# Fast Steerable Principal Component Analysis

arXiv: https://arxiv.org/abs/1412.0781 · HTML: https://mlsanity.com/paper/1412.0781/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2014.

## Built on by (most cited first, 12 of 12)

- [Ab-initio Contrast Estimation and Denoising of Cryo-EM Images](https://mlsanity.com/paper/2202.07737/) (2022)
- [Orthogonal Matrix Retrieval with Spatial Consensus for 3D Unknown-View Tomography](https://mlsanity.com/paper/2207.02985/) (2022)
- [An accelerated expectation-maximization algorithm for multi-reference alignment](https://mlsanity.com/paper/2105.07372/) (2021)
- [Fast expansion into harmonics on the disk: a steerable basis with fast radial convolutions](https://mlsanity.com/paper/2207.13674/) (2022)
- [G-invariant diffusion maps](https://mlsanity.com/paper/2306.07350/) (2023)
- [SO(3)-invariant PCA with application to molecular data](https://mlsanity.com/paper/2510.18827/) (2025)
- [An Adversarial Learning Based Approach for Unknown View Tomographic Reconstruction](https://mlsanity.com/paper/2108.09873/) (2021)
- [Probabilistic PolarGMM: Unsupervised Cluster Learning of Very Noisy Projection Images of Unknown Pose](https://mlsanity.com/paper/2206.12959/) (2022)
- [The G-invariant graph Laplacian](https://mlsanity.com/paper/2303.17001/) (2023)
- [Computerized Tomography and Reproducing Kernels](https://mlsanity.com/paper/2311.07465/) (2023)
- [Two Datasets Are Better Than One: Method of Double Moments for 3-D Reconstruction in Cryo-EM](https://mlsanity.com/paper/2511.07438/) (2025)
- [Group Invariant Spectral Embedding](https://mlsanity.com/paper/2607.08987/) (2026)

## Abstract (arXiv)

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 × 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 non-uniform fast Fourier transform. We compare the accuracy and efficiency of the new algorithm with traditional PCA and existing algorithms for steerable PCA.