基于KPCA的fMRI信号生理噪声抑制方法

第四章 基于KPCA的fMRI信号生理噪声抑制方法

4.1 引言

　　基于CCA、ICA、PCA等生理噪声抑制方法，都可归类为线性噪声抑制方法。线性方法的前提假设是fMRI数据中的信号结构是线性的，即数据中BOLD信号子空间和噪声子空间基本线性可分。Rasmussen等人[41]利用KPCA对fMRI数据进行非线性分解后，发现数据中的信号呈现出一定的非线性结构。所以，通过线性的方法不一定能恢复噪声信号的完整结构。Song等人[39][40]提出了在KPCA分解的基础上利用频谱分析方法进行生理噪声的抑制，该方法在任务态和静息态的数据中都取得了明显的效果。但是Song的方法需要外部测量的心跳和呼吸数据作为先验知识，属于有监督方法。

　　基于前人的工作，本章提出了一种新的基于KPCA的非线性生理噪声抑制方法，该方法相对于文献[40]中的方法，不需要进行外部呼吸或心跳等数据的采集，属于无监督方法。该方法首先从脑脊液区域中，估计得到若干显著性的核主成分构成生理噪声子空间；然后，利用GLM方法对大脑灰质组织经过KPCA非线性分解得到的每一个成分，抑制其中生理噪声子空间相关部分。最后，基于经过噪声抑制后的成分进行KPCA非线性重构，得到噪声抑制后的数据。通过对真实fMRI数据的处理与分析，证明了所提出方法的有效性。

4.2 线性PCA的基本原理

　　PCA可以用来提取和构造数据中能量最高、方差最大的显著性成分。呼吸和心跳等生理活动相较于背景中的热噪声具有更高的能量，因而可以利用PCA来提取生理噪声成分。fMRI数据是一种四维数据，同时包含空间域和时间域的信息。通过PCA分解，可得到四维数据的空间坐标基和时间坐标基。选取这些坐标基中最显著的一些基组成一个子空间，然后将原始数据向此子空间投影，可以得到能量最大的信号源主成分。具体计算过程如下：

4.3 非线性KPCA的基本原理

　　KPCA属于流形学习领域的知识。降噪其实也是将受噪声干扰的数据投影到干净的信号流形中，让信号和噪声得以分离的过程。KPCA方法总结起来需要三步:第一步，使用非线性映射将输入体素空间中的数据映射到高维特征空间。第二步，假设在高维特征空间中信号流形是线性的，然后在此特征空间中利用线性PCA提取信号子空间。第三步，将提取出的特征信号子空间中的数据点重构回输入体素空间。具体计算上，KPCA是对传统线性PCA的非线性扩展。在特征空间执行线性PCA，相当于在输入空间执行非线性PCA：

4.4 fMRI信号中的GLM模型

式右端的生理正则项矩阵。最后，KPCA成分在经过噪声抑制后，需要进行估计重构，这里选取了Mika等人的方法，具体推导过程可参见文献[66]。

4.5 基于KPCA的生理噪声抑制方法模型

　　无监督生理噪声抑制方法一般需要考虑以下几个方面因素：一、受噪声干扰区域如何确定；二、如何从噪声干扰区域中估计和构造生理噪声子空间；三、采取何种机制对fMRI数据中的生理噪声进行抑制。首先针对前两个问题，这里采取的解决办法是利用PCA从脑脊液中提取若干显著性成分构造生理噪声子空间。之所以选取脑脊液作为噪声干扰区域，是因为脑脊液区域是大脑的非神经区域，会同时受到心脏和呼吸等噪声影响，基本没有与大脑皮质层神经活动相关的BOLD功能信号。针对第三个问题，这里先利用KPCA对fMRI灰质数据进行非线性分解，然后利用GLM方法对分解得到的每一个成分抑制生理噪声子空间相关部分，最后对噪声抑制后的成分进行估计重构。

　　




图4-1 KPCA生理噪声抑制方法流程图

4.6实验

　　此处实验数据利用了SPM官网提供的公共听觉数据集。该实验利用Siemens 2T扫描仪进行数据采集，数据的分辨率为，体素大小为,采集参数TR约为7s。针对一个单独的被试，共采集了96个时间点的数据。作为一个任务态的数据，每一个block占6个时间点，共有16个42秒的block。实验以连续的静息态和任务刺激交替切换进行。听觉刺激是在被试双耳边以每分钟60个的频率播放双音节单词。

