Computing Steerable Principal Components of a Large Set of Images and Their Rotations
Computing Steerable Principal Components of a Large Set of Images and Their Rotations
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DOI：
10.1109/tip.2011.2147323
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发表时间：
2011-11-01
影响因子：
10.6
通讯作者：
Singer, Amit
中科院分区：
文献类型：
--
作者：
Ponce, Colin;Singer, Amit
我们在这里提出了一个有效的算法来计算主成分分析（PCA）的一个大的图像集，包括图像，并为每个图像，其在平面上的均匀旋转的集合。我们通过指出协方差矩阵的块循环结构并利用该结构计算其特征向量来做到这一点。通过数值实验，我们也证明了该算法相对于同类算法的优点。虽然它是有用的，在许多设置中，我们说明了该算法的问题的冷冻电子显微镜的具体应用。
We present here an efficient algorithm to compute the Principal Component Analysis (PCA) of a large image set consisting of images and, for each image, the set of its uniform rotations in the plane. We do this by pointing out the block circulant structure of the covariance matrix and utilizing that structure to compute its eigenvectors. We also demonstrate the advantages of this algorithm over similar ones with numerical experiments. Although it is useful in many settings, we illustrate the specific application of the algorithm to the problem of cryo-electron microscopy.