{"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/spoq-ell-p-over-ell-q-regularization-for","title":"SPOQ $\\ell_p$-Over-$\\ell_q$ Regularization for Sparse Signal Recovery applied to Mass Spectrometry","arxiv_id":"2001.08496","date":"2020-01-23","proceeding":null,"authors":["Afef Cherni","Emilie Chouzenoux","Laurent Duval","Jean-Christophe Pesquet"],"abstract":"Underdetermined or ill-posed inverse problems require additional information for \\ldd{d} sound solutions with tractable optimization algorithms. Sparsity yields consequent heuristics to that matter, with numerous applications in signal restoration, image recovery, or machine learning. Since the $\\ell_0$ count measure is barely tractable, many statistical or learning approaches have invested in computable proxies, such as the $\\ell_1$ norm. However, the latter does not exhibit the desirable property of scale invariance for sparse data. Extending the SOOT Euclidean/Taxicab $\\ell_1$-over-$\\ell_2$ norm-ratio initially introduced for blind deconvolution, we propose SPOQ, a family of smoothed (approximately) scale-invariant penalty functions. It consists of a Lipschitz-differentiable surrogate for $\\ell_p$-over-$\\ell_q$ quasi-norm/norm ratios with $p\\in\\,]0,2[$ and $q\\ge 2$. This surrogate is embedded into a novel majorize-minimize trust-region approach, generalizing the variable metric forward-backward algorithm. For naturally sparse mass-spectrometry signals, we show that SPOQ significantly outperforms $\\ell_0$, $\\ell_1$, Cauchy, Welsch, SCAD and Celo penalties on several performance measures. Guidelines on SPOQ hyperparameters tuning are also provided, suggesting simple data-driven choices.","url_abs":"http://arxiv.org/abs/2001.08496v2","url_pdf":"http://arxiv.org/pdf/2001.08496v2.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":"spoq-ell-p-over-ell-q-regularization-for","repo_url":"https://github.com/laurentduval/spoq-sparse-regularization","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"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}