{"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/sparse-low-rank-decomposition-of-annihilating","title":"Sparse + Low Rank Decomposition of Annihilating Filter-based Hankel Matrix for Impulse Noise Removal","arxiv_id":"1510.05559","date":"2015-10-19","proceeding":null,"authors":["Kyong Hwan Jin","Jong Chul Ye"],"abstract":"Recently, so called annihilating filer-based low rank Hankel matrix (ALOHA)\napproach was proposed as a powerful image inpainting method. Based on the\nobservation that smoothness or textures within an image patch corresponds to\nsparse spectral components in the frequency domain, ALOHA exploits the\nexistence of annihilating filters and the associated rank-deficient Hankel\nmatrices in the image domain to estimate the missing pixels. By extending this\nidea, here we propose a novel impulse noise removal algorithm using sparse +\nlow rank decomposition of an annihilating filter-based Hankel matrix. The new\napproach, what we call the robust ALOHA, is motivated by the observation that\nan image corrupted with impulse noises has intact pixels; so the impulse noises\ncan be modeled as sparse components, whereas the underlying image can be still\nmodeled using a low-rank Hankel structured matrix. To solve the sparse + low\nrank decomposition problem, we propose an alternating direction method of\nmultiplier (ADMM) method with initial factorized matrices coming from low rank\nmatrix fitting (LMaFit) algorithm. To adapt the local image statistics that\nhave distinct spectral distributions, the robust ALOHA is applied patch by\npatch. Experimental results from two types of impulse noises - random valued\nimpulse noises and salt/pepper noises - for both single channel and\nmulti-channel color images demonstrate that the robust ALOHA outperforms the\nexisting algorithms up to 8dB in terms of the peak signal to noise ratio\n(PSNR).","url_abs":"http://arxiv.org/abs/1510.05559v1","url_pdf":"http://arxiv.org/pdf/1510.05559v1.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":"sparse-low-rank-decomposition-of-annihilating","repo_url":"https://github.com/jongcye/RobustALOHA","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"image-inpainting","task_name":"Image Inpainting"}],"methods":[],"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}