{"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/mixed-graph-signal-analysis-of-joint-image","title":"Mixed Graph Signal Analysis of Joint Image Denoising / Interpolation","arxiv_id":"2309.10114","date":"2023-09-18","proceeding":null,"authors":["Niruhan Viswarupan","Gene Cheung","Fengbo Lan","Michael Brown"],"abstract":"A noise-corrupted image often requires interpolation. Given a linear denoiser and a linear interpolator, when should the operations be independently executed in separate steps, and when should they be combined and jointly optimized? We study joint denoising / interpolation of images from a mixed graph filtering perspective: we model denoising using an undirected graph, and interpolation using a directed graph. We first prove that, under mild conditions, a linear denoiser is a solution graph filter to a maximum a posteriori (MAP) problem regularized using an undirected graph smoothness prior, while a linear interpolator is a solution to a MAP problem regularized using a directed graph smoothness prior. Next, we study two variants of the joint interpolation / denoising problem: a graph-based denoiser followed by an interpolator has an optimal separable solution, while an interpolator followed by a denoiser has an optimal non-separable solution. Experiments show that our joint denoising / interpolation method outperformed separate approaches noticeably.","url_abs":"https://arxiv.org/abs/2309.10114v2","url_pdf":"https://arxiv.org/pdf/2309.10114v2.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":"mixed-graph-signal-analysis-of-joint-image","repo_url":"https://github.com/sybernix/icassp24-joint","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"image-denoising","task_name":"Image Denoising"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}