{"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/patch-ordering-as-a-regularization-for","title":"Patch-Ordering as a Regularization for Inverse Problems in Image Processing","arxiv_id":"1602.08510","date":"2016-02-26","proceeding":null,"authors":["Gregory Vaksman","Michael Zibulevsky","Michael Elad"],"abstract":"Recent work in image processing suggests that operating on (overlapping)\npatches in an image may lead to state-of-the-art results. This has been\ndemonstrated for a variety of problems including denoising, inpainting,\ndeblurring, and super-resolution. The work reported in [1,2] takes an extra\nstep forward by showing that ordering these patches to form an approximate\nshortest path can be leveraged for better processing. The core idea is to apply\na simple filter on the resulting 1D smoothed signal obtained after the\npatch-permutation. This idea has been also explored in combination with a\nwavelet pyramid, leading eventually to a sophisticated and highly effective\nregularizer for inverse problems in imaging. In this work we further study the\npatch-permutation concept, and harness it to propose a new simple yet effective\nregularization for image restoration problems. Our approach builds on the\nclassic Maximum A'posteriori probability (MAP), with a penalty function\nconsisting of a regular log-likelihood term and a novel permutation-based\nregularization term. Using a plain 1D Laplacian, the proposed regularization\nforces robust smoothness (L1) on the permuted pixels. Since the permutation\noriginates from patch-ordering, we propose to accumulate the smoothness terms\nover all the patches' pixels. Furthermore, we take into account the found\ndistances between adjacent patches in the ordering, by weighting the Laplacian\noutcome. We demonstrate the proposed scheme on a diverse set of problems: (i)\nsevere Poisson image denoising, (ii) Gaussian image denoising, (iii) image\ndeblurring, and (iv) single image super-resolution. In all these cases, we use\nrecent methods that handle these problems as initialization to our scheme. This\nis followed by an L-BFGS optimization of the above-described penalty function,\nleading to state-of-the-art results, and especially so for highly ill-posed\ncases.","url_abs":"http://arxiv.org/abs/1602.08510v1","url_pdf":"http://arxiv.org/pdf/1602.08510v1.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":"patch-ordering-as-a-regularization-for","repo_url":"https://github.com/grishavak/Patch_Ordering_as_a_Regularization_for_Inverse_Problems_in_Image_Processing","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"deblurring","task_name":"Deblurring"},{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"image-deblurring","task_name":"Image Deblurring"},{"task_slug":"image-denoising","task_name":"Image Denoising"},{"task_slug":"image-restoration","task_name":"Image Restoration"},{"task_slug":"image-super-resolution","task_name":"Image Super-Resolution"},{"task_slug":"super-resolution","task_name":"Super-Resolution"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}