Codes and Expansions (CodEx) Seminar

Oscar Mickelin (Princeton University):
A fast algorithm for Fourier-Bessel expansions

We present a fast algorithm to expand discretized image-valued data into the Fourier-Bessel basis, i.e., the basis consisting of eigenfunctions of the Dirichlet Laplacian on the unit disk. This basis has a number of beneficial numerical properties, since the basis functions are orthonormal, ordered by frequency and steerable. For \(L \times L\) images, the presented algorithm computes \(O(L^2)\) basis coefficients in time \(O(L^2 \log L)\) , and comes with associated accuracy guarantees. As an application, we show how to use the presented algorithm to perform rotationally invariant covariance estimation of cryo-EM images.