{"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/projected-gradient-descent-for-spectral","title":"Projected Gradient Descent for Spectral Compressed Sensing via Symmetric Hankel Factorization","arxiv_id":"2403.09031","date":"2024-03-14","proceeding":null,"authors":["Jinsheng Li","Wei Cui","Xu Zhang"],"abstract":"Current spectral compressed sensing methods via Hankel matrix completion employ symmetric factorization to demonstrate the low-rank property of the Hankel matrix. However, previous non-convex gradient methods only utilize asymmetric factorization to achieve spectral compressed sensing. In this paper, we propose a novel nonconvex projected gradient descent method for spectral compressed sensing via symmetric factorization named Symmetric Hankel Projected Gradient Descent (SHGD), which updates only one matrix and avoids a balancing regularization term. SHGD reduces about half of the computation and storage costs compared to the prior gradient method based on asymmetric factorization. {Besides, the symmetric factorization employed in our work is completely novel to the prior low-rank factorization model, introducing a new factorization ambiguity under complex orthogonal transformation}. Novel distance metrics are designed for our factorization method and a linear convergence guarantee to the desired signal is established with $O(r^2\\log(n))$ observations. Numerical simulations demonstrate the superior performance of the proposed SHGD method in phase transitions and computation efficiency compared to state-of-the-art methods.","url_abs":"https://arxiv.org/abs/2403.09031v2","url_pdf":"https://arxiv.org/pdf/2403.09031v2.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":"projected-gradient-descent-for-spectral","repo_url":"https://github.com/Jinshengg/SHGD","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"matrix-completion","task_name":"Matrix Completion"},{"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}