{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T21:24:35Z","timestamp":1773955475794,"version":"3.50.1"},"reference-count":61,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2025,7,14]],"date-time":"2025-07-14T00:00:00Z","timestamp":1752451200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,7,14]],"date-time":"2025-07-14T00:00:00Z","timestamp":1752451200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Taishan Scholar Program of Shandong","award":["tsqn202306251"],"award-info":[{"award-number":["tsqn202306251"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62302249"],"award-info":[{"award-number":["62302249"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"The Chunhui Plan Cooperative Scientific Research Project of Ministry of Education","award":["HZKY20220482"],"award-info":[{"award-number":["HZKY20220482"]}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2020MF054"],"award-info":[{"award-number":["ZR2020MF054"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1007\/s00034-025-03213-7","type":"journal-article","created":{"date-parts":[[2025,7,14]],"date-time":"2025-07-14T05:57:34Z","timestamp":1752472654000},"page":"9180-9208","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Efficient Multispectral Image Zero-Watermarking Based on Sedenion Polar Harmonic Fourier Moments"],"prefix":"10.1007","volume":"44","author":[{"given":"Chunpeng","family":"Wang","sequence":"first","affiliation":[]},{"given":"Guangze","family":"Li","sequence":"additional","affiliation":[]},{"given":"Changxu","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Bin","family":"Ma","sequence":"additional","affiliation":[]},{"given":"Ziqi","family":"Wei","sequence":"additional","affiliation":[]},{"given":"Qinghua","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Zhiqiu","family":"Xia","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,14]]},"reference":[{"key":"3213_CR1","unstructured":"W.K. Benjamin, MatvL, midaha, PGibson, RMcKinlay, Dstl Satellite Imagery Feature Detection, Kaggle (2016). https:\/\/kaggle.com\/competitions\/dstl-satellite-imagery-feature-detection."},{"key":"3213_CR2","doi-asserted-by":"publisher","first-page":"24752","DOI":"10.1038\/srep24752","volume":"6","author":"L Bian","year":"2016","unstructured":"L. Bian, J. Suo, G. Situ, Z. Li, J. Fan, F. Chen, Q. Dai, Multispectral imaging using a single bucket detector. Sci. Rep. 6, 24752 (2016)","journal-title":"Sci. Rep."},{"key":"3213_CR3","doi-asserted-by":"publisher","first-page":"16083","DOI":"10.1007\/s11042-024-19664-0","volume":"84","author":"A Bourzik","year":"2025","unstructured":"A. Bourzik, B. Bouikhalene, J. El-Mekkaoui, A. Hjouji, Accurate image reconstruction by separable krawtchouk-charlier moments with automatic parameter selection using artificial bee colony optimization. Multimed. Tools Appl. 84, 16083\u201316104 (2025)","journal-title":"Multimed. Tools Appl."},{"key":"3213_CR4","first-page":"47","volume":"28","author":"K Carmody","year":"1988","unstructured":"K. Carmody, Circular and hyperbolic quaternions, octonions, and sedenions. Appl. Math. Comput. 28, 47\u201372 (1988)","journal-title":"Appl. Math. Comput."},{"key":"3213_CR5","doi-asserted-by":"publisher","first-page":"34565","DOI":"10.1007\/s11042-023-15015-7","volume":"82","author":"R Chu","year":"2023","unstructured":"R. Chu, S. Zhang, J. Mou, X. Gao, A zero-watermarking for color image based on LWT-SVD and chaotic system. Multimed. Tools Appl. 82, 34565\u201334588 (2023)","journal-title":"Multimed. Tools Appl."},{"key":"3213_CR6","doi-asserted-by":"publisher","first-page":"8927","DOI":"10.1016\/j.jksuci.2022.08.021","volume":"34","author":"A Daoui","year":"2022","unstructured":"A. Daoui, M. Yamni, H. Karmouni, M. Sayyouri, H. Qjidaa, M. Ahmad, A.A.A. El-Latif, Color stereo image encryption and local zero-watermarking schemes using octonion Hahn moments and modified Henon map. J. King Saud Univ.-Comput. Inf. Sci. 34, 8927\u20138954 (2022)","journal-title":"J. King Saud Univ.-Comput. Inf. Sci."},{"key":"3213_CR7","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/j.jfranklin.2023.11.036","volume":"361","author":"X-F Feng","year":"2024","unstructured":"X.