{"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/constraint-matrix-factorization-for-space","title":"Constraint matrix factorization for space variant PSFs field restoration","arxiv_id":"1608.08104","date":"2016-08-29","proceeding":null,"authors":["F. M. Ngolè Mboula","J. -L. Starck","K. Okumura","J. Amiaux","P. Hudelot"],"abstract":"Context: in large-scale spatial surveys, the Point Spread Function (PSF)\nvaries across the instrument field of view (FOV). Local measurements of the\nPSFs are given by the isolated stars images. Yet, these estimates may not be\ndirectly usable for post-processings because of the observational noise and\npotentially the aliasing. Aims: given a set of aliased and noisy stars images\nfrom a telescope, we want to estimate well-resolved and noise-free PSFs at the\nobserved stars positions, in particular, exploiting the spatial correlation of\nthe PSFs across the FOV. Contributions: we introduce RCA (Resolved Components\nAnalysis) which is a noise-robust dimension reduction and super-resolution\nmethod based on matrix factorization. We propose an original way of using the\nPSFs spatial correlation in the restoration process through sparsity. The\nintroduced formalism can be applied to correlated data sets with respect to any\neuclidean parametric space. Results: we tested our method on simulated\nmonochromatic PSFs of Euclid telescope (launch planned for 2020). The proposed\nmethod outperforms existing PSFs restoration and dimension reduction methods.\nWe show that a coupled sparsity constraint on individual PSFs and their spatial\ndistribution yields a significant improvement on both the restored PSFs shapes\nand the PSFs subspace identification, in presence of aliasing. Perspectives:\nRCA can be naturally extended to account for the wavelength dependency of the\nPSFs.","url_abs":"http://arxiv.org/abs/1608.08104v3","url_pdf":"http://arxiv.org/pdf/1608.08104v3.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":"constraint-matrix-factorization-for-space","repo_url":"https://github.com/CosmoStat/rca","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"task_slug":"super-resolution","task_name":"Super-Resolution"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}