{"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/4d-dual-tree-complex-wavelets-for-time","title":"4D Dual-Tree Complex Wavelets for Time-Dependent Data","arxiv_id":"2103.15674","date":"2021-03-29","proceeding":null,"authors":["Tatiana A. Bubba","Tommi Heikkilä","Samuli Siltanen"],"abstract":"The dual-tree complex wavelet transform (DT-$\\mathbb{C}$WT) is extended to the 4D setting. Key properties of 4D DT-$\\mathbb{C}$WT, such as directional sensitivity and shift-invariance, are discussed and illustrated in a tomographic application. The inverse problem of reconstructing a dynamic three-dimensional target from X-ray projection measurements can be formulated as 4D space-time tomography. The results suggest that 4D DT-$\\mathbb{C}$WT offers simple implementations combined with useful theoretical properties for tomographic reconstruction.","url_abs":"https://arxiv.org/abs/2103.15674v1","url_pdf":"https://arxiv.org/pdf/2103.15674v1.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"4d-dual-tree-complex-wavelets-for-time","repo_url":"https://github.com/tommheik/dualtree4","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}