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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 $n$ images of size $L times L$ pixels, the computational complexity of our algorithm is $O(nL^3 + L^4)$, while existing algorithms take $O(nL^4)$. 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.
We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few calls to any b
This paper describes a fast and accurate method for obtaining steerable principal components from a large dataset of images, assuming the images are well localized in space and frequency. The obtained steerable principal components are optimal for ex
Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting underlyin
Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in some fiel
We consider the problem of principal component analysis from a data matrix where the entries of each column have undergone some unknown permutation, termed Unlabeled Principal Component Analysis (UPCA). Using algebraic geometry, we establish that for