{"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/fourier-domain-optimization-for-image","title":"Fourier-Domain Optimization for Image Processing","arxiv_id":"1809.04187","date":"2018-09-11","proceeding":null,"authors":["Majed El Helou","Frederike Dümbgen","Radhakrishna Achanta","Sabine Süsstrunk"],"abstract":"Image optimization problems encompass many applications such as spectral\nfusion, deblurring, deconvolution, dehazing, matting, reflection removal and\nimage interpolation, among others. With current image sizes in the order of\nmegabytes, it is extremely expensive to run conventional algorithms such as\ngradient descent, making them unfavorable especially when closed-form solutions\ncan be derived and computed efficiently. This paper explains in detail the\nframework for solving convex image optimization and deconvolution in the\nFourier domain. We begin by explaining the mathematical background and\nmotivating why the presented setups can be transformed and solved very\nefficiently in the Fourier domain. We also show how to practically use these\nsolutions, by providing the corresponding implementations. The explanations are\naimed at a broad audience with minimal knowledge of convolution and image\noptimization. The eager reader can jump to Section 3 for a footprint of how to\nsolve and implement a sample optimization function, and Section 5 for the more\ncomplex cases.","url_abs":"http://arxiv.org/abs/1809.04187v1","url_pdf":"http://arxiv.org/pdf/1809.04187v1.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":"fourier-domain-optimization-for-image","repo_url":"https://github.com/duembgen/fourier-deconv","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"deblurring","task_name":"Deblurring"},{"task_slug":"image-matting","task_name":"Image Matting"},{"task_slug":"reflection-removal","task_name":"Reflection Removal"}],"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}