{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T04:56:54Z","timestamp":1777870614296,"version":"3.51.4"},"reference-count":39,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T00:00:00Z","timestamp":1771804800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009112","name":"Istituto Nazionale di Alta Matematica "Francesco Severi"","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100009112","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003407","name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","award":["J53D23015950001"],"award-info":[{"award-number":["J53D23015950001"]}],"id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003407","name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","award":["P20229SH29"],"award-info":[{"award-number":["P20229SH29"]}],"id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100012740","name":"Gruppo Nazionale per l'Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100012740","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100024370","name":"Ministero dell'Istruzione dell'Universita e della Ricerca","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100024370","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.cam.2026.117540","type":"journal-article","created":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T07:45:01Z","timestamp":1771919101000},"page":"117540","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Implementation of neural network operators with applications to remote sensing data"],"prefix":"10.1016","volume":"484","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8834-8877","authenticated-orcid":false,"given":"Danilo","family":"Costarelli","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0008-9440-3383","authenticated-orcid":false,"given":"Michele","family":"Piconi","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.cam.2026.117540_bib0001","series-title":"Intelligent Systems II: Complete Approximation by Neural Network Operators","volume":"608","author":"Anastassiou","year":"2016"},{"key":"10.1016\/j.cam.2026.117540_bib0002","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1016\/j.jmaa.2014.05.013","article-title":"Interpolation by neural network operators activated by ramp functions","volume":"419","author":"Costarelli","year":"2014","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/j.cam.2026.117540_bib0003","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.neunet.2015.02.002","article-title":"Neural network operators: constructive interpolation of multivariate functions","volume":"67","author":"Costarelli","year":"2015","journal-title":"Neural Netw."},{"key":"10.1016\/j.cam.2026.117540_bib0004","doi-asserted-by":"crossref","first-page":"547","DOI":"10.3846\/mma.2022.15974","article-title":"Density results by deep neural network operators with integer weights","volume":"27","author":"Costarelli","year":"2022","journal-title":"Math. Modell. Anal."},{"key":"10.1016\/j.cam.2026.117540_bib0005","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.neunet.2013.03.015","article-title":"Approximation results for neural network operators activated by sigmoidal functions","volume":"44","author":"Costarelli","year":"2013","journal-title":"Neural Netw."},{"key":"10.1016\/j.cam.2026.117540_bib0006","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.neunet.2013.07.009","article-title":"Multivariate neural network operators with sigmoidal activation functions","volume":"48","author":"Costarelli","year":"2013","journal-title":"Neural Netw."},{"key":"10.1016\/j.cam.2026.117540_bib0007","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/s10231-013-0378-y","article-title":"Approximation by series of sigmoidal functions with applications to neural networks","volume":"194","author":"Costarelli","year":"2015","journal-title":"Ann. Mat. Pura Appl."},{"issue":"4","key":"10.1016\/j.cam.2026.117540_bib0008","doi-asserted-by":"crossref","first-page":"2564","DOI":"10.3150\/21-BEJ1323","article-title":"Over-parametrized deep neural networks do not generalize well","volume":"27","author":"Kohler","year":"2021","journal-title":"Bernoulli"},{"issue":"9","key":"10.1016\/j.cam.2026.117540_bib0009","doi-asserted-by":"crossref","first-page":"2746","DOI":"10.1109\/TNNLS.2018.2888517","article-title":"Classification by sparse neural networks","volume":"30","author":"Kurkov\u00e1","year":"2019","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"1","key":"10.1016\/j.cam.2026.117540_bib0010","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/s00211-023-01384-6","article-title":"Two-layer networks with the ReLUk activation function: barron spaces and derivative approximation","volume":"156","author":"Li","year":"2024","journal-title":"Numer. Math."