# A fast algorithm for expanding images into the harmonics on the disk and applications

# A fast algorithm for expanding images into the harmonics on the disk and applications

ABSTRACT:

We present a fast algorithm for expanding digitized L x L images into the harmonics (the Dirichlet Laplacian eigenfunctions) on the disk. Our method, which we call the Fast Disk Harmonics Transform (FDHT), runs in O(L^2 log L) operations. This basis offers several computational advantages: it is orthogonal, ordered by frequency, and steerable (images expanded in the basis can be rotated by applying a diagonal transform to the coefficients). We discuss applications of the FDHT to image processing problems related to cryo-electron microscopy (cryo-EM).

BIO: Nicholas Marshall is an Assistant Professor at Oregon State University. Previously, he was an NSF Postdoc at Princeton University. He earned his Ph.D. at Yale in 2019. His research explores the intersection of analysis, geometry, and probability, particularly in problems driven by data science