-F. Feng, M.-R. Jiang, H. Zhang, C.-P. Wang, Robust multifunctional watermarking system based zero-watermarking and polar harmonic Fourier moments. J. Frankl. Inst. 361, 319\u2013340 (2024)","journal-title":"J. Frankl. Inst."},{"key":"3213_CR8","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-Fourier moment-based robust image zero-watermarking. Multimed. Tools Appl. 74, 841\u2013858 (2015)","journal-title":"Multimed. Tools Appl."},{"key":"3213_CR9","doi-asserted-by":"publisher","DOI":"10.1016\/j.bspc.2021.103007","volume":"70","author":"KM Hosny","year":"2021","unstructured":"K.M. Hosny, M.M. Darwish, New geometrically invariant multiple zero-watermarking algorithm for color medical images. Biomed. Signal Process. Control 70, 103007 (2021)","journal-title":"Biomed. Signal Process. Control"},{"key":"3213_CR10","doi-asserted-by":"publisher","first-page":"3364","DOI":"10.1109\/JSTARS.2023.3261866","volume":"16","author":"Z Huang","year":"2023","unstructured":"Z. Huang, Q. Liu, H. Zhou, G. Gao, T. Xu, Q. Wen, Y. Wang, Building detection from panchromatic and multispectral images with dual-stream asymmetric fusion networks. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 16, 3364\u20133377 (2023)","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"3213_CR11","doi-asserted-by":"publisher","first-page":"3491","DOI":"10.18282\/gfr.v6i1.3491","volume":"6","author":"B Jin","year":"2024","unstructured":"B. Jin, X. Xu, Carbon emission allowance price forecasting for China Guangdong carbon emission exchange via the neural network. Glob. Financ. Rev. 6, 3491 (2024)","journal-title":"Glob. Financ. Rev."},{"key":"3213_CR12","doi-asserted-by":"publisher","first-page":"1927","DOI":"10.1108\/JM2-12-2023-0315","volume":"19","author":"B Jin","year":"2024","unstructured":"B. Jin, X. Xu, Pre-owned housing price index forecasts using Gaussian process regressions. J. Model. Manag. 19, 1927\u20131958 (2024)","journal-title":"J. Model. Manag."},{"key":"3213_CR13","doi-asserted-by":"publisher","DOI":"10.1177\/03019233241254891","author":"B Jin","year":"2024","unstructured":"B. Jin, X. Xu, Machine learning predictions of regional steel price indices for east China. Ironmak. Steelmak. (2024). https:\/\/doi.org\/10.1177\/03019233241254891","journal-title":"Ironmak. Steelmak."},{"key":"3213_CR14","doi-asserted-by":"publisher","DOI":"10.1108\/ajeb-01-2024-0007","author":"B Jin","year":"2024","unstructured":"B. Jin, X. Xu, Wholesale price forecasts of green grams using the neural network. Asian J. Econ. Bank. (2024). https:\/\/doi.org\/10.1108\/ajeb-01-2024-0007","journal-title":"Asian J. Econ. Bank."},{"key":"3213_CR15","doi-asserted-by":"publisher","first-page":"1399","DOI":"10.1109\/TCSVT.2024.3466961","volume":"35","author":"Q Li","year":"2025","unstructured":"Q. Li, B. Ma, X. Fu, X. Wang, C. Wang, X. Li, Robust image steganography via color conversion. IEEE Trans. Circuits Syst. Video Technol. 35, 1399\u20131408 (2025)","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"3213_CR16","first-page":"106","volume":"71","author":"Q Li","year":"2024","unstructured":"Q. Li, B. Ma, X. Wang, C. Wang, S. Gao, Image steganography in color conversion. IEEE Trans. Circuits Syst. II Express Briefs 71, 106\u2013110 (2024)","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"3213_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2024.124891","volume":"257","author":"Y Lin","year":"2024","unstructured":"Y. Lin, Z. Xie, T. Chen, X. Cheng, H. Wen, Image privacy protection scheme based on high-quality reconstruction DCT compression and nonlinear dynamics. Expert Syst. Appl. 257, 124891 (2024)","journal-title":"Expert Syst. Appl."},{"key":"3213_CR18","doi-asserted-by":"publisher","first-page":"996","DOI":"10.1049\/iet-ipr.2011.0348","volume":"6","author":"C Liu","year":"2012","unstructured":"C. Liu, X.-H. Huang, M. Wang, Fast computation of Zernike moments in polar coordinates. IET Image Proc. 6, 996\u20131004 (2012)","journal-title":"IET Image Proc."