Principal Component Analysis as a Tool for Characterizing Black Hole Images and Variability
Principal Component Analysis as a Tool for Characterizing Black Hole Images and Variability
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DOI：
10.3847/1538-4357/aad37a
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发表时间：
2018-04
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影响因子：
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通讯作者：
L. Medeiros;T. Lauer;D. Psaltis;F. Özel
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文献类型：
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作者：
L. Medeiros;T. Lauer;D. Psaltis;F. Özel
我们探讨使用主成分分析（PCA）来表征高保真度模拟和干涉观测的毫米辐射，起源于附近的吸积黑洞的视野。我们从数学上表明，PCA应用到空间域中的图像的合奏的特征图像的傅里叶变换是相同的PCA的特征向量应用到图像的傅里叶变换的合奏，这表明这种方法可以应用到建模的稀疏干涉傅里叶-维尤产生的阵列，如事件地平线望远镜。我们还表明，在空间域中的模拟本身可以用PCA衍生的特征图像的基础来表示，这允许变量观测和时间相关模型之间进行详细的比较，以及在图像的时间序列中检测异常值或罕见事件。此外，我们证明了PCA特征值的频谱是结构的功率谱的诊断，因此，在模拟和观察到的图像中的基本物理过程。
We explore the use of principal component analysis (PCA) to characterize high-fidelity simulations and interferometric observations of the millimeter emission that originates near the horizons of accreting black holes. We show mathematically that the Fourier transforms of eigenimages derived from PCA applied to an ensemble of images in the spatial domain are identical to the eigenvectors of PCA applied to the ensemble of the Fourier transforms of the images, which suggests that this approach may be applied to modeling the sparse interferometric Fourier-visibilities produced by an array such as the Event Horizon Telescope. We also show that the simulations in the spatial domain can themselves be compactly represented with a PCA-derived basis of eigenimages, which allows for detailed comparisons to be made between variable observations and time-dependent models, as well as for detection of outliers or rare events within a time series of images. Furthermore, we demonstrate that the spectrum of PCA eigenvalues is a diagnostic of the power spectrum of the structure and, hence, of the underlying physical processes in the simulated and observed images.