Many brain imaging modalities reveal interpretable patterns after the data dimensionality is reduced and summarized via data-driven approaches. In functional magnetic resonance imaging (fMRI) studies, such summarization is often achieved through independent component analysis (ICA). ICA transforms the original data into a relatively small number of interpretable bases in voxel space (referred to as ICA spatial components, or spatial maps) and corresponding bases in the time domain (referred to as time-courses of corresponding spatial maps) In this work, we use the word “basis” to broadly refer to either of the two factors resulting from the transformation. A precise summarization for fMRI requires accurately detecting co-activation of voxels by measuring temporal dependence. Accurate measurement of dependence requires a proper understanding of the underlying temporal characteristics of the data. One way to understand such characteristics is to study the frequency spectrum of fMRI data. Researchers have argued that information regarding the underlying neuronal activity might be spread over a range of frequencies as a result of the heterogeneous temporal nature of the neuronal activity, which is reflected in its frequency spectrum. Many studies have accounted for heterogeneous characteristics of the frequency of the signal by either directly inspecting the contents of frequency domain-transformed data or augmenting their analyses with such information. For example, studies on fMRI data have investigated brain functional connectivity by leveraging frequency-adjusted measures of dependence (e.g., when a correlation is measured as a function of frequency, as with “coherence”). Although these studies measure dependence as a function of frequency, the formulation does not capture all characteristics of the frequency-based dependence. Incorporating frequency information into a summarization approach would enable the retention of important frequency-related information that exists in the original space but might be lost after performing a frequency-independent summarization. We propose a novel data-driven approach built upon ICA, which is based on measuring dependence as a generalized function of frequency. Applying this approach to fMRI data provides evidence of existing cross-frequency functional connectivity between different areas of the brain.

中文翻译：

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静息态 fMRI 数据的频率感知汇总

在通过数据驱动的方法减少和汇总数据维度后，许多大脑成像模式揭示了可解释的模式。在功能磁共振成像 (fMRI) 研究中，这种总结通常是通过独立成分分析 (ICA) 实现的。ICA 将原始数据转换为体素空间中相对较少的可解释基数（称为 ICA 空间分量，或空间图）和时域中的相应基数（称为相应空间图的时间进程）在这项工作中，我们使用“基础”一词来泛指由转换产生的两个因素中的任何一个。fMRI 的精确总结需要通过测量时间依赖性来准确检测体素的共激活。准确测量相关性需要正确理解数据的潜在时间特征。了解这些特征的一种方法是研究 fMRI 数据的频谱。研究人员认为，由于神经元活动的异质时间性质（反映在其频谱中），有关潜在神经元活动的信息可能会分布在一系列频率上。许多研究通过直接检查频域转换数据的内容或使用此类信息增强分析来解释信号频率的异质特征。例如，对 fMRI 数据的研究通过利用频率调整的依赖性测量（例如，当相关性被测量为频率的函数时，如“相干性”）。尽管这些研究将相关性作为频率的函数进行测量，但公式并未涵盖基于频率的相关性的所有特征。将频率信息合并到汇总方法中可以保留原始空间中存在的重要频率相关信息，但在执行与频率无关的汇总后可能会丢失。我们提出了一种基于 ICA 的新型数据驱动方法，该方法基于将依赖性测量为频率的广义函数。将这种方法应用于 fMRI 数据提供了大脑不同区域之间现有交叉频率功能连接的证据。尽管这些研究将相关性作为频率的函数进行测量，但公式并未涵盖基于频率的相关性的所有特征。将频率信息合并到汇总方法中可以保留原始空间中存在的重要频率相关信息，但在执行与频率无关的汇总后可能会丢失。我们提出了一种基于 ICA 的新型数据驱动方法，该方法基于将依赖性测量为频率的广义函数。将这种方法应用于 fMRI 数据提供了大脑不同区域之间现有交叉频率功能连接的证据。尽管这些研究将相关性作为频率的函数进行测量，但公式并未涵盖基于频率的相关性的所有特征。将频率信息合并到汇总方法中可以保留原始空间中存在的重要频率相关信息，但在执行与频率无关的汇总后可能会丢失。我们提出了一种基于 ICA 的新型数据驱动方法，该方法基于将依赖性测量为频率的广义函数。将这种方法应用于 fMRI 数据提供了大脑不同区域之间现有交叉频率功能连接的证据。将频率信息合并到汇总方法中可以保留原始空间中存在的重要频率相关信息，但在执行与频率无关的汇总后可能会丢失。我们提出了一种基于 ICA 的新型数据驱动方法，该方法基于将依赖性测量为频率的广义函数。将这种方法应用于 fMRI 数据提供了大脑不同区域之间现有交叉频率功能连接的证据。将频率信息合并到汇总方法中可以保留原始空间中存在的重要频率相关信息，但在执行与频率无关的汇总后可能会丢失。我们提出了一种基于 ICA 的新型数据驱动方法，该方法基于将依赖性测量为频率的广义函数。将这种方法应用于 fMRI 数据提供了大脑不同区域之间现有交叉频率功能连接的证据。