Fast steerable principal component analysis

Zhizhen Zhao, Yoel Shkolnisky, Amit Singer

Research output: Contribution to journalArticlepeer-review


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(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.
Original languageEnglish (US)
Pages (from-to)1-12
Number of pages12
JournalIEEE Transactions on Computational Imaging
Issue number1
StatePublished - 2016
Externally publishedYes


  • principal component analysis
  • algorithm design and analysis
  • computational complexity
  • noise reduction
  • Fourier transforms
  • microscopy
  • steerable PCA
  • group invariance
  • non-uniform FFT
  • denoising

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