},{"issue":"2","key":"10.1016\/j.cam.2026.117540_bib0011","doi-asserted-by":"crossref","first-page":"379","DOI":"10.4208\/cicp.OA-2019-0168","article-title":"Better approximations of high dimensional smooth functions by deep neural networks with rectified power units","volume":"27","author":"Li","year":"2019","journal-title":"Commun. Comput. Phys."},{"issue":"2","key":"10.1016\/j.cam.2026.117540_bib0012","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1016\/j.acha.2019.06.004","article-title":"Universality of deep convolutional neural networks","volume":"48","author":"Zhou","year":"2020","journal-title":"Appl. Comput. Harmonic Anal."},{"key":"10.1016\/j.cam.2026.117540_bib0013","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.neunet.2020.01.018","article-title":"Theory of deep convolutional neural networks: downsampling","volume":"124","author":"Zhou","year":"2020","journal-title":"Neural Netw."},{"issue":"5-6","key":"10.1016\/j.cam.2026.117540_bib0014","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.1016\/j.mcm.2010.11.072","article-title":"Univariate hyperbolic tangent neural network approximation","volume":"53","author":"Anastassiou","year":"2011","journal-title":"Math. Comput. Model."},{"issue":"4","key":"10.1016\/j.cam.2026.117540_bib0015","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1016\/j.camwa.2010.12.029","article-title":"Multivariate hyperbolic tangent neural network approximation","volume":"61","author":"Anastassiou","year":"2011","journal-title":"Comput. Math. Appl."},{"issue":"5","key":"10.1016\/j.cam.2026.117540_bib0016","doi-asserted-by":"crossref","DOI":"10.1007\/s00009-022-02138-8","article-title":"Quantitative estimates for neural network operators implied by the asymptotic behaviour of the sigmoidal activation functions","volume":"19","author":"Coroianu","year":"2022","journal-title":"Mediterr. J. Math."},{"issue":"2","key":"10.1016\/j.cam.2026.117540_bib0017","first-page":"45","article-title":"A comparison among a fuzzy algorithm for image rescaling with other methods of digital image processing","volume":"7","author":"Costarelli","year":"2024","journal-title":"Constr. Math. Anal."},{"issue":"3","key":"10.1016\/j.cam.2026.117540_bib0018","first-page":"3045","article-title":"Fractional type multivariate neural network operators","volume":"46","author":"Kadak","year":"2023","journal-title":"Math. Appl. Sci."},{"key":"10.1016\/j.cam.2026.117540_bib0019","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF02551274","article-title":"Approximation by superpositions of a sigmoidal function","volume":"2","author":"Cybenko","year":"1989","journal-title":"Math. Contr. Signals Syst."},{"issue":"2","key":"10.1016\/j.cam.2026.117540_bib0020","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/S0893-6080(05)80020-6","article-title":"Approximation of a function and its derivative with a neural network","volume":"5","author":"Cardaliaguet","year":"1992","journal-title":"Neural Netw."},{"key":"10.1016\/j.cam.2026.117540_bib0021","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.jat.2014.06.004","article-title":"Convergence of a family of neural network operators of the Kantorovich type","volume":"185","author":"Costarelli","year":"2014","journal-title":"J. Approx. Theory"},{"key":"10.1016\/j.cam.2026.117540_bib0022","article-title":"A comparison between the sampling Kantorovich algorithm for digital image processing with some interpolation and quasi-interpolation methods","volume":"374","author":"Costarelli","year":"2020","journal-title":"Appl. Math. Comput."},{"key":"10.1016\/j.cam.2026.117540_bib0023","series-title":"2011 IEEE Symp. Adv. Type-2 Fuzzy Logic Syst","first-page":"16","article-title":"A construction method of interval-valued fuzzy sets for image processing","author":"Jurio","year":"2026"},{"key":"10.1016\/j.cam.2026.117540_bib0024","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s00025-024-02222-3","article-title":"Best approximation and inverse results for neural network operators","volume":"79","author":"Coroianu","year":"2024","journal-title":"Results Math."},{"key":"10.1016\/j.cam.2026.117540_bib0025","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s00009-024-02752-8","article-title":"Asymptotic analysis for neural network operators employing the Hardy-Littlewood maximal inequality","volume":"21","author":"Costarelli","year":"2024","journal-title":"Mediterr. J. Math."