{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T20:58:20Z","timestamp":1774645100021,"version":"3.50.1"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2025,3,1]],"date-time":"2025-03-01T00:00:00Z","timestamp":1740787200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,1]],"date-time":"2025-03-01T00:00:00Z","timestamp":1740787200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2025,7]]},"DOI":"10.1007\/s00034-025-03014-y","type":"journal-article","created":{"date-parts":[[2025,3,1]],"date-time":"2025-03-01T04:19:26Z","timestamp":1740802766000},"page":"4796-4827","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Double Robust Zero-Watermarking Algorithms Based on Fractional-Order Jacobi-Fourier Moments and FFST-Schur"],"prefix":"10.1007","volume":"44","author":[{"given":"Yu","family":"Lu","sequence":"first","affiliation":[]},{"given":"Xin-hui","family":"Lu","sequence":"additional","affiliation":[]},{"given":"Guang-yun","family":"Yang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6604-9251","authenticated-orcid":false,"given":"Xiang-guang","family":"Xiong","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,1]]},"reference":[{"issue":"15","key":"3014_CR1","doi-asserted-by":"publisher","first-page":"8963","DOI":"10.1007\/s00500-023-09130-8","volume":"28","author":"AA Abdulla","year":"2024","unstructured":"A.A. Abdulla, Digital image steganography: challenges, investigation, and recommendation for the future direction. Soft. Comput. 28(15), 8963\u20138976 (2024)","journal-title":"Soft. Comput."},{"issue":"7","key":"3014_CR2","first-page":"31","volume":"151","author":"AA Abdelmgeid","year":"2016","unstructured":"A.A. Abdelmgeid, A.A. Tarek, S.S. Al-Hussien, M.H. Shaimaa, Improving ZOH image steganography method by using braille method. Int. J. Comput. Appl. 151(7), 31\u201335 (2016)","journal-title":"Int. J. Comput. Appl."},{"issue":"9","key":"3014_CR3","first-page":"27","volume":"133","author":"AA Abdelmgeid","year":"2016","unstructured":"A.A. Abdelmgeid, A.A. Tarek, S.S. Al-Hussien, M.H. Shaimaa, New image steganography method using zero order hold zooming. Int. J. Comput. Appl. 133(9), 27\u201331 (2016)","journal-title":"Int. J. Comput. Appl."},{"key":"3014_CR4","first-page":"1123","volume":"13","author":"AM Abduldaim","year":"2022","unstructured":"A.M. Abduldaim, A.K. Faraj, Twofold of algebraic decomposition method used for the watermarking scheme with LWT over medical images. Int. J. Nonlinear Opt. Phys. 13, 1123\u20131129 (2022)","journal-title":"Int. J. Nonlinear Opt. Phys."},{"issue":"3","key":"3014_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.9734\/jamcs\/2019\/v33i330178","volume":"33","author":"AA Ali","year":"2019","unstructured":"A.A. Ali, T.A. El-Hafeez, Y.K. Mohany, An accurate system for face detection and recognition. J. Adv. Math. Comput. Sci. 33(3), 1\u201319 (2019)","journal-title":"J. Adv. Math. Comput. Sci."},{"key":"3014_CR6","first-page":"373","volume":"14","author":"Y Cao","year":"2024","unstructured":"Y. Cao, A.R. Subhashri, A. Chandrasekar, T. Radhika, K.P. Przybyszewski, Exponential state estimation for delayed competitive neural network via stochastic sampled-data control with Markov jump parameters under actuator failure. J. Artif. Intell. Soft. 14, 373\u2013385 (2024)","journal-title":"J. Artif. Intell. Soft."},{"key":"3014_CR7","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1016\/j.matcom.2023.08.007","volume":"222","author":"Y Cao","year":"2024","unstructured":"Y. Cao, A. Chandrasekar, T. Radhika, V. Vijayakumar, Input-to-state stability of stochastic Markovian jump genetic regulatory networks. Math. Comput. Simul. 222, 174\u2013187 (2024)","journal-title":"Math. Comput. Simul."},{"key":"3014_CR8","doi-asserted-by":"publisher","first-page":"408","DOI":"10.1007\/s00034-023-02479-z","volume":"43","author":"R Dwivedi","year":"2024","unstructured":"R. Dwivedi, D. Awasthi, V.K. Srivastava, An optimized dual image watermarking scheme based on redundant DWT and randomized SVD with Henon mapping encryption. Circuits Syst. Signal Process. 