Journal
IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING
Volume 2, Issue 1, Pages 1-12Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCI.2016.2514700
Keywords
Steerable PCA; group invariance; non-uniform FFT; denoising
Funding
- NIGMS [R01GM090200]
- Simons Foundation [LTR DTD 06-05-2012]
- Moore Foundation DDD Investigator Award
- Israel Science Foundation [578/14]
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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 x 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 nonuniform 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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