{"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/simpler-gradient-methods-for-blind-super","title":"Simpler Gradient Methods for Blind Super-Resolution with Lower Iteration Complexity","arxiv_id":"2409.18387","date":"2024-09-27","proceeding":null,"authors":["Jinsheng Li","Wei Cui","Xu Zhang"],"abstract":"We study the problem of blind super-resolution, which can be formulated as a low-rank matrix recovery problem via vectorized Hankel lift (VHL). The previous gradient descent method based on VHL named PGD-VHL relies on additional regularization such as the projection and balancing penalty, exhibiting a suboptimal iteration complexity. In this paper, we propose a simpler unconstrained optimization problem without the above two types of regularization and develop two new and provable gradient methods named VGD-VHL and ScalGD-VHL. A novel and sharp analysis is provided for the theoretical guarantees of our algorithms, which demonstrates that our methods offer lower iteration complexity than PGD-VHL. In addition, ScalGD-VHL has the lowest iteration complexity while being independent of the condition number. Furthermore, our novel analysis reveals that the blind super-resolution problem is less incoherence-demanding, thereby eliminating the necessity for incoherent projections to achieve linear convergence. Empirical results illustrate that our methods exhibit superior computational efficiency while achieving comparable recovery performance to prior arts.","url_abs":"https://arxiv.org/abs/2409.18387v1","url_pdf":"https://arxiv.org/pdf/2409.18387v1.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"simpler-gradient-methods-for-blind-super","repo_url":"https://github.com/Jinshengg/SimplerGDs-VHL","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}