},{"key":"3213_CR19","doi-asserted-by":"publisher","first-page":"5449","DOI":"10.1109\/TPAMI.2024.3366769","volume":"46","author":"Y Liu","year":"2024","unstructured":"Y. Liu, C. Wang, M. Lu, J. Yang, J. Gui, S. Zhang, From simple to complex scenes: learning robust feature representations for accurate human parsing. IEEE Trans. Pattern Anal. Mach. Intell. 46, 5449\u20135462 (2024)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"3213_CR20","doi-asserted-by":"publisher","DOI":"10.1016\/j.bspc.2024.106557","volume":"96","author":"Y Lu","year":"2024","unstructured":"Y. Lu, X. Lu, G. Yang, X. Xiong, Robust zero-watermarking algorithm for multi-medical images based on FFST-Schur and Tent mapping. Biomed. Signal Process. Control 96, 106557 (2024)","journal-title":"Biomed. Signal Process. Control"},{"key":"3213_CR21","doi-asserted-by":"crossref","unstructured":"B. Ma, L. Chang, C. Wang, J. Li, Y. Wang, Remote sensing image zero-watermarking algorithm based on accurate polar harmonic Fourier moment. In Artificial Intelligence and Security: 6th International Conference, Hohhot, China (2020), pp. 659\u2013673.","DOI":"10.1007\/978-981-15-8083-3_59"},{"key":"3213_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.marpolbul.2024.116860","volume":"207","author":"L Natarajan","year":"2024","unstructured":"L. Natarajan, M. Vajravelu, M. Chandrasekaran, S.G. Ramakrishnan, T. Kaviarasan, P.V. Babu, S.K. Dash, K. Ramu, M.V.R. Murthy, Capability of space borne multispectral image for detecting discoloration in optically complex coastal waters. Mar. Pollut. Bull. 207, 116860 (2024)","journal-title":"Mar. Pollut. Bull."},{"key":"3213_CR23","doi-asserted-by":"publisher","first-page":"1298","DOI":"10.5858\/arpa.2022-0228-OA","volume":"147","author":"R Pandey","year":"2023","unstructured":"R. Pandey, D. Fournier, G. Root, M. Riccio, A. Shirvalkar, G. Zamora, N. Daigneault, M. Sapack, M. Zhong, M. Harigopal, AI-Powered Biomolecular-Specific and Label-Free multispectral imaging rapidly detects malignant neoplasm in surgically excised breast tissue specimens. Arch. Pathol. Lab. Med. 147, 1298\u20131306 (2023)","journal-title":"Arch. Pathol. Lab. Med."},{"key":"3213_CR24","volume":"86","author":"N Ren","year":"2024","unstructured":"N. Ren, Y. Hu, C. Zhu, S. Guo, X. Zhu, Moment invariants based zero watermarking algorithm for trajectory data. J. Inf. Secur. Appl. 86, 103867 (2024)","journal-title":"J. Inf. Secur. Appl."},{"key":"3213_CR25","doi-asserted-by":"publisher","first-page":"36507","DOI":"10.1007\/s11042-023-15074-w","volume":"82","author":"H Shi","year":"2023","unstructured":"H. Shi, S. Zhou, M. Chen, M. Li, A novel zero-watermarking algorithm based on multi-feature and DNA encryption for medical images. Multimed. Tools Appl. 82, 36507\u201336552 (2023)","journal-title":"Multimed. Tools Appl."},{"key":"3213_CR26","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/s11554-012-0252-y","volume":"10","author":"C Singh","year":"2015","unstructured":"C. Singh, A. Kaur, Fast computation of polar harmonic transforms. J. Real-Time Image Proc. 10, 59\u201366 (2015)","journal-title":"J. Real-Time Image Proc."},{"key":"3213_CR27","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1007\/s10851-012-0335-1","volume":"44","author":"C Singh","year":"2012","unstructured":"C. Singh, R. Upneja, Accurate computation of orthogonal Fourier-Mellin moments. J. Math. Imaging Vis. 44, 411\u2013431 (2012)","journal-title":"J. Math. Imaging Vis."},{"key":"3213_CR28","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/j.dsp.2013.12.004","volume":"27","author":"C Singh","year":"2014","unstructured":"C. Singh, R. Upneja, Accurate calculation of high order pseudo-Zernike moments and their numerical stability. Digit. Signal Proc. 27, 95\u2013106 (2014)","journal-title":"Digit. Signal Proc."},{"key":"3213_CR29","doi-asserted-by":"publisher","first-page":"8667","DOI":"10.1007\/s11042-020-10028-y","volume":"80","author":"V Sisaudia","year":"2021","unstructured":"V. Sisaudia, V.P. Vishwakarma, Copyright protection using KELM-PSO based multi-spectral image watermarking in DCT domain with local texture information based selection. Multimed. Tools Appl. 80, 8667\u20138688 (2021)","journal-title":"Multimed. Tools Appl."