43, 408\u2013456 (2024)","journal-title":"Circuits Syst. Signal Process."},{"key":"3014_CR9","unstructured":"C. Dong, H. Zhang, J. Li, Y. Chen, Robust zero-watermarking for medical image based on DCT, in 2011 6th International Conference on Computer Sciences and Convergence Information Technology (ICCIT) (2019), pp. 900\u2013904"},{"issue":"15","key":"3014_CR10","doi-asserted-by":"publisher","first-page":"6727","DOI":"10.3390\/s23156727","volume":"23","author":"M Eman","year":"2023","unstructured":"M. Eman, T.M. Mahmoud, M.M. Ibrahim, T.A. El-Hafeez, Innovative hybrid approach for masked face recognition using pretrained mask detection and segmentation, robust PCA, and KNN classifier. Sensors 23(15), 6727 (2023)","journal-title":"Sensors"},{"key":"3014_CR11","doi-asserted-by":"crossref","unstructured":"A. Fierro-Radilla, M. Nakano-Miyatake, M. Cedillo-Hernandez, L. Cleofas-Sanchez, H. Perez-Meana, A robust image zero-watermarking using convolutional neural networks, in 2019 7th International Workshop on Biometrics and Forensics (IWBF) (2019), pp. 1\u20135","DOI":"10.1109\/IWBF.2019.8739245"},{"key":"3014_CR12","unstructured":"M. Garg, J.S. Ubhi, A.K. Aggarwal, Steganography and its advancements in spatial domain. EasyChair No. 2177 (2019)"},{"key":"3014_CR13","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1002\/9781119847717.ch17","volume":"66","author":"M Garg","year":"2024","unstructured":"M. Garg, J.S. Ubhi, A.K. Aggarwal, Current advancements in steganography: a review. Model. Optim. Signals Using Mach. Learn. Tech. 66, 327\u2013348 (2024)","journal-title":"Model. Optim. Signals Using Mach. Learn. Tech."},{"key":"3014_CR14","volume":"65","author":"J Gao","year":"2022","unstructured":"J. Gao, L. Zhi, B. Fan, An efficient robust zero watermarking scheme for diffusion tensor-Magnetic resonance imaging high-dimensional data. J. Inf. Secur. Appl. 65, 103106 (2022)","journal-title":"J. Inf. Secur. Appl."},{"issue":"3","key":"3014_CR15","doi-asserted-by":"publisher","first-page":"841","DOI":"10.1007\/s11042-013-1701-8","volume":"74","author":"G Gao","year":"2015","unstructured":"G. Gao, G. Jiang, Bessel\u2013Fourier moment-based robust image zero-watermarking. Multimed. Tools Appl. 74(3), 841\u2013858 (2015)","journal-title":"Multimed. Tools Appl."},{"issue":"7","key":"3014_CR16","doi-asserted-by":"publisher","DOI":"10.3390\/math10071154","volume":"10","author":"T Huang","year":"2022","unstructured":"T. Huang, J. Xu, Y. Yang, B. Han, Robust zero-watermarking algorithm for medical images using double-tree complex wavelet transform and Hessenberg decomposition. Mathematics 10(7), 101154 (2022)","journal-title":"Mathematics"},{"key":"3014_CR17","first-page":"1","volume":"66","author":"B Han","year":"2023","unstructured":"B. Han, H. Wang, D. Qiao, J. Xu, T. Yan, Application of zero-watermarking scheme based on Swin transformer for securing the metaverse healthcare data. IEEE J. Biomed. Health 66, 1\u201310 (2023)","journal-title":"IEEE J. Biomed. Health"},{"key":"3014_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.bspc.2022.104478","volume":"81","author":"T Huang","year":"2023","unstructured":"T. Huang, J. Xu, S. Tu, B. Han, Robust zero-watermarking scheme based on a depthwise overparameterized VGG network in healthcare information security. Biomed. Signal Proces. 81, 104478 (2023)","journal-title":"Biomed. Signal Proces."},{"key":"3014_CR19","doi-asserted-by":"publisher","first-page":"5551520","DOI":"10.1155\/2021\/5551520","volume":"2021","author":"B Han","year":"2021","unstructured":"B. Han, J. Du, Y. Jia, H. Zhu, Zero-watermarking algorithm for medical image based on VGG19 deep convolution neural network. J. Healthc. Eng. 2021, 5551520 (2021)","journal-title":"J. Healthc. Eng."