Functional magnetic resonance imaging (fMRI) data are originally acquired as complex-valued images, which motivates the use of complex-valued data analysis methods. Due to the high dimension and high noise level of fMRI data, order selection and dimension reduction are important procedures for multivariate analysis methods such as independent component analysis (ICA). In this work, we develop a complex-valued order selection method to estimate the dimension of signal subspace using information-theoretic criteria. To correct the effect of sample dependence to information-theoretic criteria, we develop a general entropy rate measure for complex Gaussian random process to calibrate the independent and identically distributed (i.i.d.) sampling scheme in the complex domain. We show the effectiveness of the approach for order selection on both simulated and actual fMRI data. A comparison between the results of order selection and ICA on real-valued and complex-valued fMRI data demonstrates that a fully complex analysis extracts more information about brain activation.

中文翻译：

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复值 FMRI 数据的线性混合模型的阶次选择。

功能磁共振成像 (fMRI) 数据最初是作为复值图像获取的，这激发了复值数据分析方法的使用。由于 fMRI 数据的高维和高噪声水平，顺序选择和降维是多变量分析方法（如独立成分分析（ICA））的重要步骤。在这项工作中，我们开发了一种复值阶数选择方法来使用信息论标准估计信号子空间的维度。为了纠正样本依赖对信息论标准的影响，我们为复杂的高斯随机过程开发了一种通用的熵率度量，以校准复杂域中的独立同分布 (iid) 采样方案。我们展示了该方法对模拟和实际 fMRI 数据的顺序选择的有效性。顺序选择和 ICA 对实值和复值 fMRI 数据的比较表明，完全复杂的分析可以提取更多有关大脑激活的信息。