{"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-local-block-coordinate-descent-algorithm","title":"A Local Block Coordinate Descent Algorithm for the Convolutional Sparse Coding Model","arxiv_id":"1811.00312","date":"2018-11-01","proceeding":null,"authors":["Ev Zisselman","Jeremias Sulam","Michael Elad"],"abstract":"The Convolutional Sparse Coding (CSC) model has recently gained considerable\ntraction in the signal and image processing communities. By providing a global,\nyet tractable, model that operates on the whole image, the CSC was shown to\novercome several limitations of the patch-based sparse model while achieving\nsuperior performance in various applications. Contemporary methods for pursuit\nand learning the CSC dictionary often rely on the Alternating Direction Method\nof Multipliers (ADMM) in the Fourier domain for the computational convenience\nof convolutions, while ignoring the local characterizations of the image. A\nrecent work by Papyan et al. suggested the SBDL algorithm for the CSC, while\noperating locally on image patches. SBDL demonstrates better performance\ncompared to the Fourier-based methods, albeit still relying on the ADMM. In\nthis work we maintain the localized strategy of the SBDL, while proposing a new\nand much simpler approach based on the Block Coordinate Descent algorithm -\nthis method is termed Local Block Coordinate Descent (LoBCoD). Furthermore, we\nintroduce a novel stochastic gradient descent version of LoBCoD for training\nthe convolutional filters. The Stochastic-LoBCoD leverages the benefits of\nonline learning, while being applicable to a single training image. We\ndemonstrate the advantages of the proposed algorithms for image inpainting and\nmulti-focus image fusion, achieving state-of-the-art results.","url_abs":"http://arxiv.org/abs/1811.00312v1","url_pdf":"http://arxiv.org/pdf/1811.00312v1.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-local-block-coordinate-descent-algorithm","repo_url":"https://github.com/EvZissel/LoBCoD","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"a-local-block-coordinate-descent-algorithm","repo_url":"https://github.com/Ian-Liao/LoBCoD","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"image-inpainting","task_name":"Image Inpainting"},{"task_slug":"multi-focus-image-fusion","task_name":"Multi Focus Image Fusion"}],"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}