},{"issue":"10","key":"3014_CR20","first-page":"2172","volume":"82","author":"R Ito","year":"1999","unstructured":"R. Ito, S. Member, H. Kuwakado, Image size invariant visual cryptography. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 82(10), 2172\u20132177 (1999)","journal-title":"IEICE Trans. Fundam. Electron. Commun. Comput. Sci."},{"key":"3014_CR21","doi-asserted-by":"publisher","first-page":"4339","DOI":"10.1007\/s00034-024-02651-z","volume":"43","author":"SB Jabra","year":"2024","unstructured":"S.B. Jabra, M.B. Farah, Deep learning-based watermarking techniques challenges: a review of current and future trends. Circuits Syst. Signal Process. 43, 4339\u20134368 (2024)","journal-title":"Circuits Syst. Signal Process."},{"key":"3014_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2022.118529","volume":"210","author":"G Liu","year":"2022","unstructured":"G. Liu, R. Xiang, J. Liu, R. Pan, Z. Zhang, An invisible and robust watermarking scheme using convolutional neural networks. Expert Syst. Appl. 210, 118529 (2022)","journal-title":"Expert Syst. Appl."},{"key":"3014_CR23","doi-asserted-by":"crossref","unstructured":"D. Labate, W. Lim, G. Kutyniok, G. Weiss, Sparse multidimensional representation using Shearlets. Wavelets XI 5914, 59140U-59140U9 (2005)","DOI":"10.1117\/12.613494"},{"key":"3014_CR24","doi-asserted-by":"publisher","DOI":"10.1016\/j.compeleceng.2024.109371","volume":"118","author":"P Meesala","year":"2024","unstructured":"P. Meesala, D.M. Thounaojam, Integrating fresnelet transform and spiking cortical model for robust medical image cryptosystem in zero-watermarking. Comput. Electr. Eng. 118, 109371 (2024)","journal-title":"Comput. Electr. Eng."},{"key":"3014_CR25","doi-asserted-by":"publisher","first-page":"1160","DOI":"10.1007\/s10851-021-01048-w","volume":"63","author":"B Ma","year":"2021","unstructured":"B. Ma, L. Chang, C. Wang, J. Li, G. Li, Z. Xia, X. Wang, Double medical images zero-watermarking algorithm based on the chaotic system and ternary accurate polar complex exponential transform. J. Math. Imaging Vis. 63, 1160\u20131178 (2021)","journal-title":"J. Math. Imaging Vis."},{"key":"3014_CR26","first-page":"659","volume":"1252","author":"B Ma","year":"2020","unstructured":"B. Ma, L. Chang, C. Wang, J. Li, Y. Wang, Remote sensing image zero-watermarking algorithm based on accurate polar harmonic Fourier moment. Artif. Intell. Secur. 1252, 659\u2013673 (2020)","journal-title":"Artif. Intell. Secur."},{"key":"3014_CR27","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1007\/s10851-022-01084-0","volume":"64","author":"P Niu","year":"2022","unstructured":"P. Niu, L. Wang, F. Wang, H. Yang, X. Wang, Fast quaternion log-polar radial harmonic Fourier moments for color image zero-watermarking. J. Math. Imaging Vis. 64, 537\u2013568 (2022)","journal-title":"J. Math. Imaging Vis."},{"key":"3014_CR28","doi-asserted-by":"crossref","unstructured":"M. Naor, A. Shamir, Visual cryptography, in Advances in Cryptology\u2014EUROCRYPT'94 (1995), pp. 1\u201312","DOI":"10.1007\/BFb0053419"},{"issue":"40","key":"3014_CR29","doi-asserted-by":"publisher","first-page":"1245","DOI":"10.1016\/j.patcog.2006.07.016","volume":"4","author":"Z Ping","year":"2007","unstructured":"Z. Ping, H. Ren, J. Zou, Y. Sheng, W. Bo, Generic orthogonal moments: Jacobi\u2013Fourier moments for invariant image description. Pattern Recogn. 4(40), 1245\u20131254 (2007)","journal-title":"Pattern Recogn."},{"key":"3014_CR30","first-page":"179","volume":"12240","author":"F Qin","year":"2020","unstructured":"F. Qin, J. Li, H. Li, J. Liu, S.A. Nawaz, Y. Liu, A robust zero-watermarking algorithm for medical images using Curvelet-DCT and RSA pseudo-random sequences. Artif. Intell. Secur. 12240, 179\u2013190 (2020)","journal-title":"Artif. Intell. Secur."