{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/fast-expansion-into-harmonics-on-the-disk-a","title":"Fast expansion into harmonics on the disk: a steerable basis with fast radial convolutions","arxiv_id":"2207.13674","date":"2022-07-27","proceeding":null,"authors":["Nicholas F. Marshall","Oscar Mickelin","Amit Singer"],"abstract":"We present a fast and numerically accurate method for expanding digitized $L \\times L$ images representing functions on $[-1,1]^2$ supported on the disk $\\{x \\in \\mathbb{R}^2 : |x|<1\\}$ in the harmonics (Dirichlet Laplacian eigenfunctions) on the disk. Our method, which we refer to as the Fast Disk Harmonics Transform (FDHT), runs in $O(L^2 \\log L)$ operations. This basis is also known as the Fourier-Bessel basis, and it has several computational advantages: it is orthogonal, ordered by frequency, and steerable in the sense that images expanded in the basis can be rotated by applying a diagonal transform to the coefficients. Moreover, we show that convolution with radial functions can also be efficiently computed by applying a diagonal transform to the coefficients.","url_abs":"https://arxiv.org/abs/2207.13674v2","url_pdf":"https://arxiv.org/pdf/2207.13674v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"fast-expansion-into-harmonics-on-the-disk-a","repo_url":"https://github.com/nmarshallf/fle_2d","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}