{"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/fast-and-robust-spectrally-sparse-signal","title":"Accelerated Structured Alternating Projections for Robust Spectrally Sparse Signal Recovery","arxiv_id":"1910.05859","date":"2019-10-13","proceeding":null,"authors":["HanQin Cai","Jian-Feng Cai","Tianming Wang","Guojian Yin"],"abstract":"Consider a spectrally sparse signal $\\boldsymbol{x}$ that consists of $r$ complex sinusoids with or without damping. We study the robust recovery problem for the spectrally sparse signal under the fully observed setting, which is about recovering $\\boldsymbol{x}$ and a sparse corruption vector $\\boldsymbol{s}$ from their sum $\\boldsymbol{z}=\\boldsymbol{x}+\\boldsymbol{s}$. In this paper, we exploit the low-rank property of the Hankel matrix formed by $\\boldsymbol{x}$, and formulate the problem as the robust recovery of a corrupted low-rank Hankel matrix. We develop a highly efficient non-convex algorithm, coined Accelerated Structured Alternating Projections (ASAP). The high computational efficiency and low space complexity of ASAP are achieved by fast computations involving structured matrices, and a subspace projection method for accelerated low-rank approximation. Theoretical recovery guarantee with a linear convergence rate has been established for ASAP, under some mild assumptions on $\\boldsymbol{x}$ and $\\boldsymbol{s}$. Empirical performance comparisons on both synthetic and real-world data confirm the advantages of ASAP, in terms of computational efficiency and robustness aspects.","url_abs":"https://arxiv.org/abs/1910.05859v3","url_pdf":"https://arxiv.org/pdf/1910.05859v3.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":"fast-and-robust-spectrally-sparse-signal","repo_url":"https://github.com/caesarcai/AAP-Hankel","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"fast-and-robust-spectrally-sparse-signal","repo_url":"https://github.com/caesarcai/ASAP-Hankel","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}