{"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/a-spectral-method-for-stable-bispectrum","title":"A Spectral Method for Stable Bispectrum Inversion with Application to Multireference Alignment","arxiv_id":"1802.10493","date":"2018-02-28","proceeding":null,"authors":[],"abstract":"We focus on an alignment-free method to estimate the underlying signal from a\nlarge number of noisy randomly shifted observations. Specifically, we estimate\nthe mean, power spectrum, and bispectrum of the signal from the observations.\nSince bispectrum contains the phase information of the signal, reliable\nalgorithms for bispectrum inversion is useful in many applications. We propose\na new algorithm using spectral decomposition of the normalized bispectrum\nmatrix for this task. For clean signals, we show that the eigenvectors of the\nnormalized bispectrum matrix correspond to the true phases of the signal and\nits shifted copies. In addition, the spectral method is robust to noise. It can\nbe used as a stable and efficient initialization technique for local non-convex\noptimization for bispectrum inversion.","url_abs":"http://arxiv.org/abs/1802.10493v1","url_pdf":"http://arxiv.org/pdf/1802.10493v1.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":"a-spectral-method-for-stable-bispectrum","repo_url":"https://github.com/ARKEYTECT/Bispectrum_Inversion","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}