内源光学功能成像数据的时空分析研究
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摘要
本文对内源光学数据的时空分析方法及低频自发振荡信号的时空模式做了深入研究。
提出了利用时间兼空间结构信息进行脑成像数据盲源信号分离的思想。其基本假设为:相对于噪声,感兴趣信号无论在时间上还是在空间上变化都较为平滑,即一个小的邻域内的采样点数值上相近。在此思想下,设计了包含时间兼空间邻域特征的目标函数,并给出了令该目标函数最大化的解析求解公式,将其归结为一个特征向量求解问题。在实现上述思想的过程中,主要解决了三个具体问题:(a)构建了一个新的指标来定义时间信号源的空间分布图,这使得数学上量化描述时间信号源的空间邻域特征成为可能;(b)提出了一种最大化信号自相关系数的新的实现手段,使推导过程摆脱了“延迟协方差矩阵对称条件”;(c)利用奇异值分解工具,提出了不损失信息的条件下低维度实现时间分析的流程,该流程既可以用来低维度实现上述目标函数的求解,也可以用来改进传统时间分析方法,在不降维的条件下降低其时间复杂度。
在时间盲信号分离过程中引入直接图像投影技术。对直接图像投影技术进行了矩阵形式的描述,并从时间/空间分析的角度出发,揭示了它与时间分析、空间分析手段的联系与区别。提出了“广义时间序列”的概念,“广义时间序列”的样本之间既包含时间轴的信息,又包含空间上行或列内的信息,所以可以同时定义“广义时间序列”的时间邻域特征和空间邻域特征,这使得从另外一个角度最大化时间兼空间邻域特征成为可能。
研究了内源光学成像手段在人脑研究应用中的重要问题——皮层运动的消除。提出了对标志点进行分组弱化的薄板样条算法对皮层图像序列进行配准。使用薄板样条插值函数拟合形变函数的过程中弱化标志点约束条件,允许标志点与匹配点之间存在一定误差。结合标志点定位精度的量化衡量技术,对标志点按定位精度分组,并对不同组的标志点以不同的权值进行弱化。定义了衡量图像配准效果的代价函数,通过最小化该代价函数确定各组的权值。
利用盲源分离技术和傅立叶谱分析手段对低频自发振荡信号的时空特性进行研究,发现了刺激调制下该信号幅度增强、相位跳变和空间趋于同步的现象,尽我们所知,此现象在国内外尚未有报道。并据上述现象探讨了低频自发振荡信号的形成机理,提出了如下观点:细小动脉的舒缩对绿光(~546nm,下同)下皮层中的自发振荡贡献很大。根据振荡信号在动静脉和皮层的相位差别特点,得出以下结论:红光(~605nm)下的相位差反应了代谢产物在动静脉中的流动方向和路径。绿光下没有明显的相位差可能源于在血管处采集的振荡信号与皮层处采集的振荡信号的形成机理存在不同。
This dissertation is focused on the spatial/temporal analysis methods for intrinsic optical imaging dataset and their applications in spatio-temporal pattern analysis of spontaneous low frequency oscillations.
In blind separation of brain mapping signals, the spatial plus temporal structure information is utilized. It is assumed that the interesting signals alter smoothly cross both space and time, i.e. the neighboring sample-points are similar. Then the object function which quantifies and integrates temporal and spatial structure information is defined and maximized. Three problems are solved in this procedure. (a) A new definition of the spatial pattern of a temporal signal is given. This makes it possible to quantify the spatial structure information for a temporal source. (b) A novel method for maximizing autocorrelation is proposed. Unlike traditional methods, it does not rely on the so-called“symmetry assumption for delayed/shifted covariance matrix”. (c) A low dimensional procedure for temporal analysis is developed. It could be applied to any traditional temporal analysis methods and reduce their computational complexity without losing any information.
The straightforward image projection technique is introduced into the temporal source separation. By represented it in the matrix format, the differences and relationship between this technique and the temporal/spatial analysis are revealed. It is indicated that the straightforward image projection technique performs the data analysis from a novel viewpoint by traditional procedure. The concept of“generalized timecourse”is proposed. Because there are both temporal and spatial relationships among the sample points in one“generalized timecourse”, it is possible to define temporal plus spatial structure information and maximize it.
The critical problem in OI for human brain, the cortex movement reduction, is also studied in this dissertation. A new cortex image registration algorithm based on thin-plate splines is proposed. In the splines interpolation, the point constraints are weakened and the interpolation function needs not to exactly go through the landmarks. Based on estimating the localization accuracy of each landmark, all landmarks are categorized into several groups. Each group is weakened by different weight values. A cost function which quantifies the registration errors is given, and the weight values are decided by minimizing this cost function.
By the blind source separation method and Fourier spectrum analysis technique, the spatio-temporal pattern of spontaneous low frequency oscillations is studied. After the electrical stimulation, it is observed that the phases of the LFO signals are changed, the amplitudes are increased, and most importantly, the signals in the bilateral somatosensory cortex tend to be synchronized. Based on these phenomena, the origin of the LFO signals is discussed. It is argued that the arteriole vasomotion may be the major contribution to the LFO signals under green illumination (~546nm). The phase relationship among the LFO signals of arteries, veins and cortex is also studied. Based on the phase relationship under red/green illumination, it is suggested that remarkable phase difference at ~605nm shows the motion of deoxy-hemoglobin and none phase difference at ~546nm may imply different mechanism of the LFO signals of cortexes and vessels.