},{"key":"3213_CR30","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1016\/j.image.2008.01.005","volume":"23","author":"H Song","year":"2008","unstructured":"H. Song, S. Yu, X. Yang, L. Song, C. Wang, Contourlet-based image adaptive watermarking. Signal Process. Image Commun. 23, 162\u2013178 (2008)","journal-title":"Signal Process. Image Commun."},{"key":"3213_CR31","doi-asserted-by":"crossref","unstructured":"J.M. Sudki, G.R. Fonseca de Oliveira, A.D. de Medeiros, T. Mastrangelo, V. Arthur, E.A. Amaral da Silva, C.B. Mastrangelo, Fungal identification in peanuts seeds through multispectral images: technological advances to enhance sanitary quality. Front. Plant Sci. 14 (2023)","DOI":"10.3389\/fpls.2023.1112916"},{"key":"3213_CR32","doi-asserted-by":"publisher","first-page":"1112916","DOI":"10.3389\/fpls.2023.1112916","volume":"14","author":"JM Sudki","year":"2023","unstructured":"J.M. Sudki, G.R. Fonseca de Oliveira, A.D. de Medeiros, T. Mastrangelo, V. Arthur, E.A. Amaral da Silva, C.B. Mastrangelo, Fungal identification in peanuts seeds through multispectral images: technological advances to enhance sanitary quality. Front. Plant Sci. 14, 1112916 (2023)","journal-title":"Front. Plant Sci."},{"key":"3213_CR33","doi-asserted-by":"publisher","DOI":"10.1016\/j.fcr.2022.108786","volume":"291","author":"R Tanabe","year":"2023","unstructured":"R. Tanabe, T. Matsui, T.S.T. Tanaka, Winter wheat yield prediction using convolutional neural networks and UAV-based multispectral imagery. Field Crop Res 291, 108786 (2023)","journal-title":"Field Crop Res"},{"key":"3213_CR34","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2023.119786","volume":"654","author":"Y Tang","year":"2024","unstructured":"Y. Tang, K. Li, C. Wang, S. Bian, Q. Huang, A two-stage robust reversible watermarking using polar harmonic transform for high robustness and capacity. Inf. Sci. 654, 119786 (2024)","journal-title":"Inf. Sci."},{"key":"3213_CR35","doi-asserted-by":"publisher","DOI":"10.1016\/j.jhydrol.2023.129087","volume":"617","author":"TC Tayer","year":"2023","unstructured":"T.C. Tayer, L.S. Beesley, M.M. Douglas, S.A. Bourke, J.N. Callow, K. Meredith, D. McFarlane, Ecohydrological metrics derived from multispectral images to characterize surface water in an intermittent river. J. Hydrol. 617, 129087 (2023)","journal-title":"J. Hydrol."},{"key":"3213_CR36","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1016\/j.jss.2012.08.040","volume":"86","author":"H-H Tsai","year":"2013","unstructured":"H.-H. Tsai, Y.-S. Lai, S.-C. Lo, A zero-watermark scheme with geometrical invariants using SVM and PSO against geometrical attacks for image protection. J. Syst. Softw. 86, 335\u2013348 (2013)","journal-title":"J. Syst. Softw."},{"key":"3213_CR37","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1016\/j.jss.2009.12.026","volume":"83","author":"H-H Tsai","year":"2010","unstructured":"H.-H. Tsai, H.-C. Tseng, Y.-S. Lai, Robust lossless image watermarking based on \u03b1-trimmed mean algorithm and support vector machine. J. Syst. Softw. 83, 1015\u20131028 (2010)","journal-title":"J. Syst. Softw."},{"key":"3213_CR38","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/s11554-010-0172-7","volume":"7","author":"E Walia","year":"2012","unstructured":"E. Walia, C. Singh, A. Goyal, On the fast computation of orthogonal Fourier-Mellin moments with improved numerical stability. J. Real-Time Image Proc. 7, 247\u2013256 (2012)","journal-title":"J. Real-Time Image Proc."},{"key":"3213_CR39","doi-asserted-by":"publisher","first-page":"26355","DOI":"10.1007\/s11042-016-4130-7","volume":"76","author":"C-P Wang","year":"2017","unstructured":"C.-P. Wang, X.-Y. Wang, X.-J. 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."},{"key":"3213_CR40","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2021.104450","volume":"106","author":"C Wang","year":"2021","unstructured":"C. Wang, Q. Hao, B. Ma, X. Wu, J. Li, Z. Xia, H. Gao, Octonion continuous orthogonal moments and their applications in color stereoscopic image reconstruction and zero-watermarking. Eng. Appl. Artif. Intell. 