{"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/quantization-for-spectral-super-resolution","title":"Quantization for spectral super-resolution","arxiv_id":"2103.00079","date":"2021-02-26","proceeding":null,"authors":["C. Sinan Güntürk","Weilin Li"],"abstract":"We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is redundancy in the number of measurements. More precisely, we define the oversampling ratio $\\lambda$ as the largest integer such that $\\lfloor M/\\lambda\\rfloor - 1\\geq 4/\\Delta$, where $M$ denotes the number of Fourier measurements and $\\Delta$ is the minimum separation distance associated with the atomic measure to be resolved. We prove that for any number $K\\geq 2$ of quantization levels available for the real and imaginary parts of the measurements, our quantization method combined with either TV-min/BLASSO or ESPRIT guarantees reconstruction accuracy of order $O(M^{1/4}\\lambda^{5/4} K^{- \\lambda/2})$ and $O(M^{3/2} \\lambda^{1/2} K^{- \\lambda})$ respectively, where the implicit constants are independent of $M$, $K$ and $\\lambda$. In contrast, naive rounding or memoryless scalar quantization for the same alphabet offers a guarantee of order $O(M^{-1}K^{-1})$ only, regardless of the reconstruction algorithm.","url_abs":"https://arxiv.org/abs/2103.00079v2","url_pdf":"https://arxiv.org/pdf/2103.00079v2.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":"quantization-for-spectral-super-resolution","repo_url":"https://github.com/weilinlimath/Quan-SR","is_official":0,"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}