{"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/convolutional-dictionary-learning","title":"Convolutional Dictionary Learning: Acceleration and Convergence","arxiv_id":"1707.00389","date":"2017-07-03","proceeding":null,"authors":["Il Yong Chun","Jeffrey A. Fessler"],"abstract":"Convolutional dictionary learning (CDL or sparsifying CDL) has many\napplications in image processing and computer vision. There has been growing\ninterest in developing efficient algorithms for CDL, mostly relying on the\naugmented Lagrangian (AL) method or the variant alternating direction method of\nmultipliers (ADMM). When their parameters are properly tuned, AL methods have\nshown fast convergence in CDL. However, the parameter tuning process is not\ntrivial due to its data dependence and, in practice, the convergence of AL\nmethods depends on the AL parameters for nonconvex CDL problems. To moderate\nthese problems, this paper proposes a new practically feasible and convergent\nBlock Proximal Gradient method using a Majorizer (BPG-M) for CDL. The\nBPG-M-based CDL is investigated with different block updating schemes and\nmajorization matrix designs, and further accelerated by incorporating some\nmomentum coefficient formulas and restarting techniques. All of the methods\ninvestigated incorporate a boundary artifacts removal (or, more generally,\nsampling) operator in the learning model. Numerical experiments show that,\nwithout needing any parameter tuning process, the proposed BPG-M approach\nconverges more stably to desirable solutions of lower objective values than the\nexisting state-of-the-art ADMM algorithm and its memory-efficient variant do.\nCompared to the ADMM approaches, the BPG-M method using a multi-block updating\nscheme is particularly useful in single-threaded CDL algorithm handling large\ndatasets, due to its lower memory requirement and no polynomial computational\ncomplexity. Image denoising experiments show that, for relatively strong\nadditive white Gaussian noise, the filters learned by BPG-M-based CDL\noutperform those trained by the ADMM approach.","url_abs":"http://arxiv.org/abs/1707.00389v2","url_pdf":"http://arxiv.org/pdf/1707.00389v2.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":"convolutional-dictionary-learning","repo_url":"https://github.com/mechatoz/convolt","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"dictionary-learning","task_name":"Dictionary Learning"},{"task_slug":"image-denoising","task_name":"Image Denoising"}],"methods":[{"method_slug":"admm","method_name":"ADMM"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}