the scalp is called EEG source imaging. Accurate estimation of the location and size of brain activity helps us to understand the basic mechanism of the cognitive process and the pathological features of brain damage. In clinical, such as epilepsy treatment, the exact location and size of the lesion is of great significance to the surgical treatment..EEG source imaging is a severe and ill conditioned problem, and there is an infinite number of solutions that satisfy the EEG record. So we need a priori hypothesis constrained solution space to obtain unique solutions. The traditional methods include 2 norm constraint based and sparse constraint based source imaging methods. However, the result of the source imaging method based on the 2 norm constraint is too diffuse and insensitive to the source size. The results of the imaging algorithm are overly localized and can not reconstruct the size of the dispersion source. It is still a very challenging problem to reconstruct the location and size of the dispersion source accurately. Because of the rich time domain information in the EEG signal, many studies have proved that the performance of the high source imaging can be proposed by using the time domain information in the EEG signal. Under the frame, the EEG dispersion source imaging algorithm is studied using Bayesian inference and convex optimization techniques to reconstruct brain activity more accurately. The main contributions of this paper are as follows: 1. based on Bayesian probability framework, a EEG source imaging method based on state space expression is proposed: spatio-temporal regularized EEG dispersion imaging algorithm (SP Atio-temporally regularized algorithm for M/EEG patch source imaging, STRAPS). This method uses a multivariable autoregressive model to express the correlation between source signals in time and space. Considering the challenge of Calman filter in storage and computing, STRAPS uses recursive least squares to calculate the approximate solution of source signals. The traditional method, STRAPS can more accurately estimate the location, size and waveform of the dispersion source. Compared with the similar model, STRAPS obtains a more satisfactory estimate and has lower computational complexity and storage requirements.2. under the empirical Bias framework, a source imaging algorithm based on Markov random field and time base function is proposed: Bias The dispersion source electromagnetic spatiotemporal imaging (Bayesian Electromagnetic Spatio-Temporal Imaging of Extended Sources, BESTIES).BESTIES uses the Markov random field to express the relationship between the source and the space. In time, the source signal is assumed to be a linear combination of some time base functions. The contribution of.MRF parameter and time base function to source signal is completely determined by EEG data. With the traditional algorithm based on 2 norm and sparse constraint, BESTIES obtains more accurate brain activity space and time mode estimation.3. based on Bayesian probability frame, and proposes a sparse and time base based on the difference domain. The source imaging algorithm of a function: Variation Sparse Source Imaging based on Conditional Mean for Electromagnetic Extended Sources, based on conditional mean values, reconstruct the size of the dispersion source using the sparsity of the source signal on the difference domain (the difference between the adjacent sources). The G record and the source signal are projected simultaneously to the subspace.VSSI-CM composed of several time base functions. The Laplace prior distribution is used to realize the sparsity of the source signal in the difference domain. Unlike the traditional MAP estimation, VSSI-CM takes the posterior mean as the source signal estimation. Using the convex analysis, the Laplace distribution is represented as the upper bound of the Gauss distribution of different scales. At the same time, a complete data self driving algorithm is obtained by using the double loop algorithm. The experimental results show that VSSI-CM can estimate the location and size of cortical activity more accurately than the traditional method. At the same time, VSSI-CM also gets better reconstruction result than MAP estimation..4. based on the empirical Bayesian framework, the source imaging based on matrix decomposition is proposed. The framework: Spatio-Temporal Basis Functions Source Imaging (STBFSI).STBFSI based on space-time basis function (Imaging, STBFSI).STBFSI decomposes the source signal into a linear superposition of a number of unknown time base functions. In space, the empirical Bayesian framework is used to assume that the co variance of the source signal is the weighted sum of some covariance bases. The automatic relevance determination (ARD) mechanism automatically determines the spatial covariance base related to the source signal according to the EEG signal. The number of time base functions and the respective waveform.STBFSI provide a framework for the source imaging algorithm based on time space constraints, so that other imaging modalities can be used flexibly (such as f MRI). Information.

【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：R741.044

【相似文献】