{"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/efficient-sum-of-outer-products-dictionary-1","title":"Efficient Sum of Outer Products Dictionary Learning (SOUP-DIL) and Its Application to Inverse Problems","arxiv_id":"1511.06333","date":"2015-11-19","proceeding":null,"authors":["Saiprasad Ravishankar","Raj Rao Nadakuditi","Jeffrey A. Fessler"],"abstract":"The sparsity of signals in a transform domain or dictionary has been\nexploited in applications such as compression, denoising and inverse problems.\nMore recently, data-driven adaptation of synthesis dictionaries has shown\npromise compared to analytical dictionary models. However, dictionary learning\nproblems are typically non-convex and NP-hard, and the usual alternating\nminimization approaches for these problems are often computationally expensive,\nwith the computations dominated by the NP-hard synthesis sparse coding step.\nThis paper exploits the ideas that drive algorithms such as K-SVD, and\ninvestigates in detail efficient methods for aggregate sparsity penalized\ndictionary learning by first approximating the data with a sum of sparse\nrank-one matrices (outer products) and then using a block coordinate descent\napproach to estimate the unknowns. The resulting block coordinate descent\nalgorithms involve efficient closed-form solutions. Furthermore, we consider\nthe problem of dictionary-blind image reconstruction, and propose novel and\nefficient algorithms for adaptive image reconstruction using block coordinate\ndescent and sum of outer products methodologies. We provide a convergence study\nof the algorithms for dictionary learning and dictionary-blind image\nreconstruction. Our numerical experiments show the promising performance and\nspeed-ups provided by the proposed methods over previous schemes in sparse data\nrepresentation and compressed sensing-based image reconstruction.","url_abs":"http://arxiv.org/abs/1511.06333v4","url_pdf":"http://arxiv.org/pdf/1511.06333v4.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":"efficient-sum-of-outer-products-dictionary-1","repo_url":"https://github.com/guanhuaw/mirtorch","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"dictionary-learning","task_name":"Dictionary Learning"},{"task_slug":"image-reconstruction","task_name":"Image Reconstruction"},{"task_slug":"compressed-sensing","task_name":"compressed sensing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}