{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T11:44:21Z","timestamp":1750765461001,"version":"3.37.3"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,7,15]],"date-time":"2022-07-15T00:00:00Z","timestamp":1657843200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,7,15]],"date-time":"2022-07-15T00:00:00Z","timestamp":1657843200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100011322","name":"Macau University of Science and Technology Foundation","doi-asserted-by":"crossref","award":["No. FRG-21-020-FI"],"award-info":[{"award-number":["No. FRG-21-020-FI"]}],"id":[{"id":"10.13039\/501100011322","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"published-print":{"date-parts":[[2023,1]]},"DOI":"10.1007\/s11227-022-04691-1","type":"journal-article","created":{"date-parts":[[2022,7,15]],"date-time":"2022-07-15T18:02:57Z","timestamp":1657908177000},"page":"677-701","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An image super-resolution method based on polynomial exponential function and non-uniform rectangular partition"],"prefix":"10.1007","volume":"79","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6222-6927","authenticated-orcid":false,"given":"Weikang","family":"Zhao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"KinTak","family":"U","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huibin","family":"Luo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,7,15]]},"reference":[{"issue":"3","key":"4691_CR1","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/1049-9652(91)90045-L","volume":"53","author":"M Irani","year":"1991","unstructured":"Irani M, Peleg S (1991) Improving resolution by image registration. CVGIP Graphic Models Image Process 53(3):231\u2013239. https:\/\/doi.org\/10.1016\/1049-9652(91)90045-L","journal-title":"CVGIP Graphic Models Image Process"},{"key":"4691_CR2","doi-asserted-by":"publisher","first-page":"787","DOI":"10.1007\/s11227-017-2160-1","volume":"78","author":"JS Shim","year":"2018","unstructured":"Shim JS, Ju YW, Park SC (2018) Design and implementation of a pedestrian recognition algorithm using trilinear interpolation based on HOG-UDP. J Supercomput 78:787\u2013800. https:\/\/doi.org\/10.1007\/s11227-017-2160-1","journal-title":"J Supercomput"},{"key":"4691_CR3","doi-asserted-by":"publisher","first-page":"1426","DOI":"10.1109\/TMM.2020.2997126","volume":"23","author":"X Yao","year":"2021","unstructured":"Yao X, Wu Q, Zhang P, Bao F (2021) Weighted adaptive image super-resolution scheme based on local fractal feature and image roughness. IEEE Trans Multimed 23:1426\u20131441. https:\/\/doi.org\/10.1109\/TMM.2020.2997126","journal-title":"IEEE Trans Multimed"},{"issue":"9","key":"4691_CR4","doi-asserted-by":"publisher","first-page":"1707","DOI":"10.1109\/TMM.2016.2593039","volume":"18","author":"S Zhu","year":"2016","unstructured":"Zhu S, Zeng B, Zeng L, Gabbouj M (2016) Image interpolation based on non-local geometric similarities and directional gradients. IEEE Trans Multimed 18(9):1707\u20131719. https:\/\/doi.org\/10.1109\/TMM.2016.2593039","journal-title":"IEEE Trans Multimed"},{"key":"4691_CR5","doi-asserted-by":"publisher","unstructured":"Caiming Z, Xin Z, Xuemei L, Fuhua C (2013) Cubic surface fitting to image with edges as constraints. In: 2013 IEEE International Conference on Image Processing, pp. 1046\u20131050 https:\/\/doi.org\/10.1109\/ICIP.2013.6738216","DOI":"10.1109\/ICIP.2013.6738216"},{"key":"4691_CR6","doi-asserted-by":"publisher","unstructured":"Allebach J, Wong PW (1996) Edge-directed interpolation. In: Proceedings of 3rd IEEE International Conference on Image Processing, pp. 707\u2013710 . https:\/\/doi.org\/10.1109\/ICIP.1996.560768","DOI":"10.1109\/ICIP.1996.560768"},{"key":"4691_CR7","doi-asserted-by":"publisher","unstructured":"Jing G, Choi YK, Wang J, Wang W (2014) Gradient guided image interpolation. In: 2014 IEEE International Conference on Image Processing (ICIP), pp. 1822\u20131826 , https:\/\/doi.org\/10.1109\/ICIP.2014.7025365","DOI":"10.1109\/ICIP.2014.7025365"},{"key":"4691_CR8","doi-asserted-by":"publisher","first-page":"7521","DOI":"10.1007\/s13369-018-3150-1","volume":"43","author":"R Nayak","year":"2018","unstructured":"Nayak