},{"issue":"9","key":"3014_CR31","first-page":"2023","volume":"4","author":"L Sun","year":"2015","unstructured":"L. Sun, J. Xu, X. Zhang, W. Dong, Y. Tian, A novel generalized Arnold transform-based zero-watermarking scheme. Appl. Math. Inf. Sci. 4(9), 2023\u20132035 (2015)","journal-title":"Appl. Math. Inf. Sci."},{"key":"3014_CR32","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1007\/s00500-019-03924-5","volume":"24","author":"Q Su","year":"2019","unstructured":"Q. Su, X. Zhang, G. Wang, An improved watermarking algorithm for color image using Schur decomposition. Soft. Comput. 24, 445\u2013460 (2019)","journal-title":"Soft. Comput."},{"key":"3014_CR33","doi-asserted-by":"crossref","unstructured":"A.A. Saabia, T.A. El-Hafeez, A.M. Zaki, Face recognition based on Grey Wolf Optimization for feature selection, in Proceedings of the International Conference on Advanced Intelligent Systems and Informatics, vol. 4 (2018), pp. 273\u2013283","DOI":"10.1007\/978-3-319-99010-1_25"},{"issue":"3","key":"3014_CR34","first-page":"25","volume":"13","author":"ME Taha","year":"2023","unstructured":"M.E. Taha, T. Mostafa, A. El-Rahman, T.A. El-Hafeez, A novel hybrid approach to masked face recognition using robust PCA and GOA optimizer. Sci. J. Damietta Facul. Sci. 13(3), 25\u201335 (2023)","journal-title":"Sci. J. Damietta Facul. Sci."},{"key":"3014_CR35","first-page":"3503267","volume":"2019","author":"L Tan","year":"2019","unstructured":"L. Tan, X. Yu, Medical image fusion based on fast finite Shearlet transform and sparse representation. Comput. Math. Method. M. 2019, 3503267 (2019)","journal-title":"Comput. Math. Method. M."},{"issue":"31","key":"3014_CR36","first-page":"214","volume":"2","author":"Q Wen","year":"2003","unstructured":"Q. Wen, P. Sun, S. Wang, Concept and application of zero watermarking. Acta Automatica Sinica 2(31), 214\u2013216 (2003)","journal-title":"Acta Automatica Sinica"},{"key":"3014_CR37","doi-asserted-by":"publisher","first-page":"3175","DOI":"10.1007\/s00371-022-02544-9","volume":"38","author":"X Wang","year":"2022","unstructured":"X. Wang, M. Wen, X. Tan, H. Zhang, J. Hu, H. Qin, A novel zero-watermarking algorithm based on robust statistical features for natural images. Visual Comput. 38, 3175\u20133188 (2022)","journal-title":"Visual Comput."},{"key":"3014_CR38","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/j.ins.2018.08.028","volume":"470","author":"C Wang","year":"2019","unstructured":"C. Wang, X. Wang, Z. Xia, C. Zhang, Ternary radial harmonic Fourier moments based robust stereo image zero-watermarking algorithm. Inform. Sci. 470, 109\u2013120 (2019)","journal-title":"Inform. Sci."},{"key":"3014_CR39","doi-asserted-by":"publisher","first-page":"6844","DOI":"10.1007\/s00034-022-02076-6","volume":"41","author":"H Wang","year":"2022","unstructured":"H. Wang, Y. Chen, T. Zhao, Modified Zernike moments and its application in geometrically resilient image zero-watermarking. Circuits Syst. Signal Process. 41, 6844\u20136861 (2022)","journal-title":"Circuits Syst. Signal Process."},{"key":"3014_CR40","doi-asserted-by":"publisher","first-page":"26355","DOI":"10.1007\/s11042-016-4130-7","volume":"76","author":"C Wang","year":"2017","unstructured":"C. Wang, X. Wang, X. Chen, C. Zhang, Robust zero-watermarking algorithm based on polar complex exponential transform and logistic mapping. Multimed. Tools Appl. 76, 26355\u201326376 (2017)","journal-title":"Multimed. Tools Appl."},{"issue":"44","key":"3014_CR41","first-page":"160","volume":"1","author":"X Xiong","year":"2018","unstructured":"X. Xiong, Spatial domain robust zero watermarking scheme. Acta Automatica Sinica 1(44), 160\u2013175 (2018)","journal-title":"Acta Automatica Sinica"},{"key":"3014_CR42","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2020.107864","volume":"180","author":"Z Xia","year":"2021","unstructured":"Z. Xia, X. Wang, B. Han, Q. Li, X. Wang, C. Wang, T. Zhao, Color image triple zero-watermarking using decimal-order polar harmonic transforms and chaotic system. Signal Process. 