4.6.1 实验数据的预处理

　　采集数据的预处理操作主要基于SPM8工具箱，包含如下步骤：(1)首先，对被试的功能像数据进行刚体头动矫正，在此过程中会得到一个头动矫正后的功能平均像；(2)对被试的结构像和功能平均像进行协配准；(3)对协配准后的结构像进行组织分割提取脑脊液模板；(4)对被试头动矫正后的功能像进行标准化；(5)对标准化后的功能像按照全宽半高为6的高斯核进行平滑。

4.6.2 实验结果的空间域分析

图4-2 噪声抑制前后特定脑区激活图对比。(a)噪声抑制前；(b)噪声抑制后。

　　在图4-2中可发现，经过噪声抑制后，绿色矩形框内的边缘叶（limbic lobe）部分的激活几乎被完全消除，而下叶（sub-lobar）区域的激活却有所增强。在原始数据中，将抑制的边缘叶部分体素提取出来，可以发现其与标准刺激范式波形的相关性偏低，如图4-3所示。



图4-3 被去除的下叶体素相较全部激活体素的相关系数对比

但是在空间整体特征上，去除的体素和增加的体素基本都是处于原有激活区边缘的一些体素，大部分激活体素的位置保持不变，如图4-4所示。图4-4中，蓝色区域为噪声抑制前后都判定为激活体素的区域，绿色区域为噪声抑制后由激活变为非激活的体素区域，而红色区域为新增加的激活体素区域。



　　图4-4听觉刺激试验激活图。图中蓝色区域为噪声抑制前后都判定为激活的体素(unchanged)，绿色区域为噪声抑制后由激活变为非激活的体素(removed)，而红色区域为新增加的激活体素(added)。

4.6.3 实验结果的时间域分析

　　评价任务态实验的分析效果时，可以通过比较提取得到的激活体素平均时间过程与实验标准刺激范式之间的相似度与相关性，来对噪声抑制效果进行评价。如图4-5(b)所示，可以发现经过噪声抑制后激活体素的平均时间过程和实验刺激范式波形相似度更高。并且，图4-5(b)中两波形的相关系数为0.6830，较之于图4-5(a)中未经噪声处理的两波形相关系数0.4627要高。由此可见，经过噪声处理之后激活体素时间过程和实验刺激范式拟合度更高。



　　图4-5 噪声抑制前后激活体素相似度与相关性对比。(a)噪声抑制前激活体素平均时间过程；(b)噪声抑制后激活体素平均时间过程；(c)噪声抑制后新增加激活体素平均时间过程对比。

　　统计发现，经过噪声抑制处理之后的所提取激活体素数目也发生了变化：从原有的激活体素中去除了120个体素，但是也增加了481个新的激活体素。这些增加和抑制体素的时间过程及空间位置有所差别。新增加的481个体素平均时间过程与实验范式波形的相关性由0.3222上升到0.6831。可以说明，噪声抑制之后提取激活体素的时间过程与刺激范式更相似。

　　并且，计算每个激活体素与实验刺激范式之间的相关系数可得到激活体素的相关系数分布直方图，如图4-6所示。在图4-6中，原始数据所提取激活体素的相关系数分布是一个以0.4为均值的正太分布。经过噪声抑制之后，相关系数分布整体向右倾斜，且分布更加集中，主要局限在0.5至0.7之间，与实验刺激范式相关性大的体素占整体大多数。



图4-6 噪声抑制前后激活体素时间过程与实验刺激范式相关系数分布

(a)噪声抑制前激活体素相关系数分布；(b)噪声抑制后激活体素相关系数分布。

4.7 本章小结

　　本章提出了一种新的基于KPCA的非线性生理噪声抑制方法。该方法相对于其他基于KPCA的生理噪声抑制方法，不需要进行外部呼吸或心跳等生理数据的采集，也不需要知道实验刺激范式等先验知识，可以灵活地融入到fMRI实验预处理环节中。在听觉数据中，噪声抑制后的SPM激活检测结果，证明了所提出方法的有效性及可靠性。

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