R, Patra D (2018) Enhanced iterative back-projection based super-resolution reconstruction of digital images. Arab J Sci Eng 43:7521\u20137547. https:\/\/doi.org\/10.1007\/s13369-018-3150-1","journal-title":"Arab J Sci Eng"},{"key":"4691_CR9","doi-asserted-by":"publisher","unstructured":"Tang Z, Deng M, Xiao C, Yu J (2011) Projection onto convex sets super-resolution image reconstruction based on wavelet bi-cubic interpolation. In: Proceedings of 2011 International Conference on Electronic Mechanical Engineering and Information Technology, pp. 351\u2013354 , https:\/\/doi.org\/10.1109\/EMEIT.2011.6022950","DOI":"10.1109\/EMEIT.2011.6022950"},{"key":"4691_CR10","doi-asserted-by":"crossref","unstructured":"Freeman WT, Liu C (2011) Markov random fields for super-resolution and texture synthesis. The MIT Press, Massachusetts","DOI":"10.7551\/mitpress\/8579.003.0012"},{"key":"4691_CR11","doi-asserted-by":"publisher","unstructured":"Belekos SP, Galatsanos NP, Babacan, SD, Katsaggelos, AK (2009) Maximum a posteriori super-resolution of compressed video using a new multichannel image prior. In: 2009 16th IEEE International Conference on Image Processing (ICIP), pp. 2797\u20132800, https:\/\/doi.org\/10.1109\/ICIP.2009.5414174","DOI":"10.1109\/ICIP.2009.5414174"},{"issue":"2","key":"4691_CR12","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1109\/TPAMI.2015.2439281","volume":"38","author":"C Dong","year":"2016","unstructured":"Dong C, Loy CC, He K, Tang X (2016) Image super-resolution using deep convolutional networks. IEEE Trans Pattern Anal Mach Intell 38(2):295\u2013307. https:\/\/doi.org\/10.1109\/TPAMI.2015.2439281","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"4691_CR13","doi-asserted-by":"publisher","unstructured":"Kim J, Lee JK, Lee KM (2016) Accurate image super-resolution using very deep convolutional networks. In: 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1646\u20131654, https:\/\/doi.org\/10.1109\/CVPR.2016.182","DOI":"10.1109\/CVPR.2016.182"},{"key":"4691_CR14","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1016\/j.neucom.2016.02.046","volume":"194","author":"Y Liang","year":"2016","unstructured":"Liang Y, Wang J, Zhou S, Gong Y, Zheng N (2016) Incorporating image priors with deep convolutional neural networks for image super-resolution. Neurocomputing 194:340\u2013347. https:\/\/doi.org\/10.1016\/j.neucom.2016.02.046","journal-title":"Neurocomputing"},{"key":"4691_CR15","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1109\/TIP.2019.2928121","volume":"29","author":"X Sun","year":"2020","unstructured":"Sun X, Nasrabadi NM, Tran TD (2020) Supervised deep sparse coding networks for image classification. IEEE Trans Image Process 29:405\u2013418. https:\/\/doi.org\/10.1109\/TIP.2019.2928121","journal-title":"IEEE Trans Image Process"},{"key":"4691_CR16","doi-asserted-by":"publisher","unstructured":"Gu S, Zuo W, Xie Q, Meng D, Feng X, Zhang L (2015) Convolutional sparse coding for image super-resolution. In: 2015 IEEE International Conference on Computer Vision (ICCV), pp. 1823\u20131831 ,https:\/\/doi.org\/10.1109\/ICCV.2015.212","DOI":"10.1109\/ICCV.2015.212"},{"issue":"1","key":"4691_CR17","doi-asserted-by":"publisher","first-page":"1687","DOI":"10.1186\/s13640-016-0125-6","volume":"3","author":"H Yu","year":"2017","unstructured":"Yu H, Huang T-Z, Deng L-J, Zhao X-L (2017) Super-resolution via a fast deconvolution with kernel estimation. EURASIP J Image Video Process 3(1):1687\u20135281. https:\/\/doi.org\/10.1186\/s13640-016-0125-6","journal-title":"EURASIP J Image Video Process"},{"key":"4691_CR18","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1038\/s41592-020-01048-5","volume":"18","author":"C Qiao","year":"2021","unstructured":"Qiao C, Li D, Guo Y, Liu C, Jiang T, Dai Q, Li D (2021) Evaluation and development of deep neural networks for image super-resolution in optical microscopy. Nat Methods 18:194\u2013202. https:\/\/doi.org\/10.1038\/s41592-020-01048-5","journal-title":"Nat Methods"},{"key":"4691_CR19","doi-asserted-by":"publisher","first-page":"3098","DOI":"10.1109\/TIP.2021.3058764","volume":"30","author":"X Deng","year":"2021","unstructured":"Deng X, Zhang Y, Xu M, Gu S, Duan