106, 104450 (2021)","journal-title":"Eng. Appl. Artif. Intell."},{"key":"3213_CR41","doi-asserted-by":"publisher","first-page":"1998","DOI":"10.1109\/TCSVT.2021.3094882","volume":"32","author":"C Wang","year":"2022","unstructured":"C. Wang, B. Ma, Z. Xia, J. Li, Q. Li, Y.-Q. Shi, Stereoscopic image description with trinion fractional-order continuous orthogonal moments. IEEE Trans. Circuits Syst. Video Technol. 32, 1998\u20132012 (2022)","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"3213_CR42","doi-asserted-by":"publisher","first-page":"4440","DOI":"10.1109\/TCSVT.2019.2960507","volume":"30","author":"C Wang","year":"2020","unstructured":"C. Wang, X. Wang, Z. Xia, B. Ma, Y.-Q. Shi, Image description with polar harmonic fourier moments. IEEE Trans. Circuits Syst. Video Technol. 30, 4440\u20134452 (2020)","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"3213_CR43","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. Inf. Sci. 470, 109\u2013120 (2019)","journal-title":"Inf. Sci."},{"key":"3213_CR44","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/j.jvcir.2016.10.004","volume":"41","author":"C Wang","year":"2016","unstructured":"C. Wang, X. Wang, Z. Xia, C. Zhang, X. Chen, Geometrically resilient color image zero-watermarking algorithm based on quaternion Exponent moments. J. Vis. Commun. Image Represent. 41, 247\u2013259 (2016)","journal-title":"J. Vis. Commun. Image Represent."},{"key":"3213_CR45","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/j.sigpro.2016.12.010","volume":"134","author":"C Wang","year":"2017","unstructured":"C. Wang, X. Wang, C. Zhang, Z. Xia, Geometric correction based color image watermarking using fuzzy least squares support vector machine and Bessel K form distribution. Signal Process. 134, 197\u2013208 (2017)","journal-title":"Signal Process."},{"key":"3213_CR46","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2022.104970","volume":"113","author":"C Wang","year":"2022","unstructured":"C. Wang, Q. Zhang, B. Ma, Z. Xia, J. Li, T. Luo, Q. Li, Light-field image watermarking based on geranion polar harmonic Fourier moments. Eng. Appl. Artif. Intell. 113, 104970 (2022)","journal-title":"Eng. Appl. Artif. Intell."},{"key":"3213_CR47","doi-asserted-by":"publisher","first-page":"708","DOI":"10.1007\/s10851-020-01002-2","volume":"63","author":"X-Y Wang","year":"2021","unstructured":"X.-Y. Wang, L. Wang, J.-L. Tian, P.-P. Niu, H.-Y. Yang, Color image zero-watermarking using accurate quaternion generalized orthogonal Fourier-Mellin moments. J. Math. Imaging Vis. 63, 708\u2013734 (2021)","journal-title":"J. Math. Imaging Vis."},{"key":"3213_CR48","doi-asserted-by":"publisher","first-page":"23068","DOI":"10.1364\/OE.21.023068","volume":"21","author":"SS Welsh","year":"2013","unstructured":"S.S. Welsh, M.P. Edgar, R. Bowman, P. Jonathan, B. Sun, M.J. Padgett, Fast full-color computational imaging with single-pixel detectors. Opt. Express 21, 23068\u201323074 (2013)","journal-title":"Opt. Express"},{"key":"3213_CR49","first-page":"214","volume":"31","author":"Q Wen","year":"2003","unstructured":"Q. Wen, T. Sun, S. Wang, Concept and application of zero-watermark. Acta Electonica Sin. 31, 214\u2013216 (2003)","journal-title":"Acta Electonica Sin."},{"key":"3213_CR50","unstructured":"Q. Wen, Y. Sun, S. Wang, Based zero-watermark digital watermarking technology. In The Third China Information Hiding and Multimedia Security Workshop. Xidian University Press Xi'an, China (2001), pp. 102\u2013109"},{"key":"3213_CR51","doi-asserted-by":"publisher","DOI":"10.1016\/j.dsp.2023.104097","volume":"140","author":"Z Xia","year":"2023","unstructured":"Z. Xia, C. Wang, B. Ma, Q. Li, H. Zhang, M. Wang, X. Wang, Geometric attacks resistant double zero-watermarking using discrete Fourier transform and fractional-order Exponent-Fourier moments. Digit. Signal Process. 140, 104097 (2023)","journal-title":"Digit. Signal Process."},{"key":"3213_CR52","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":"3213_CR53","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1016\/j.sigpro.2018.11.011","volume":"157","author":"Z Xia","year":"2019","unstructured":"Z. Xia, X. Wang, W. Zhou, R. Li, C. Wang, C. Zhang, Color medical image lossless watermarking using chaotic system and accurate quaternion polar harmonic transforms. Signal Process. 