{"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/a-framework-for-fast-image-deconvolution-with","title":"A Framework for Fast Image Deconvolution with Incomplete Observations","arxiv_id":"1602.01410","date":"2016-02-03","proceeding":null,"authors":["Miguel Simões","Luis B. Almeida","José Bioucas-Dias","Jocelyn Chanussot"],"abstract":"In image deconvolution problems, the diagonalization of the underlying\noperators by means of the FFT usually yields very large speedups. When there\nare incomplete observations (e.g., in the case of unknown boundaries), standard\ndeconvolution techniques normally involve non-diagonalizable operators,\nresulting in rather slow methods, or, otherwise, use inexact convolution\nmodels, resulting in the occurrence of artifacts in the enhanced images. In\nthis paper, we propose a new deconvolution framework for images with incomplete\nobservations that allows us to work with diagonalized convolution operators,\nand therefore is very fast. We iteratively alternate the estimation of the\nunknown pixels and of the deconvolved image, using, e.g., an FFT-based\ndeconvolution method. This framework is an efficient, high-quality alternative\nto existing methods of dealing with the image boundaries, such as edge\ntapering. It can be used with any fast deconvolution method. We give an example\nin which a state-of-the-art method that assumes periodic boundary conditions is\nextended, through the use of this framework, to unknown boundary conditions.\nFurthermore, we propose a specific implementation of this framework, based on\nthe alternating direction method of multipliers (ADMM). We provide a proof of\nconvergence for the resulting algorithm, which can be seen as a \"partial\" ADMM,\nin which not all variables are dualized. We report experimental comparisons\nwith other primal-dual methods, where the proposed one performed at the level\nof the state of the art. Four different kinds of applications were tested in\nthe experiments: deconvolution, deconvolution with inpainting, superresolution,\nand demosaicing, all with unknown boundaries.","url_abs":"http://arxiv.org/abs/1602.01410v2","url_pdf":"http://arxiv.org/pdf/1602.01410v2.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":"a-framework-for-fast-image-deconvolution-with","repo_url":"https://github.com/alfaiate/DeconvolutionIncompleteObs","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"demosaicking","task_name":"Demosaicking"},{"task_slug":"image-deconvolution","task_name":"Image Deconvolution"}],"methods":[{"method_slug":"admm","method_name":"ADMM"},{"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}