提出了利用时间兼空间结构信息进行脑成像数据盲源信号分离的思想。其基本假设为:相对于噪声,感兴趣信号无论在时间上还是在空间上变化都较为平滑,即一个小的邻域内的采样点数值上相近。在此思想下,设计了包含时间兼空间邻域特征的目标函数,并给出了令该目标函数最大化的解析求解公式,将其归结为一个特征向量求解问题。在实现上述思想的过程中,主要解决了三个具体问题:(a)构建了一个新的指标来定义时间信号源的空间分布图,这使得数学上量化描述时间信号源的空间邻域特征成为可能;(b)提出了一种最大化信号自相关系数的新的实现手段,使推导过程摆脱了“延迟协方差矩阵对称条件”;(c)利用奇异值分解工具,提出了不损失信息的条件下低维度实现时间分析的流程,该流程既可以用来低维度实现上述目标函数的求解,也可以用来改进传统时间分析方法,在不降维的条件下降低其时间复杂度。
在时间盲信号分离过程中引入直接图像投影技术。对直接图像投影技术进行了矩阵形式的描述,并从时间/空间分析的角度出发,揭示了它与时间分析、空间分析手段的联系与区别。提出了“广义时间序列”的概念,“广义时间序列”的样本之间既包含时间轴的信息,又包含空间上行或列内的信息,所以可以同时定义“广义时间序列”的时间邻域特征和空间邻域特征,这使得从另外一个角度最大化时间兼空间邻域特征成为可能。
研究了内源光学成像手段在人脑研究应用中的重要问题——皮层运动的消除。提出了对标志点进行分组弱化的薄板样条算法对皮层图像序列进行配准。使用薄板样条插值函数拟合形变函数的过程中弱化标志点约束条件,允许标志点与匹配点之间存在一定误差。结合标志点定位精度的量化衡量技术,对标志点按定位精度分组,并对不同组的标志点以不同的权值进行弱化。定义了衡量图像配准效果的代价函数,通过最小化该代价函数确定各组的权值。
利用盲源分离技术和傅立叶谱分析手段对低频自发振荡信号的时空特性进行研究,发现了刺激调制下该信号幅度增强、相位跳变和空间趋于同步的现象,尽我们所知,此现象在国内外尚未有报道。并据上述现象探讨了低频自发振荡信号的形成机理,提出了如下观点:细小动脉的舒缩对绿光(~546nm,下同)下皮层中的自发振荡贡献很大。根据振荡信号在动静脉和皮层的相位差别特点,得出以下结论:红光(~605nm)下的相位差反应了代谢产物在动静脉中的流动方向和路径。绿光下没有明显的相位差可能源于在血管处采集的振荡信号与皮层处采集的振荡信号的形成机理存在不同。
This dissertation is focused on the spatial/temporal analysis methods for intrinsic optical imaging dataset and their applications in spatio-temporal pattern analysis of spontaneous low frequency oscillations.
In blind separation of brain mapping signals, the spatial plus temporal structure information is utilized. It is assumed that the interesting signals alter smoothly cross both space and time, i.e. the neighboring sample-points are similar. Then the object function which quantifies and integrates temporal and spatial structure information is defined and maximized. Three problems are solved in this procedure. (a) A new definition of the spatial pattern of a temporal signal is given. This makes it possible to quantify the spatial structure information for a temporal source. (b) A novel method for maximizing autocorrelation is proposed. Unlike traditional methods, it does not rely on the so-called“symmetry assumption for delayed/shifted covariance matrix”. (c) A low dimensional procedure for temporal analysis is developed. It could be applied to any traditional temporal analysis methods and reduce their computational complexity without losing any information.
The straightforward image projection technique is introduced into the temporal source separation. By represented it in the matrix format, the differences and relationship between this technique and the temporal/spatial analysis are revealed. It is indicated that the straightforward image projection technique performs the data analysis from a novel viewpoint by traditional procedure. The concept of“generalized timecourse”is proposed. Because there are both temporal and spatial relationships among the sample points in one“generalized timecourse”, it is possible to define temporal plus spatial structure information and maximize it.
The critical problem in OI for human brain, the cortex movement reduction, is also studied in this dissertation. A new cortex image registration algorithm based on thin-plate splines is proposed. In the splines interpolation, the point constraints are weakened and the interpolation function needs not to exactly go through the landmarks. Based on estimating the localization accuracy of each landmark, all landmarks are categorized into several groups. Each group is weakened by different weight values. A cost function which quantifies the registration errors is given, and the weight values are decided by minimizing this cost function.
By the blind source separation method and Fourier spectrum analysis technique, the spatio-temporal pattern of spontaneous low frequency oscillations is studied. After the electrical stimulation, it is observed that the phases of the LFO signals are changed, the amplitudes are increased, and most importantly, the signals in the bilateral somatosensory cortex tend to be synchronized. Based on these phenomena, the origin of the LFO signals is discussed. It is argued that the arteriole vasomotion may be the major contribution to the LFO signals under green illumination (~546nm). The phase relationship among the LFO signals of arteries, veins and cortex is also studied. Based on the phase relationship under red/green illumination, it is suggested that remarkable phase difference at ~605nm shows the motion of deoxy-hemoglobin and none phase difference at ~546nm may imply different mechanism of the LFO signals of cortexes and vessels.
引文
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