},{"key":"10.1016\/j.cam.2026.117540_bib0026","doi-asserted-by":"crossref","first-page":"4581","DOI":"10.1007\/s12190-024-02146-9","article-title":"The approximation capabilities of Durrmeyer-type neural network operators","volume":"70","author":"Coroianu","year":"2024","journal-title":"J. Appl. Math. Comput."},{"key":"10.1016\/j.cam.2026.117540_bib0027","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1007\/s43037-024-00377-3","article-title":"Convergence and high order of approximation by Steklov sampling operators","volume":"18","author":"Costarelli","year":"2024","journal-title":"Banach J. Math. Anal."},{"key":"10.1016\/j.cam.2026.117540_bib0028","series-title":"Approximation by Steklov neural network operators","author":"Acar","year":"2024"},{"issue":"4","key":"10.1016\/j.cam.2026.117540_bib0029","doi-asserted-by":"crossref","first-page":"758","DOI":"10.1016\/j.camwa.2009.05.001","article-title":"The approximation operators with sigmoidal functions","volume":"58","author":"Chen","year":"2009","journal-title":"Comput. Math. Appl."},{"key":"10.1016\/j.cam.2026.117540_bib0030","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2021.116087","article-title":"Structural similarity index (SSIM) revisited: a data-driven approach","volume":"189","author":"Bakurov","year":"2022","journal-title":"Expert Syst. Appl."},{"issue":"11","key":"10.1016\/j.cam.2026.117540_bib0031","doi-asserted-by":"crossref","first-page":"1921","DOI":"10.1016\/j.aml.2012.03.001","article-title":"Geodesics of the structural similarity index","volume":"25","author":"Brunet","year":"2012","journal-title":"Appl. Math. Lett."},{"issue":"4","key":"10.1016\/j.cam.2026.117540_bib0032","doi-asserted-by":"crossref","first-page":"1488","DOI":"10.1109\/TIP.2011.2173206","article-title":"On the mathematical properties of the structural similarity index","volume":"21","author":"Brunet","year":"2011","journal-title":"IEEE Trans. Image Process."},{"key":"10.1016\/j.cam.2026.117540_bib0033","series-title":"Remote Sensing Imagery Using Diffusion Models and Structural Similarity Index (SSIM)","article-title":"Novel change detection framework","author":"Kiruluta","year":"2024"},{"key":"10.1016\/j.cam.2026.117540_bib0034","series-title":"2011 Sixth Int. Conf. Image Graph","first-page":"117","article-title":"Optimized-SSIM based quantization in optical remote sensing image compression","author":"Yang","year":"2026"},{"issue":"1","key":"10.1016\/j.cam.2026.117540_bib0035","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1016\/j.jmaa.2008.11.074","article-title":"Inversion of analytically perturbed linear operators that are singular at the origin","volume":"353","author":"Howlett","year":"2009","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/j.cam.2026.117540_bib0036","series-title":"Lectures on the Nearest Neighbor Method","volume":"246","author":"Biau","year":"2015"},{"key":"10.1016\/j.cam.2026.117540_bib0037","doi-asserted-by":"crossref","first-page":"1977","DOI":"10.1137\/22M147637X","article-title":"Convergence results in image interpolation with the continuous SSIM","volume":"15","author":"Marchetti","year":"2022","journal-title":"SIAM J. Imaging Sci."},{"key":"10.1016\/j.cam.2026.117540_bib0038","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1007\/s10851-022-01135-6","article-title":"Image scaling by de la Vall\u00e9e-Poussin filtered interpolation","volume":"65","author":"Occorsio","year":"2023","journal-title":"J. Math. Imaging Vis."},{"key":"10.1016\/j.cam.2026.117540_bib0039","series-title":"Monte Carlo Sampling Methods using Markov Chains and Their Applications","first-page":"97","author":"Hastings","year":"1970"}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726001457?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726001457?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T16:23:05Z","timestamp":1777566185000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042726001457"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":39,"alternative-id":["S0377042726001457"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2026.117540","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Implementation of neural network operators with applications to remote sensing data","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2026.117540","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Author(s). Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"117540"}}