Fast Steerable Principal Component Analysis
This is an incremental improvement for researchers in cryo-electron microscopy, enabling faster analysis of large image datasets.
The paper tackles the computational bottleneck of performing principal component analysis (PCA) on large sets of 2D cryo-electron microscopy images, introducing an algorithm that reduces complexity from O(nL^4) to O(nL^3 + L^4) while maintaining accuracy.
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.