{"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/testing-gaussian-process-with-applications-to","title":"Testing Gaussian Process with Applications to Super-Resolution","arxiv_id":"1706.00679","date":"2017-06-02","proceeding":null,"authors":["Jean-Marc Azaïs","Yohann De Castro","Stéphane Mourareau"],"abstract":"This article introduces exact testing procedures on the mean of a Gaussian process $X$ derived from the outcomes of $\\ell_1$-minimization over the space of complex valued measures. The process $X$ can be thought as the sum of two terms: first, the convolution between some kernel and a target atomic measure (mean of the process); second, a random perturbation by an additive centered Gaussian process. The first testing procedure considered is based on a dense sequence of grids on the index set of~$X$ and we establish that it converges (as the grid step tends to zero) to a randomized testing procedure: the decision of the test depends on the observation $X$ and also on an independent random variable. The second testing procedure is based on the maxima and the Hessian of $X$ in a grid-less manner. We show that both testing procedures can be performed when the variance is unknown (and the correlation function of $X$ is known). These testing procedures can be used for the problem of deconvolution over the space of complex valued measures, and applications in frame of the Super-Resolution theory are presented. As a byproduct, numerical investigations may demonstrate that our grid-less method is more powerful (it~detects sparse alternatives) than tests based on very thin grids.","url_abs":"http://arxiv.org/abs/1706.00679v2","url_pdf":"http://arxiv.org/pdf/1706.00679v2.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":"testing-gaussian-process-with-applications-to","repo_url":"https://github.com/ydecastro/super-resolution-testing","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}