180, 107864 (2021)","journal-title":"Signal Process."},{"key":"3014_CR43","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1016\/j.sigpro.2019.06.025","volume":"164","author":"Z Xia","year":"2019","unstructured":"Z. Xia, X. Wang, X. Li, C. Wang, S. Unar, M. Wang, T. Zhao, Efficient copyright protection for three CT images based on quaternion polar harmonic Fourier moments. Signal Process. 164, 368\u2013379 (2019)","journal-title":"Signal Process."},{"key":"3014_CR44","doi-asserted-by":"crossref","unstructured":"K. Yang, W. Wang, Z. Yuan, W. Zhao, Strong robust zero watermarking algorithm based on NSCT transform and image normalization, in IEEE 3rd Advanced Information Technology, Electronic and Automation Control Conference (IAEAC) (2018), pp. 236\u2013240","DOI":"10.1109\/IAEAC.2018.8577943"},{"key":"3014_CR45","doi-asserted-by":"publisher","DOI":"10.1016\/j.image.2019.115747","volume":"82","author":"H Yang","year":"2020","unstructured":"H. Yang, S. Qi, P. Niu, X. Wang, Color image zero-watermarking based on fast quaternion generic polar complex exponential transform. Signal Process. Image 82, 115747 (2020)","journal-title":"Signal Process. Image"},{"key":"3014_CR46","doi-asserted-by":"crossref","unstructured":"M. Yamni, H. Karmouni, A. Daoui, O. Elogri, M. Sayyouri, H. Qjidaa, Blind image zero-watermarking algorithm based on radial Krawtchouk moments and chaotic system, in International Conference on Intelligent Systems Computer Vision (ISCV) (2020), pp. 1\u20137","DOI":"10.1109\/ISCV49265.2020.9204071"},{"key":"3014_CR47","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2021.107898","volume":"115","author":"H Yang","year":"2021","unstructured":"H. Yang, S. Qi, J. Tian, P. Niu, X. Wang, Robust and discriminative image representation: fractional-order Jacobi-Fourier moments. Pattern Recogn. 115, 107898 (2021)","journal-title":"Pattern Recogn."},{"issue":"1","key":"3014_CR48","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1049\/cit2.12282","volume":"9","author":"Y Yuan","year":"2024","unstructured":"Y. Yuan, J. Li, J. Liu, U.A. Bhatti, Z. Liu, Robust zero-watermarking algorithm based on discrete wavelet transform and daisy descriptors for encrypted medical image. CAAI Trans. Intell. Technol. 9(1), 40\u201353 (2024)","journal-title":"CAAI Trans. Intell. Technol."},{"key":"3014_CR49","unstructured":"The USC-SIPI image database. http:\/\/sipi.usc.edu\/database\/"},{"key":"3014_CR50","unstructured":"COVID-19 image database. https:\/\/github.com\/ieee8023\/covid-chestxray-dataset"}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-025-03014-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00034-025-03014-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-025-03014-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T21:01:49Z","timestamp":1751403709000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00034-025-03014-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,1]]},"references-count":50,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2025,7]]}},"alternative-id":["3014"],"URL":"https:\/\/doi.org\/10.1007\/s00034-025-03014-y","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"value":"0278-081X","type":"print"},{"value":"1531-5878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,1]]},"assertion":[{"value":"29 July 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 January 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 January 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 March 2025","order":4,"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 there is no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Ethics approval is not required in this manuscript as all the materials like related work, etc. taken from other sources have been cited properly in this paper.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}}]}}