{"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/deep-fractional-fourier-transform","title":"Deep Fractional Fourier Transform","arxiv_id":null,"date":"2023-09-21","proceeding":"NeurIPS 2023 11","authors":[],"abstract":"Existing deep learning-based computer vision methods usually operate in the spatial and frequency domains, which are two orthogonal \\textbf{individual} perspectives for image processing.\nIn this paper, we introduce a new spatial-frequency analysis tool, Fractional Fourier Transform (FRFT), to provide comprehensive \\textbf{unified} spatial-frequency perspectives.\nThe FRFT is a unified continuous spatial-frequency transform that simultaneously reflects an image's spatial and frequency representations, making it optimal for processing non-stationary image signals.\nWe explore the properties of the FRFT for image processing and present a fast implementation of the 2D FRFT, which facilitates its widespread use.\nBased on these explorations, we introduce a simple yet effective operator, Multi-order FRactional Fourier Convolution (MFRFC), which exhibits the remarkable merits of processing images from more perspectives in the spatial-frequency plane. Our proposed MFRFC is a general and basic operator that can be easily integrated into various tasks for performance improvement.\nWe experimentally evaluate the MFRFC on various computer vision tasks, including object detection, image classification, guided super-resolution, denoising, dehazing, deraining, and low-light enhancement. Our proposed MFRFC consistently outperforms baseline methods by significant margins across all tasks.","url_abs":"https://openreview.net/forum?id=YsYKv95jy9","url_pdf":"https://openreview.net/pdf?id=YsYKv95jy9","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":"deep-fractional-fourier-transform","repo_url":"https://github.com/yuhuustc/frft","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}