Y (2021) Deep coupled feedback network for joint exposure fusion and image super-resolution. IEEE Trans Image Process 30:3098\u20133112. https:\/\/doi.org\/10.1109\/TIP.2021.3058764","journal-title":"IEEE Trans Image Process"},{"key":"4691_CR20","doi-asserted-by":"publisher","unstructured":"Andreas L, Martin D, Luc VG, Radu T (2020) Srflow: Learning the super-resolution space with normalizing flow. In: Computer Vision \u2013ECCV 2020, pp. 715\u2013732, https:\/\/doi.org\/10.1007\/978-3-030-58558-7_42","DOI":"10.1007\/978-3-030-58558-7_42"},{"key":"4691_CR21","doi-asserted-by":"publisher","unstructured":"Niu B, Wen W, Ren W, Zhang X, Yang L, Wang S, Zhang K, Cao X, Shen H (2020) Single image super-resolution via a holistic attention network. In: Computer Vision \u2013ECCV 2020, pp. 191\u2013207, Springer, Cham https:\/\/doi.org\/10.1007\/978-3-030-58610-2_12","DOI":"10.1007\/978-3-030-58610-2_12"},{"issue":"1","key":"4691_CR22","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1109\/TCYB.2015.2501373","volume":"47","author":"K Zeng","year":"2017","unstructured":"Zeng K, Yu J, Wang R, Li C, Tao D (2017) Coupled deep autoencoder for single image super-resolution. IEEE Trans Cybern 47(1):27\u201337. https:\/\/doi.org\/10.1109\/TCYB.2015.2501373","journal-title":"IEEE Trans Cybern"},{"key":"4691_CR23","doi-asserted-by":"publisher","unstructured":"Huang JB, Singh A, Ahuja N (2015) Single image super-resolution from transformed self-exemplars. In: 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 5197\u20135206 https:\/\/doi.org\/10.1109\/CVPR.2015.7299156","DOI":"10.1109\/CVPR.2015.7299156"},{"issue":"8","key":"4691_CR24","doi-asserted-by":"publisher","first-page":"3782","DOI":"10.1109\/TIP.2018.2826139","volume":"27","author":"Y Zhang","year":"2018","unstructured":"Zhang Y, Fan Q, Bao F, Liu Y, Zhang C (2018) Single-image super-resolution based on rational fractal interpolation. IEEE Trans Image Process 27(8):3782\u20133797. https:\/\/doi.org\/10.1109\/TIP.2018.2826139","journal-title":"IEEE Trans Image Process"},{"issue":"6","key":"4691_CR25","doi-asserted-by":"publisher","first-page":"1407","DOI":"10.1109\/TMM.2019.2943750","volume":"22","author":"Y Zhang","year":"2020","unstructured":"Zhang Y, Wang P, Bao F, Yao X, Zhang C, Lin H (2020) A single-image super-resolution method based on progressive-iterative approximation. IEEE Trans Multimed 22(6):1407\u20131422. https:\/\/doi.org\/10.1109\/TMM.2019.2943750","journal-title":"IEEE Trans Multimed"},{"key":"4691_CR26","doi-asserted-by":"publisher","first-page":"1069","DOI":"10.1109\/TMM.2020.2992940","volume":"23","author":"Y Zhang","year":"2021","unstructured":"Zhang Y, Cai Z, Xiong G (2021) A new image compression algorithm based on non-uniform partition and u-system. IEEE Trans Multimed 23:1069\u20131082. https:\/\/doi.org\/10.1109\/TMM.2020.2992940","journal-title":"IEEE Trans Multimed"},{"key":"4691_CR27","doi-asserted-by":"publisher","unstructured":"U K, He X, Yang B, Qi D, Tang Z (2010) A novel image denoising algorithm based on non-uniform rectangular partition and interpolation. In: Proceedings of the 2010 International Conference on Multimedia Communications. MEDIACOM \u201910, pp. 9\u201312. IEEE Computer Society, USA ,https:\/\/doi.org\/10.1109\/MEDIACOM.2010.25","DOI":"10.1109\/MEDIACOM.2010.25"},{"issue":"6","key":"4691_CR28","doi-asserted-by":"publisher","first-page":"1372","DOI":"10.1109\/TMM.2018.2881069","volume":"21","author":"X Yuan","year":"2019","unstructured":"Yuan X, Cai Z (2019) An adaptive triangular partition algorithm for digital images. IEEE Trans Multimed 21(6):1372\u20131383. https:\/\/doi.org\/10.1109\/TMM.2018.2881069","journal-title":"IEEE Trans Multimed"},{"key":"4691_CR29","doi-asserted-by":"publisher","unstructured":"Li Y, U K (2021) Zero-watermark method based on non-uniform btc partition. In: 2021 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR), pp. 1\u20136 https:\/\/doi.org\/10.1109\/ICWAPR54887.2021.9736187","DOI":"10.1109\/ICWAPR54887.2021.9736187"},{"issue":"1","key":"4691_CR30","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1016\/j.jde.2017.09.003","volume":"264","author":"Z-T Wen","year":"2018","unstructured":"Wen Z-T, Gundersen