Work

Fast Steerable Principal Component Analysis

Year: 2016

Type: article

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 of n images of size L × L pixels, the computational complexity of our algorithm is O(nL3+ L4), while existing algorithms take O(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.

Source: IEEE Transactions on Computational Imaging

DOI: 10.1109/tci.2016.2514700

Authors: Zhizhen Zhao, Yoel Shkolnisky, Amit Singer

Institutions: Courant Institute of Mathematical Sciences, New York University, Tel Aviv University, Princeton University

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Simons Foundation, Gordon and Betty Moore Foundation, Israel Science Foundation, National Institute of General Medical Sciences

Awards: G2911566336, Improved Algorithms for Macromolecular Structure Determination by cyro-EM, G4608464917, G7483473437