157, 108\u2013118 (2019)","journal-title":"Signal Process."},{"key":"3213_CR54","doi-asserted-by":"publisher","first-page":"8822126","DOI":"10.1155\/2020\/8822126","volume":"2020","author":"S Xu","year":"2020","unstructured":"S. Xu, Q. Hao, B. Ma, C. Wang, J. Li, Accurate computation of fractional-order exponential moments. Secur. Commun. Netw. 2020, 8822126 (2020)","journal-title":"Secur. Commun. Netw."},{"key":"3213_CR55","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1016\/j.aeue.2014.10.012","volume":"69","author":"H-Y Yang","year":"2015","unstructured":"H.-Y. Yang, X.-Y. Wang, P. Wang, P.-P. Niu, Geometrically resilient digital watermarking scheme based on radial harmonic Fourier moments magnitude. AEU-Int. J. Electron. Commun. 69, 389\u2013399 (2015)","journal-title":"AEU-Int. J. Electron. Commun."},{"key":"3213_CR56","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, Chongqing, China (2018), pp. 236\u2013240.","DOI":"10.1109\/IAEAC.2018.8577943"},{"key":"3213_CR57","doi-asserted-by":"publisher","first-page":"852","DOI":"10.1364\/JOSAA.514567","volume":"41","author":"S Yang","year":"2024","unstructured":"S. Yang, A. Deng, Quaternion fast and accurate polar harmonic Fourier moments for color image analysis and object recognition. J. Opt. Soc. Am. A 41, 852\u2013862 (2024)","journal-title":"J. Opt. Soc. Am. A"},{"key":"3213_CR58","doi-asserted-by":"crossref","unstructured":"Y. Yuan, S. Shen, S. Yu, D. Duan, H. Lv, H. Lin, Geometric attacks resistant zero-watermarking for color images using local multi-channel fractional-order exponential moments and SPM Chaos mapping. In Asia-Pacific Conference on Image Processing, Electronics and Computers, Dalian, China (2024), pp. 177\u2013190.","DOI":"10.1109\/IPEC61310.2024.00040"},{"key":"3213_CR59","first-page":"1074","volume":"52","author":"B Zhang","year":"2023","unstructured":"B. Zhang, L. Gao, J. Li, D. Hong, K. Zheng, Advances and prospects in hyperspectral and multispectral remote sensing image super-resolution fusion. Acta Geod. Cartogr. Sin. 52, 1074\u20131089 (2023)","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"3213_CR60","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2024.107391","volume":"362","author":"H Zhang","year":"2025","unstructured":"H. Zhang, Z. Li, Y. Chen, C. Lu, P. Yan, Fast image reconstruction method using radial harmonic Fourier moments and its application in digital watermarking. J. Frankl. Inst. 362, 107391 (2025)","journal-title":"J. Frankl. Inst."},{"key":"3213_CR61","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2023.109010","volume":"209","author":"Q Zhang","year":"2023","unstructured":"Q. Zhang, C. Wang, B. Ma, Z. Xia, J. Li, H. Zhang, Q. Li, Sedenion polar harmonic Fourier moments and their application in multi-view color image watermarking. Signal Process. 209, 109010 (2023)","journal-title":"Signal Process."}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-025-03213-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00034-025-03213-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-025-03213-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,30]],"date-time":"2025-11-30T05:01:41Z","timestamp":1764478901000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00034-025-03213-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,14]]},"references-count":61,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["3213"],"URL":"https:\/\/doi.org\/10.1007\/s00034-025-03213-7","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"value":"0278-081X","type":"print"},{"value":"1531-5878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,14]]},"assertion":[{"value":"23 January 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 May 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 May 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 July 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 they have no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}