GG, Heittokangas J (2018) Dual exponential polynomials and linear differential equations. J Differ Equ 264(1):98\u2013114. https:\/\/doi.org\/10.1016\/j.jde.2017.09.003","journal-title":"J Differ Equ"},{"key":"4691_CR31","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/j.sigpro.2013.10.017","volume":"97","author":"F Vincent","year":"2014","unstructured":"Vincent F, Besson O, Chaumette E (2014) Approximate maximum likelihood estimation of two closely spaced sources. Signal Process 97:83\u201390. https:\/\/doi.org\/10.1016\/j.sigpro.2013.10.017","journal-title":"Signal Process"},{"issue":"4","key":"4691_CR32","doi-asserted-by":"publisher","first-page":"968","DOI":"10.1109\/78.668550","volume":"46","author":"MS Spurbeck","year":"1998","unstructured":"Spurbeck MS, Mullis CT (1998) Least squares approximation of perfect reconstruction filter banks. IEEE Trans Signal Process 46(4):968\u2013978. https:\/\/doi.org\/10.1109\/78.668550","journal-title":"IEEE Trans Signal Process"},{"key":"4691_CR33","doi-asserted-by":"publisher","first-page":"766","DOI":"10.1016\/j.amc.2019.06.025","volume":"361","author":"X Han","year":"2019","unstructured":"Han X, Han J (2019) Bicubic b-spline surfaces constrained by the biharmonic PDE. Appl Math Comput 361:766\u2013776. https:\/\/doi.org\/10.1016\/j.amc.2019.06.025","journal-title":"Appl Math Comput"},{"key":"4691_CR34","doi-asserted-by":"publisher","unstructured":"Bevilacqua M, Roumy A, Guillemot C, Morel MlA (2012) Low-complexity single-image super-resolution based on nonnegative neighbor embedding. In: Proceedings of the British Machine Vision Conference, pp. 13501\u201313510 https:\/\/doi.org\/10.5244\/C.26.135","DOI":"10.5244\/C.26.135"},{"key":"4691_CR35","doi-asserted-by":"publisher","unstructured":"Zeyde R, Elad M, Protter M (2012) On single image scale-up using sparse-representations. In: Curves and Surfaces, Berlin, Heidelberg, pp. 711\u2013730 https:\/\/doi.org\/10.1007\/978-3-642-27413-8_47","DOI":"10.1007\/978-3-642-27413-8_47"},{"issue":"5","key":"4691_CR36","doi-asserted-by":"publisher","first-page":"898","DOI":"10.1109\/TPAMI.2010.161","volume":"33","author":"P Arbel\u00e1ez","year":"2011","unstructured":"Arbel\u00e1ez P, Maire M, Fowlkes C, Malik J (2011) Contour detection and hierarchical image segmentation. IEEE Trans Pattern Anal Mach Intell 33(5):898\u2013916. https:\/\/doi.org\/10.1109\/TPAMI.2010.161","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"7","key":"4691_CR37","doi-asserted-by":"publisher","first-page":"1002","DOI":"10.1109\/68.593380","volume":"9","author":"GJ Pendock","year":"1997","unstructured":"Pendock GJ, Sampson DD (1997) Signal-to-noise ratio of modulated sources of ASE transmitted over dispersive fiber. IEEE Photonics Technol Lett 9(7):1002\u20131004. https:\/\/doi.org\/10.1109\/68.593380","journal-title":"IEEE Photonics Technol Lett"},{"issue":"11","key":"4691_CR38","doi-asserted-by":"publisher","first-page":"2385","DOI":"10.1109\/TIP.2009.2025923","volume":"18","author":"MP Sampat","year":"2009","unstructured":"Sampat MP, Wang Z, Gupta S, Bovik AC, Markey MK (2009) Complex wavelet structural similarity: a new image similarity index. IEEE Trans Image Process 18(11):2385\u20132401. https:\/\/doi.org\/10.1109\/TIP.2009.2025923","journal-title":"IEEE Trans Image Process"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-022-04691-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-022-04691-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-022-04691-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,24]],"date-time":"2023-11-24T16:41:32Z","timestamp":1700844092000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-022-04691-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,15]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,1]]}},"alternative-id":["4691"],"URL":"https:\/\/doi.org\/10.1007\/s11227-022-04691-1","relation":{},"ISSN":["0920-8542","1573-0484"],"issn-type":[{"type":"print","value":"0920-8542"},{"type":"electronic","value":"1573-0484"}],"subject":[],"published":{"date-parts":[[2022,7,15]]},"assertion":[{"value":"23 June 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 July 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}