title: Fast Steerable Principal Component Analysis.
abstract: Cryo-electron microscopy nowadays often requires the analysis of hundreds of thousands of 2-D 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 2-D images, and, for each image, the set of its uniform rotations in the plane and their reflections. For a dataset consisting ofnimages of sizeL×Lpixels, the computational complexity of our algorithm isO(nL3+L4), while existing algorithms takeO(nL4). The new algorithm computes the expansion coefficients of the images in a Fourier-Bessel basis efficiently using the nonuniform fast Fourier transform. We compare the accuracy and efficiency of the new algorithm with traditional PCA and existing algorithms for steerable PCA.
authors: Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA.
authors: Zhizhen
authors: Z
authors: Zhao
authors: Department of Applied Mathematics, School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
authors: Yoel
authors: Y
authors: Shkolnisky
authors: Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544 USA.
authors: Amit
authors: A
authors: Singer
keywords: Steerable PCA; denoising; group invariance; non-uniform FFT