{"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/theoretical-linear-convergence-of-unfolded","title":"Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds","arxiv_id":"1808.10038","date":"2018-08-29","proceeding":"NeurIPS 2018 12","authors":["Xiaohan Chen","Jialin Liu","Zhangyang Wang","Wotao Yin"],"abstract":"In recent years, unfolding iterative algorithms as neural networks has become\nan empirical success in solving sparse recovery problems. However, its\ntheoretical understanding is still immature, which prevents us from fully\nutilizing the power of neural networks. In this work, we study unfolded ISTA\n(Iterative Shrinkage Thresholding Algorithm) for sparse signal recovery. We\nintroduce a weight structure that is necessary for asymptotic convergence to\nthe true sparse signal. With this structure, unfolded ISTA can attain a linear\nconvergence, which is better than the sublinear convergence of ISTA/FISTA in\ngeneral cases. Furthermore, we propose to incorporate thresholding in the\nnetwork to perform support selection, which is easy to implement and able to\nboost the convergence rate both theoretically and empirically. Extensive\nsimulations, including sparse vector recovery and a compressive sensing\nexperiment on real image data, corroborate our theoretical results and\ndemonstrate their practical usefulness. We have made our codes publicly\navailable: https://github.com/xchen-tamu/linear-lista-cpss.","url_abs":"http://arxiv.org/abs/1808.10038v2","url_pdf":"http://arxiv.org/pdf/1808.10038v2.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":"theoretical-linear-convergence-of-unfolded","repo_url":"https://github.com/xchen-tamu/linear-lista-cpss","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"theoretical-linear-convergence-of-unfolded","repo_url":"https://github.com/TAMU-VITA/LISTA-CPSS","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"theoretical-linear-convergence-of-unfolded","repo_url":"https://github.com/vita-group/lista-cpss","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}}],"tasks":[{"task_slug":"compressive-sensing","task_name":"Compressive Sensing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1808.10038","atlas_url":"https://app.syntology.ai/?focus=1808.10038","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}