Fast Steerable Principal Component Analysis

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 its reflection. For a dataset consisting of $n$ images of size $L \times L$ pixels, the computational complexity of our algorithm is $O(nL^3+L^4)$ which is $L$ times faster than existing algorithms. The new algorithm computes the Fourier-Bessel expansion coefficients more efficiently than its predecessor Fourier-Bessel steerable PCA (FBsPCA) using the non-uniform FFT. We compare the accuracy and efficiency of the new algorithm with traditional PCA and FBsPCA.