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    Fast Steerable Principal Component Analysis

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    Cryo-electron microscopy nowadays often requires the analysis of hundreds of thousands of 2D images as large as a few hundred pixels in each direction. Here we introduce an algorithm that efficiently and accurately performs principal component analysis (PCA) for a large set of two-dimensional images, and, for each image, the set of its uniform rotations in the plane and their reflections. For a dataset consisting of nn images of size L×LL \times L pixels, the computational complexity of our algorithm is O(nL3+L4)O(nL^3 + L^4), while existing algorithms take O(nL4)O(nL^4). The new algorithm computes the expansion coefficients of the images in a Fourier-Bessel basis efficiently using the non-uniform fast Fourier transform. We compare the accuracy and efficiency of the new algorithm with traditional PCA and existing algorithms for steerable PCA
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